id	sid	tid	token	lemma	pos
ejde-390	1	1	electronic	electronic	ADJ
ejde-390	1	2	journal	journal	NOUN
ejde-390	1	3	of	of	ADP
ejde-390	1	4	differential	differential	ADJ
ejde-390	1	5	equations	equation	NOUN
ejde-390	1	6	,	,	PUNCT
ejde-390	1	7	vol	vol	NOUN
ejde-390	1	8	.	.	PUNCT
ejde-390	1	9	2020	2020	NUM
ejde-390	1	10	(	(	PUNCT
ejde-390	1	11	2020	2020	NUM
ejde-390	1	12	)	)	PUNCT
ejde-390	1	13	,	,	PUNCT
ejde-390	1	14	no	no	INTJ
ejde-390	1	15	.	.	NOUN
ejde-390	1	16	12	12	NUM
ejde-390	1	17	,	,	PUNCT
ejde-390	1	18	pp	pp	ADJ
ejde-390	1	19	.	.	PUNCT
ejde-390	2	1	1–20	1–20	PROPN
ejde-390	2	2	.	.	PUNCT
ejde-390	3	1	issn	issn	PROPN
ejde-390	3	2	:	:	PUNCT
ejde-390	3	3	1072	1072	NUM
ejde-390	3	4	-	-	SYM
ejde-390	3	5	6691	6691	NUM
ejde-390	3	6	.	.	PUNCT
ejde-390	4	1	url	url	PROPN
ejde-390	4	2	:	:	PUNCT
ejde-390	4	3	http://ejde.math.txstate.edu	http://ejde.math.txstate.edu	PROPN
ejde-390	4	4	or	or	CCONJ
ejde-390	4	5	http://ejde.math.unt.edu	http://ejde.math.unt.edu	VERB
ejde-390	4	6	positive	positive	ADJ
ejde-390	4	7	and	and	CCONJ
ejde-390	4	8	nodal	nodal	ADJ
ejde-390	4	9	solutions	solution	NOUN
ejde-390	4	10	for	for	ADP
ejde-390	4	11	nonlinear	nonlinear	ADJ
ejde-390	4	12	nonhomogeneous	nonhomogeneous	ADJ
ejde-390	4	13	parametric	parametric	PROPN
ejde-390	4	14	neumann	neumann	PROPN
ejde-390	4	15	problems	problems	PROPN
ejde-390	4	16	nikolaos	nikolaos	PROPN
ejde-390	4	17	s.	s.	PROPN
ejde-390	4	18	papageorgiou	papageorgiou	PROPN
ejde-390	4	19	,	,	PUNCT
ejde-390	4	20	calogero	calogero	PROPN
ejde-390	4	21	vetro	vetro	PROPN
ejde-390	4	22	,	,	PUNCT
ejde-390	4	23	francesca	francesca	PROPN
ejde-390	4	24	vetro	vetro	PROPN
ejde-390	4	25	abstract	abstract	NOUN
ejde-390	4	26	.	.	PUNCT
ejde-390	5	1	we	we	PRON
ejde-390	5	2	consider	consider	VERB
ejde-390	5	3	a	a	DET
ejde-390	5	4	parametric	parametric	ADJ
ejde-390	5	5	neumann	neumann	PROPN
ejde-390	5	6	problem	problem	NOUN
ejde-390	5	7	driven	drive	VERB
ejde-390	5	8	by	by	ADP
ejde-390	5	9	a	a	DET
ejde-390	5	10	nonlinear	nonlinear	ADJ
ejde-390	5	11	nonhomogeneous	nonhomogeneous	ADJ
ejde-390	5	12	differential	differential	NOUN
ejde-390	5	13	operator	operator	NOUN
ejde-390	5	14	plus	plus	CCONJ
ejde-390	5	15	an	an	DET
ejde-390	5	16	indefinite	indefinite	ADJ
ejde-390	5	17	potential	potential	ADJ
ejde-390	5	18	term	term	NOUN
ejde-390	5	19	.	.	PUNCT
ejde-390	6	1	the	the	DET
ejde-390	6	2	reaction	reaction	NOUN
ejde-390	6	3	term	term	NOUN
ejde-390	6	4	is	be	AUX
ejde-390	6	5	superlinear	superlinear	ADJ
ejde-390	6	6	but	but	CCONJ
ejde-390	6	7	does	do	AUX
ejde-390	6	8	not	not	PART
ejde-390	6	9	satisfy	satisfy	VERB
ejde-390	6	10	the	the	DET
ejde-390	6	11	ambrosetti	ambrosetti	NOUN
ejde-390	6	12	-	-	PUNCT
ejde-390	6	13	rabinowitz	rabinowitz	NOUN
ejde-390	6	14	condition	condition	NOUN
ejde-390	6	15	.	.	PUNCT
ejde-390	7	1	first	first	ADV
ejde-390	7	2	we	we	PRON
ejde-390	7	3	prove	prove	VERB
ejde-390	7	4	a	a	DET
ejde-390	7	5	bifurcation	bifurcation	NOUN
ejde-390	7	6	-	-	PUNCT
ejde-390	7	7	type	type	NOUN
ejde-390	7	8	result	result	NOUN
ejde-390	7	9	describing	describe	VERB
ejde-390	7	10	in	in	ADP
ejde-390	7	11	a	a	DET
ejde-390	7	12	precise	precise	ADJ
ejde-390	7	13	way	way	NOUN
ejde-390	7	14	the	the	DET
ejde-390	7	15	dependence	dependence	NOUN
ejde-390	7	16	of	of	ADP
ejde-390	7	17	the	the	DET
ejde-390	7	18	set	set	NOUN
ejde-390	7	19	of	of	ADP
ejde-390	7	20	positive	positive	ADJ
ejde-390	7	21	solutions	solution	NOUN
ejde-390	7	22	on	on	ADP
ejde-390	7	23	the	the	DET
ejde-390	7	24	parameter	parameter	NOUN
ejde-390	7	25	λ	λ	PROPN
ejde-390	7	26	>	>	X
ejde-390	7	27	0	0	X
ejde-390	7	28	.	.	PUNCT
ejde-390	8	1	we	we	PRON
ejde-390	8	2	also	also	ADV
ejde-390	8	3	show	show	VERB
ejde-390	8	4	the	the	DET
ejde-390	8	5	existence	existence	NOUN
ejde-390	8	6	of	of	ADP
ejde-390	8	7	a	a	DET
ejde-390	8	8	smallest	small	ADJ
ejde-390	8	9	positive	positive	ADJ
ejde-390	8	10	solution	solution	NOUN
ejde-390	8	11	.	.	PUNCT
ejde-390	9	1	similar	similar	ADJ
ejde-390	9	2	results	result	NOUN
ejde-390	9	3	hold	hold	VERB
ejde-390	9	4	for	for	ADP
ejde-390	9	5	the	the	DET
ejde-390	9	6	negative	negative	ADJ
ejde-390	9	7	solutions	solution	NOUN
ejde-390	9	8	and	and	CCONJ
ejde-390	9	9	in	in	ADP
ejde-390	9	10	this	this	DET
ejde-390	9	11	case	case	NOUN
ejde-390	9	12	we	we	PRON
ejde-390	9	13	have	have	VERB
ejde-390	9	14	a	a	DET
ejde-390	9	15	biggest	big	ADJ
ejde-390	9	16	negative	negative	ADJ
ejde-390	9	17	solution	solution	NOUN
ejde-390	9	18	.	.	PUNCT
ejde-390	10	1	finally	finally	ADV
ejde-390	10	2	using	use	VERB
ejde-390	10	3	the	the	DET
ejde-390	10	4	extremal	extremal	ADJ
ejde-390	10	5	constant	constant	ADJ
ejde-390	10	6	sign	sign	NOUN
ejde-390	10	7	solutions	solution	NOUN
ejde-390	10	8	we	we	PRON
ejde-390	10	9	produce	produce	VERB
ejde-390	10	10	a	a	DET
ejde-390	10	11	smooth	smooth	ADJ
ejde-390	10	12	nodal	nodal	NOUN
ejde-390	10	13	solution	solution	NOUN
ejde-390	10	14	.	.	PUNCT
ejde-390	11	1	1	1	X
ejde-390	11	2	.	.	X
ejde-390	11	3	introduction	introduction	NOUN
ejde-390	11	4	let	let	VERB
ejde-390	11	5	ω	ω	PROPN
ejde-390	11	6	⊆	⊆	NUM
ejde-390	11	7	rn	rn	AUX
ejde-390	11	8	be	be	AUX
ejde-390	11	9	a	a	DET
ejde-390	11	10	bounded	bounded	ADJ
ejde-390	11	11	domain	domain	NOUN
ejde-390	11	12	with	with	ADP
ejde-390	11	13	a	a	DET
ejde-390	11	14	c2	c2	PROPN
ejde-390	11	15	-	-	PUNCT
ejde-390	11	16	boundary	boundary	NOUN
ejde-390	11	17	∂ω	∂ω	PROPN
ejde-390	11	18	.	.	PUNCT
ejde-390	12	1	in	in	ADP
ejde-390	12	2	this	this	DET
ejde-390	12	3	paper	paper	NOUN
ejde-390	12	4	we	we	PRON
ejde-390	12	5	study	study	VERB
ejde-390	12	6	the	the	DET
ejde-390	12	7	following	follow	VERB
ejde-390	12	8	nonlinear	nonlinear	ADJ
ejde-390	12	9	nonhomogeneous	nonhomogeneous	PROPN
ejde-390	12	10	neumann	neumann	PROPN
ejde-390	12	11	problem	problem	NOUN
ejde-390	12	12	−div	−div	PROPN
ejde-390	12	13	a(∇u(z	a(∇u(z	NOUN
ejde-390	12	14	)	)	PUNCT
ejde-390	12	15	)	)	PUNCT
ejde-390	13	1	+	+	CCONJ
ejde-390	13	2	[	[	X
ejde-390	13	3	ξ(z	ξ(z	NOUN
ejde-390	13	4	)	)	PUNCT
ejde-390	13	5	+	+	CCONJ
ejde-390	13	6	λ]u(z)p−1	λ]u(z)p−1	NOUN
ejde-390	13	7	=	=	SYM
ejde-390	13	8	f(z	f(z	PROPN
ejde-390	13	9	,	,	PUNCT
ejde-390	13	10	u(z	u(z	NOUN
ejde-390	13	11	)	)	PUNCT
ejde-390	13	12	)	)	PUNCT
ejde-390	13	13	in	in	ADP
ejde-390	13	14	ω	ω	NUM
ejde-390	13	15	,	,	PUNCT
ejde-390	13	16	∂u	∂u	PROPN
ejde-390	13	17	∂n	∂n	PROPN
ejde-390	13	18	=	=	PUNCT
ejde-390	13	19	0	0	NUM
ejde-390	13	20	on	on	ADP
ejde-390	13	21	∂ω	∂ω	PROPN
ejde-390	13	22	,	,	PUNCT
ejde-390	13	23	u	u	NOUN
ejde-390	13	24	>	>	X
ejde-390	13	25	0	0	PROPN
ejde-390	13	26	,	,	PUNCT
ejde-390	13	27	λ	λ	X
ejde-390	13	28	>	>	X
ejde-390	13	29	0	0	NUM
ejde-390	13	30	,	,	PUNCT
ejde-390	13	31	1	1	NUM
ejde-390	13	32	<	<	X
ejde-390	13	33	p	p	X
ejde-390	13	34	<	<	X
ejde-390	13	35	+	+	PROPN
ejde-390	13	36	∞.	∞.	PROPN
ejde-390	13	37	(	(	PUNCT
ejde-390	13	38	1.1	1.1	NUM
ejde-390	13	39	)	)	PUNCT
ejde-390	13	40	in	in	ADP
ejde-390	13	41	this	this	DET
ejde-390	13	42	problem	problem	NOUN
ejde-390	13	43	the	the	DET
ejde-390	13	44	map	map	NOUN
ejde-390	13	45	a	a	DET
ejde-390	13	46	:	:	PUNCT
ejde-390	13	47	rn	rn	PROPN
ejde-390	13	48	→	→	SYM
ejde-390	13	49	rn	rn	PROPN
ejde-390	13	50	involved	involve	VERB
ejde-390	13	51	in	in	ADP
ejde-390	13	52	the	the	DET
ejde-390	13	53	definition	definition	NOUN
ejde-390	13	54	of	of	ADP
ejde-390	13	55	the	the	DET
ejde-390	13	56	differential	differential	ADJ
ejde-390	13	57	operator	operator	NOUN
ejde-390	13	58	is	be	AUX
ejde-390	13	59	strictly	strictly	ADV
ejde-390	13	60	monotone	monotone	ADJ
ejde-390	13	61	and	and	CCONJ
ejde-390	13	62	continuous	continuous	ADJ
ejde-390	13	63	,	,	PUNCT
ejde-390	13	64	thus	thus	ADV
ejde-390	13	65	maximal	maximal	ADJ
ejde-390	13	66	monotone	monotone	NOUN
ejde-390	13	67	too	too	ADV
ejde-390	13	68	.	.	PUNCT
ejde-390	14	1	also	also	ADV
ejde-390	14	2	it	it	PRON
ejde-390	14	3	satisfies	satisfy	VERB
ejde-390	14	4	certain	certain	ADJ
ejde-390	14	5	other	other	ADJ
ejde-390	14	6	regularity	regularity	NOUN
ejde-390	14	7	and	and	CCONJ
ejde-390	14	8	growth	growth	NOUN
ejde-390	14	9	conditions	condition	NOUN
ejde-390	14	10	listed	list	VERB
ejde-390	14	11	in	in	ADP
ejde-390	14	12	hypotheses	hypothesis	NOUN
ejde-390	14	13	(	(	PUNCT
ejde-390	14	14	h1	h1	NOUN
ejde-390	14	15	)	)	PUNCT
ejde-390	14	16	(	(	PUNCT
ejde-390	14	17	see	see	VERB
ejde-390	14	18	section	section	NOUN
ejde-390	14	19	2	2	NUM
ejde-390	14	20	)	)	PUNCT
ejde-390	14	21	.	.	PUNCT
ejde-390	15	1	these	these	DET
ejde-390	15	2	conditions	condition	NOUN
ejde-390	15	3	are	be	AUX
ejde-390	15	4	not	not	PART
ejde-390	15	5	restrictive	restrictive	ADJ
ejde-390	15	6	and	and	CCONJ
ejde-390	15	7	incorporate	incorporate	VERB
ejde-390	15	8	in	in	ADP
ejde-390	15	9	our	our	PRON
ejde-390	15	10	framework	framework	NOUN
ejde-390	15	11	many	many	ADJ
ejde-390	15	12	differential	differential	ADJ
ejde-390	15	13	operators	operator	NOUN
ejde-390	15	14	of	of	ADP
ejde-390	15	15	interest	interest	NOUN
ejde-390	15	16	such	such	ADJ
ejde-390	15	17	as	as	ADP
ejde-390	15	18	the	the	DET
ejde-390	15	19	p	p	NOUN
ejde-390	15	20	-	-	PUNCT
ejde-390	15	21	laplacian	laplacian	NOUN
ejde-390	15	22	(	(	PUNCT
ejde-390	15	23	1	1	NUM
ejde-390	15	24	<	<	X
ejde-390	15	25	p	p	X
ejde-390	15	26	<	<	X
ejde-390	15	27	+	+	NOUN
ejde-390	15	28	∞	∞	NOUN
ejde-390	15	29	)	)	PUNCT
ejde-390	15	30	and	and	CCONJ
ejde-390	15	31	the	the	DET
ejde-390	15	32	(	(	PUNCT
ejde-390	15	33	p	p	NOUN
ejde-390	15	34	,	,	PUNCT
ejde-390	15	35	q)-laplacian	q)-laplacian	PUNCT
ejde-390	15	36	(	(	PUNCT
ejde-390	15	37	1	1	NUM
ejde-390	15	38	<	<	X
ejde-390	15	39	q	q	X
ejde-390	15	40	<	<	X
ejde-390	15	41	p	p	X
ejde-390	15	42	<	<	X
ejde-390	15	43	+	+	NOUN
ejde-390	15	44	∞	∞	NOUN
ejde-390	15	45	)	)	PUNCT
ejde-390	15	46	,	,	PUNCT
ejde-390	15	47	that	that	ADV
ejde-390	15	48	is	is	ADV
ejde-390	15	49	,	,	PUNCT
ejde-390	15	50	the	the	DET
ejde-390	15	51	sum	sum	NOUN
ejde-390	15	52	of	of	ADP
ejde-390	15	53	a	a	DET
ejde-390	15	54	p	p	NOUN
ejde-390	15	55	-	-	PUNCT
ejde-390	15	56	laplacian	laplacian	NOUN
ejde-390	15	57	and	and	CCONJ
ejde-390	15	58	of	of	ADP
ejde-390	15	59	a	a	DET
ejde-390	15	60	q	q	NOUN
ejde-390	15	61	-	-	PUNCT
ejde-390	15	62	laplacian	laplacian	NOUN
ejde-390	15	63	.	.	PUNCT
ejde-390	16	1	the	the	DET
ejde-390	16	2	differential	differential	ADJ
ejde-390	16	3	operator	operator	NOUN
ejde-390	16	4	of	of	ADP
ejde-390	16	5	(	(	PUNCT
ejde-390	16	6	1.1	1.1	NUM
ejde-390	16	7	)	)	PUNCT
ejde-390	16	8	is	be	AUX
ejde-390	16	9	not	not	PART
ejde-390	16	10	homogeneous	homogeneous	ADJ
ejde-390	16	11	and	and	CCONJ
ejde-390	16	12	this	this	PRON
ejde-390	16	13	is	be	AUX
ejde-390	16	14	a	a	DET
ejde-390	16	15	source	source	NOUN
ejde-390	16	16	of	of	ADP
ejde-390	16	17	difficulties	difficulty	NOUN
ejde-390	16	18	in	in	ADP
ejde-390	16	19	the	the	DET
ejde-390	16	20	analysis	analysis	NOUN
ejde-390	16	21	of	of	ADP
ejde-390	16	22	problem	problem	NOUN
ejde-390	16	23	(	(	PUNCT
ejde-390	16	24	1.1	1.1	NUM
ejde-390	16	25	)	)	PUNCT
ejde-390	16	26	.	.	PUNCT
ejde-390	17	1	there	there	PRON
ejde-390	17	2	is	be	VERB
ejde-390	17	3	also	also	ADV
ejde-390	17	4	a	a	DET
ejde-390	17	5	parametric	parametric	ADJ
ejde-390	17	6	potential	potential	ADJ
ejde-390	17	7	term	term	NOUN
ejde-390	17	8	u	u	NOUN
ejde-390	17	9	→	→	SYM
ejde-390	17	10	[	[	X
ejde-390	17	11	ξ(z	ξ(z	NOUN
ejde-390	17	12	)	)	PUNCT
ejde-390	17	13	+	+	CCONJ
ejde-390	17	14	λ]up−1	λ]up−1	X
ejde-390	17	15	with	with	ADP
ejde-390	17	16	the	the	DET
ejde-390	17	17	potential	potential	ADJ
ejde-390	17	18	function	function	NOUN
ejde-390	17	19	ξ	ξ	PROPN
ejde-390	17	20	∈	∈	PROPN
ejde-390	17	21	l∞(ω	l∞(ω	X
ejde-390	17	22	)	)	PUNCT
ejde-390	17	23	being	be	AUX
ejde-390	17	24	indefinite	indefinite	ADJ
ejde-390	17	25	(	(	PUNCT
ejde-390	17	26	that	that	PRON
ejde-390	17	27	is	is	ADV
ejde-390	17	28	,	,	PUNCT
ejde-390	17	29	sign	sign	NOUN
ejde-390	17	30	-	-	PUNCT
ejde-390	17	31	changing	change	VERB
ejde-390	17	32	)	)	PUNCT
ejde-390	17	33	.	.	PUNCT
ejde-390	18	1	hence	hence	ADV
ejde-390	18	2	the	the	DET
ejde-390	18	3	left	left	ADJ
ejde-390	18	4	hand	hand	NOUN
ejde-390	18	5	side	side	NOUN
ejde-390	18	6	of	of	ADP
ejde-390	18	7	(	(	PUNCT
ejde-390	18	8	1.1	1.1	NUM
ejde-390	18	9	)	)	PUNCT
ejde-390	18	10	is	be	AUX
ejde-390	18	11	not	not	PART
ejde-390	18	12	in	in	ADP
ejde-390	18	13	general	general	ADJ
ejde-390	18	14	coercive	coercive	ADJ
ejde-390	18	15	and	and	CCONJ
ejde-390	18	16	this	this	PRON
ejde-390	18	17	is	be	AUX
ejde-390	18	18	another	another	DET
ejde-390	18	19	feature	feature	NOUN
ejde-390	18	20	of	of	ADP
ejde-390	18	21	problem	problem	NOUN
ejde-390	18	22	(	(	PUNCT
ejde-390	18	23	1.1	1.1	NUM
ejde-390	18	24	)	)	PUNCT
ejde-390	18	25	that	that	PRON
ejde-390	18	26	complicates	complicate	VERB
ejde-390	18	27	our	our	PRON
ejde-390	18	28	arguments	argument	NOUN
ejde-390	18	29	.	.	PUNCT
ejde-390	19	1	the	the	DET
ejde-390	19	2	reaction	reaction	NOUN
ejde-390	19	3	term	term	NOUN
ejde-390	19	4	f(z	f(z	PROPN
ejde-390	19	5	,	,	PUNCT
ejde-390	19	6	x	x	X
ejde-390	19	7	)	)	PUNCT
ejde-390	19	8	is	be	AUX
ejde-390	19	9	a	a	DET
ejde-390	19	10	carathéodory	carathéodory	NOUN
ejde-390	19	11	function	function	NOUN
ejde-390	19	12	(	(	PUNCT
ejde-390	19	13	that	that	PRON
ejde-390	19	14	is	is	ADV
ejde-390	19	15	,	,	PUNCT
ejde-390	19	16	for	for	SCONJ
ejde-390	19	17	all	all	PRON
ejde-390	19	18	x	x	SYM
ejde-390	19	19	∈	∈	PROPN
ejde-390	19	20	r	r	NOUN
ejde-390	19	21	,	,	PUNCT
ejde-390	19	22	z	z	NOUN
ejde-390	19	23	→	→	SYM
ejde-390	19	24	f(z	f(z	PROPN
ejde-390	19	25	,	,	PUNCT
ejde-390	19	26	x	x	X
ejde-390	19	27	)	)	PUNCT
ejde-390	19	28	is	be	AUX
ejde-390	19	29	measurable	measurable	ADJ
ejde-390	19	30	and	and	CCONJ
ejde-390	19	31	for	for	ADP
ejde-390	19	32	a.a	a.a	PROPN
ejde-390	19	33	.	.	PROPN
ejde-390	19	34	z	z	PROPN
ejde-390	19	35	∈	∈	PROPN
ejde-390	19	36	ω	ω	PROPN
ejde-390	19	37	,	,	PUNCT
ejde-390	19	38	x	x	X
ejde-390	19	39	→	→	SYM
ejde-390	19	40	f(z	f(z	PROPN
ejde-390	19	41	,	,	PUNCT
ejde-390	19	42	x	x	X
ejde-390	19	43	)	)	PUNCT
ejde-390	19	44	is	be	AUX
ejde-390	19	45	continuous	continuous	ADJ
ejde-390	19	46	)	)	PUNCT
ejde-390	19	47	.	.	PUNCT
ejde-390	20	1	we	we	PRON
ejde-390	20	2	assume	assume	VERB
ejde-390	20	3	that	that	SCONJ
ejde-390	20	4	for	for	ADP
ejde-390	20	5	a.a	a.a	PROPN
ejde-390	20	6	.	.	PROPN
ejde-390	20	7	z	z	PROPN
ejde-390	20	8	∈	∈	PROPN
ejde-390	20	9	ω	ω	NUM
ejde-390	20	10	the	the	DET
ejde-390	20	11	function	function	NOUN
ejde-390	20	12	x→	x→	PUNCT
ejde-390	20	13	f(z	f(z	PROPN
ejde-390	20	14	,	,	PUNCT
ejde-390	20	15	x	x	X
ejde-390	20	16	)	)	PUNCT
ejde-390	20	17	is	be	AUX
ejde-390	20	18	(	(	PUNCT
ejde-390	20	19	p−	p−	NOUN
ejde-390	20	20	1)-superlinear	1)-superlinear	NUM
ejde-390	20	21	near	near	ADP
ejde-390	20	22	+	+	PROPN
ejde-390	20	23	∞.	∞.	PROPN
ejde-390	20	24	however	however	ADV
ejde-390	20	25	,	,	PUNCT
ejde-390	20	26	the	the	DET
ejde-390	20	27	superlinearity	superlinearity	NOUN
ejde-390	20	28	of	of	ADP
ejde-390	20	29	f(z	f(z	PROPN
ejde-390	20	30	,	,	PUNCT
ejde-390	20	31	·	·	PUNCT
ejde-390	20	32	)	)	PUNCT
ejde-390	20	33	is	be	AUX
ejde-390	20	34	not	not	PART
ejde-390	20	35	expressed	express	VERB
ejde-390	20	36	via	via	ADP
ejde-390	20	37	the	the	DET
ejde-390	20	38	usual	usual	ADJ
ejde-390	20	39	for	for	ADP
ejde-390	20	40	such	such	ADJ
ejde-390	20	41	2010	2010	NUM
ejde-390	20	42	mathematics	mathematic	NOUN
ejde-390	20	43	subject	subject	NOUN
ejde-390	20	44	classification	classification	NOUN
ejde-390	20	45	.	.	PUNCT
ejde-390	21	1	35j20	35j20	NUM
ejde-390	21	2	,	,	PUNCT
ejde-390	21	3	35j60	35j60	NUM
ejde-390	21	4	,	,	PUNCT
ejde-390	21	5	58e05	58e05	NUM
ejde-390	21	6	.	.	PUNCT
ejde-390	22	1	key	key	ADJ
ejde-390	22	2	words	word	NOUN
ejde-390	22	3	and	and	CCONJ
ejde-390	22	4	phrases	phrase	NOUN
ejde-390	22	5	.	.	PUNCT
ejde-390	23	1	nonlinear	nonlinear	ADJ
ejde-390	23	2	nonhomogeneous	nonhomogeneous	ADJ
ejde-390	23	3	differential	differential	NOUN
ejde-390	23	4	operator	operator	NOUN
ejde-390	23	5	;	;	PUNCT
ejde-390	23	6	nonlinear	nonlinear	ADJ
ejde-390	23	7	regularity	regularity	NOUN
ejde-390	23	8	theory	theory	NOUN
ejde-390	23	9	;	;	PUNCT
ejde-390	23	10	nonlinear	nonlinear	ADJ
ejde-390	23	11	maximum	maximum	ADJ
ejde-390	23	12	principle	principle	NOUN
ejde-390	23	13	;	;	PUNCT
ejde-390	23	14	strong	strong	ADJ
ejde-390	23	15	comparison	comparison	NOUN
ejde-390	23	16	;	;	PUNCT
ejde-390	23	17	bifurcation	bifurcation	NOUN
ejde-390	23	18	-	-	PUNCT
ejde-390	23	19	type	type	NOUN
ejde-390	23	20	theorem	theorem	NOUN
ejde-390	23	21	;	;	PUNCT
ejde-390	23	22	nodal	nodal	NOUN
ejde-390	23	23	solution	solution	NOUN
ejde-390	23	24	;	;	PUNCT
ejde-390	23	25	critical	critical	ADJ
ejde-390	23	26	group	group	NOUN
ejde-390	23	27	.	.	PUNCT
ejde-390	24	1	c	c	X
ejde-390	24	2	©	©	PROPN
ejde-390	24	3	2020	2020	NUM
ejde-390	24	4	texas	texas	PROPN
ejde-390	24	5	state	state	PROPN
ejde-390	24	6	university	university	PROPN
ejde-390	24	7	.	.	PUNCT
ejde-390	25	1	submitted	submit	VERB
ejde-390	25	2	february	february	PROPN
ejde-390	25	3	11	11	NUM
ejde-390	25	4	,	,	PUNCT
ejde-390	25	5	2019	2019	NUM
ejde-390	25	6	.	.	PUNCT
ejde-390	26	1	published	publish	VERB
ejde-390	26	2	january	january	PROPN
ejde-390	26	3	24	24	NUM
ejde-390	26	4	,	,	PUNCT
ejde-390	26	5	2020	2020	NUM
ejde-390	26	6	.	.	PUNCT
ejde-390	27	1	1	1	NUM
ejde-390	27	2	2	2	NUM
ejde-390	27	3	n.	n.	NOUN
ejde-390	27	4	s.	s.	PROPN
ejde-390	27	5	papageorgiou	papageorgiou	PROPN
ejde-390	27	6	,	,	PUNCT
ejde-390	27	7	c.	c.	PROPN
ejde-390	27	8	vetro	vetro	PROPN
ejde-390	27	9	,	,	PUNCT
ejde-390	27	10	f.	f.	PROPN
ejde-390	27	11	vetro	vetro	PROPN
ejde-390	27	12	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	27	13	problems	problem	NOUN
ejde-390	27	14	ambrosetti	ambrosetti	NOUN
ejde-390	27	15	-	-	PUNCT
ejde-390	27	16	rabinowitz	rabinowitz	NOUN
ejde-390	27	17	condition	condition	NOUN
ejde-390	27	18	(	(	PUNCT
ejde-390	27	19	the	the	DET
ejde-390	27	20	ar	ar	NOUN
ejde-390	27	21	-	-	NOUN
ejde-390	27	22	condition	condition	NOUN
ejde-390	27	23	for	for	ADP
ejde-390	27	24	short	short	ADJ
ejde-390	27	25	)	)	PUNCT
ejde-390	27	26	.	.	PUNCT
ejde-390	28	1	instead	instead	ADV
ejde-390	28	2	we	we	PRON
ejde-390	28	3	employ	employ	VERB
ejde-390	28	4	an	an	DET
ejde-390	28	5	alternative	alternative	NOUN
ejde-390	28	6	less	less	ADV
ejde-390	28	7	restrictive	restrictive	ADJ
ejde-390	28	8	condition	condition	NOUN
ejde-390	28	9	which	which	PRON
ejde-390	28	10	permits	permit	VERB
ejde-390	28	11	the	the	DET
ejde-390	28	12	consideration	consideration	NOUN
ejde-390	28	13	of	of	ADP
ejde-390	28	14	(	(	PUNCT
ejde-390	28	15	p	p	NOUN
ejde-390	28	16	−	−	PROPN
ejde-390	28	17	1)-superlinear	1)-superlinear	NUM
ejde-390	28	18	nonlinearities	nonlinearitie	NOUN
ejde-390	28	19	with	with	ADP
ejde-390	28	20	“	"	PUNCT
ejde-390	28	21	slower	slow	ADJ
ejde-390	28	22	”	"	PUNCT
ejde-390	28	23	growth	growth	NOUN
ejde-390	28	24	near	near	ADP
ejde-390	28	25	+	+	PROPN
ejde-390	28	26	∞.	∞.	PROPN
ejde-390	28	27	near	near	ADP
ejde-390	28	28	0	0	NUM
ejde-390	28	29	+	+	NUM
ejde-390	28	30	we	we	PRON
ejde-390	28	31	assume	assume	VERB
ejde-390	28	32	that	that	SCONJ
ejde-390	28	33	f(z	f(z	PROPN
ejde-390	28	34	,	,	PUNCT
ejde-390	28	35	·	·	PUNCT
ejde-390	28	36	)	)	PUNCT
ejde-390	28	37	is	be	AUX
ejde-390	28	38	(	(	PUNCT
ejde-390	28	39	q	q	NOUN
ejde-390	28	40	−	−	PROPN
ejde-390	28	41	1)-superlinear	1)-superlinear	NUM
ejde-390	28	42	with	with	ADP
ejde-390	28	43	1	1	NUM
ejde-390	28	44	<	<	X
ejde-390	28	45	q	q	X
ejde-390	28	46	<	<	X
ejde-390	28	47	p.	p.	NOUN
ejde-390	28	48	using	use	VERB
ejde-390	28	49	variational	variational	ADJ
ejde-390	28	50	tools	tool	NOUN
ejde-390	28	51	from	from	ADP
ejde-390	28	52	the	the	DET
ejde-390	28	53	critical	critical	ADJ
ejde-390	28	54	point	point	NOUN
ejde-390	28	55	theory	theory	NOUN
ejde-390	28	56	together	together	ADV
ejde-390	28	57	with	with	ADP
ejde-390	28	58	suitable	suitable	ADJ
ejde-390	28	59	truncation	truncation	NOUN
ejde-390	28	60	,	,	PUNCT
ejde-390	28	61	perturbation	perturbation	NOUN
ejde-390	28	62	and	and	CCONJ
ejde-390	28	63	comparison	comparison	NOUN
ejde-390	28	64	techniques	technique	NOUN
ejde-390	28	65	,	,	PUNCT
ejde-390	28	66	we	we	PRON
ejde-390	28	67	prove	prove	VERB
ejde-390	28	68	a	a	DET
ejde-390	28	69	bifurcation	bifurcation	NOUN
ejde-390	28	70	-	-	PUNCT
ejde-390	28	71	type	type	NOUN
ejde-390	28	72	result	result	NOUN
ejde-390	28	73	which	which	PRON
ejde-390	28	74	describes	describe	VERB
ejde-390	28	75	the	the	DET
ejde-390	28	76	dependence	dependence	NOUN
ejde-390	28	77	on	on	ADP
ejde-390	28	78	the	the	DET
ejde-390	28	79	parameter	parameter	NOUN
ejde-390	29	1	λ	λ	PROPN
ejde-390	29	2	>	>	X
ejde-390	29	3	0	0	NUM
ejde-390	29	4	of	of	ADP
ejde-390	29	5	the	the	DET
ejde-390	29	6	set	set	NOUN
ejde-390	29	7	of	of	ADP
ejde-390	29	8	positive	positive	ADJ
ejde-390	29	9	solutions	solution	NOUN
ejde-390	29	10	of	of	ADP
ejde-390	29	11	problem	problem	NOUN
ejde-390	29	12	(	(	PUNCT
ejde-390	29	13	1.1	1.1	NUM
ejde-390	29	14	)	)	PUNCT
ejde-390	29	15	.	.	PUNCT
ejde-390	30	1	more	more	ADV
ejde-390	30	2	precisely	precisely	ADV
ejde-390	30	3	,	,	PUNCT
ejde-390	30	4	we	we	PRON
ejde-390	30	5	show	show	VERB
ejde-390	30	6	that	that	SCONJ
ejde-390	30	7	there	there	PRON
ejde-390	30	8	exists	exist	VERB
ejde-390	30	9	a	a	DET
ejde-390	30	10	critical	critical	ADJ
ejde-390	30	11	parameter	parameter	NOUN
ejde-390	30	12	value	value	NOUN
ejde-390	30	13	λ∗	λ∗	PROPN
ejde-390	30	14	>	>	X
ejde-390	30	15	0	0	PUNCT
ejde-390	30	16	such	such	ADJ
ejde-390	30	17	that	that	DET
ejde-390	30	18	•	•	NOUN
ejde-390	30	19	for	for	ADP
ejde-390	30	20	all	all	DET
ejde-390	30	21	λ	λ	PROPN
ejde-390	30	22	>	>	X
ejde-390	30	23	λ∗	λ∗	PROPN
ejde-390	30	24	problem	problem	NOUN
ejde-390	30	25	(	(	PUNCT
ejde-390	30	26	1.1	1.1	NUM
ejde-390	30	27	)	)	PUNCT
ejde-390	30	28	has	have	AUX
ejde-390	30	29	at	at	ADV
ejde-390	30	30	least	least	ADV
ejde-390	30	31	two	two	NUM
ejde-390	30	32	positive	positive	ADJ
ejde-390	30	33	solutions	solution	NOUN
ejde-390	30	34	;	;	PUNCT
ejde-390	30	35	•	•	ADP
ejde-390	30	36	for	for	ADP
ejde-390	30	37	λ	λ	PROPN
ejde-390	30	38	=	=	SYM
ejde-390	30	39	λ∗	λ∗	PROPN
ejde-390	30	40	problem	problem	NOUN
ejde-390	30	41	(	(	PUNCT
ejde-390	30	42	1.1	1.1	NUM
ejde-390	30	43	)	)	PUNCT
ejde-390	30	44	has	have	VERB
ejde-390	30	45	at	at	ADP
ejde-390	30	46	least	least	ADJ
ejde-390	30	47	a	a	DET
ejde-390	30	48	positive	positive	ADJ
ejde-390	30	49	solution	solution	NOUN
ejde-390	30	50	;	;	PUNCT
ejde-390	30	51	•	•	ADP
ejde-390	30	52	for	for	ADP
ejde-390	30	53	all	all	DET
ejde-390	30	54	λ	λ	X
ejde-390	30	55	∈	∈	PROPN
ejde-390	30	56	(	(	PUNCT
ejde-390	30	57	0	0	NUM
ejde-390	30	58	,	,	PUNCT
ejde-390	30	59	λ∗	λ∗	NOUN
ejde-390	30	60	)	)	PUNCT
ejde-390	30	61	problem	problem	NOUN
ejde-390	30	62	(	(	PUNCT
ejde-390	30	63	1.1	1.1	NUM
ejde-390	30	64	)	)	PUNCT
ejde-390	30	65	has	have	VERB
ejde-390	30	66	no	no	DET
ejde-390	30	67	positive	positive	ADJ
ejde-390	30	68	solution	solution	NOUN
ejde-390	30	69	.	.	PUNCT
ejde-390	31	1	in	in	ADP
ejde-390	31	2	addition	addition	NOUN
ejde-390	31	3	we	we	PRON
ejde-390	31	4	show	show	VERB
ejde-390	31	5	that	that	SCONJ
ejde-390	31	6	for	for	ADP
ejde-390	31	7	every	every	DET
ejde-390	31	8	λ	λ	PROPN
ejde-390	31	9	∈	∈	NOUN
ejde-390	31	10	l	l	NOUN
ejde-390	31	11	=	=	PUNCT
ejde-390	32	1	[	[	X
ejde-390	32	2	λ∗,+∞	λ∗,+∞	X
ejde-390	32	3	)	)	PUNCT
ejde-390	32	4	,	,	PUNCT
ejde-390	32	5	problem	problem	NOUN
ejde-390	32	6	(	(	PUNCT
ejde-390	32	7	1.1	1.1	NUM
ejde-390	32	8	)	)	PUNCT
ejde-390	32	9	has	have	VERB
ejde-390	32	10	a	a	DET
ejde-390	32	11	smallest	small	ADJ
ejde-390	32	12	positive	positive	ADJ
ejde-390	32	13	solution	solution	NOUN
ejde-390	32	14	uλ	uλ	ADV
ejde-390	33	1	and	and	CCONJ
ejde-390	33	2	we	we	PRON
ejde-390	33	3	examine	examine	VERB
ejde-390	33	4	the	the	DET
ejde-390	33	5	monotonicity	monotonicity	NOUN
ejde-390	33	6	and	and	CCONJ
ejde-390	33	7	continuity	continuity	NOUN
ejde-390	33	8	properties	property	NOUN
ejde-390	33	9	of	of	ADP
ejde-390	33	10	the	the	DET
ejde-390	33	11	map	map	NOUN
ejde-390	33	12	λ→	λ→	PUNCT
ejde-390	33	13	uλ	uλ	NOUN
ejde-390	33	14	.	.	PUNCT
ejde-390	34	1	with	with	ADP
ejde-390	34	2	the	the	DET
ejde-390	34	3	conditions	condition	NOUN
ejde-390	34	4	valid	valid	ADJ
ejde-390	34	5	on	on	ADP
ejde-390	34	6	the	the	DET
ejde-390	34	7	negative	negative	ADJ
ejde-390	34	8	semiaxis	semiaxis	NOUN
ejde-390	34	9	r−	r−	PROPN
ejde-390	34	10	=	=	SYM
ejde-390	34	11	(	(	PUNCT
ejde-390	34	12	−∞	−∞	NOUN
ejde-390	34	13	,	,	PUNCT
ejde-390	34	14	0	0	NUM
ejde-390	34	15	]	]	PUNCT
ejde-390	34	16	,	,	PUNCT
ejde-390	34	17	we	we	PRON
ejde-390	34	18	can	can	AUX
ejde-390	34	19	have	have	VERB
ejde-390	34	20	analogous	analogous	ADJ
ejde-390	34	21	results	result	NOUN
ejde-390	34	22	for	for	ADP
ejde-390	34	23	the	the	DET
ejde-390	34	24	negative	negative	ADJ
ejde-390	34	25	solutions	solution	NOUN
ejde-390	34	26	.	.	PUNCT
ejde-390	35	1	in	in	ADP
ejde-390	35	2	particular	particular	ADJ
ejde-390	35	3	we	we	PRON
ejde-390	35	4	can	can	AUX
ejde-390	35	5	produce	produce	VERB
ejde-390	35	6	a	a	DET
ejde-390	35	7	biggest	big	ADJ
ejde-390	35	8	negative	negative	ADJ
ejde-390	35	9	solution	solution	NOUN
ejde-390	35	10	vλ	vλ	ADP
ejde-390	35	11	for	for	ADP
ejde-390	35	12	problem	problem	NOUN
ejde-390	35	13	(	(	PUNCT
ejde-390	35	14	1.1	1.1	NUM
ejde-390	35	15	)	)	PUNCT
ejde-390	35	16	.	.	PUNCT
ejde-390	36	1	when	when	SCONJ
ejde-390	36	2	the	the	DET
ejde-390	36	3	conditions	condition	NOUN
ejde-390	36	4	are	be	AUX
ejde-390	36	5	bilateral	bilateral	ADJ
ejde-390	36	6	(	(	PUNCT
ejde-390	36	7	that	that	ADV
ejde-390	36	8	is	is	ADV
ejde-390	36	9	,	,	PUNCT
ejde-390	36	10	valid	valid	ADJ
ejde-390	36	11	for	for	ADP
ejde-390	36	12	all	all	DET
ejde-390	36	13	x	x	SYM
ejde-390	36	14	∈	∈	NOUN
ejde-390	36	15	r	r	NOUN
ejde-390	36	16	and	and	CCONJ
ejde-390	36	17	not	not	PART
ejde-390	36	18	only	only	ADV
ejde-390	36	19	on	on	ADP
ejde-390	36	20	the	the	DET
ejde-390	36	21	semiaxes	semiaxe	NOUN
ejde-390	36	22	)	)	PUNCT
ejde-390	36	23	,	,	PUNCT
ejde-390	36	24	then	then	ADV
ejde-390	36	25	using	use	VERB
ejde-390	36	26	the	the	DET
ejde-390	36	27	two	two	NUM
ejde-390	36	28	extremal	extremal	ADJ
ejde-390	36	29	constant	constant	ADJ
ejde-390	36	30	sign	sign	NOUN
ejde-390	36	31	solutions	solution	NOUN
ejde-390	36	32	uλ	uλ	ADV
ejde-390	36	33	and	and	CCONJ
ejde-390	36	34	vλ	vλ	INTJ
ejde-390	36	35	,	,	PUNCT
ejde-390	36	36	we	we	PRON
ejde-390	36	37	produce	produce	VERB
ejde-390	36	38	a	a	DET
ejde-390	36	39	nodal	nodal	NOUN
ejde-390	36	40	(	(	PUNCT
ejde-390	36	41	sign	sign	NOUN
ejde-390	36	42	-	-	PUNCT
ejde-390	36	43	changing	change	VERB
ejde-390	36	44	)	)	PUNCT
ejde-390	36	45	solution	solution	NOUN
ejde-390	36	46	for	for	ADP
ejde-390	36	47	problem	problem	NOUN
ejde-390	36	48	(	(	PUNCT
ejde-390	36	49	1.1	1.1	NUM
ejde-390	36	50	)	)	PUNCT
ejde-390	36	51	.	.	PUNCT
ejde-390	37	1	our	our	PRON
ejde-390	37	2	work	work	NOUN
ejde-390	37	3	here	here	ADV
ejde-390	37	4	continues	continue	VERB
ejde-390	37	5	and	and	CCONJ
ejde-390	37	6	extends	extend	VERB
ejde-390	37	7	the	the	DET
ejde-390	37	8	ones	one	NOUN
ejde-390	37	9	by	by	ADP
ejde-390	37	10	motreanu	motreanu	NOUN
ejde-390	37	11	-	-	PUNCT
ejde-390	37	12	motreanupapageorgiou	motreanupapageorgiou	NOUN
ejde-390	37	13	[	[	X
ejde-390	37	14	8	8	NUM
ejde-390	37	15	]	]	PUNCT
ejde-390	37	16	,	,	PUNCT
ejde-390	37	17	averna	averna	NOUN
ejde-390	37	18	-	-	PUNCT
ejde-390	37	19	papageorgiou	papageorgiou	NOUN
ejde-390	37	20	-	-	PUNCT
ejde-390	37	21	tornatore	tornatore	NOUN
ejde-390	37	22	[	[	X
ejde-390	37	23	1	1	NUM
ejde-390	37	24	]	]	PUNCT
ejde-390	37	25	and	and	CCONJ
ejde-390	37	26	papageorgiou	papageorgiou	NOUN
ejde-390	37	27	-	-	PUNCT
ejde-390	37	28	rǎdulescu	rǎdulescu	NOUN
ejde-390	37	29	[	[	X
ejde-390	37	30	11	11	NUM
ejde-390	37	31	]	]	PUNCT
ejde-390	37	32	.	.	PUNCT
ejde-390	38	1	in	in	ADP
ejde-390	38	2	[	[	X
ejde-390	38	3	8	8	NUM
ejde-390	38	4	]	]	X
ejde-390	38	5	the	the	DET
ejde-390	38	6	differential	differential	ADJ
ejde-390	38	7	operator	operator	NOUN
ejde-390	38	8	is	be	AUX
ejde-390	38	9	also	also	ADV
ejde-390	38	10	nonhomogeneous	nonhomogeneous	ADJ
ejde-390	38	11	but	but	CCONJ
ejde-390	38	12	the	the	DET
ejde-390	38	13	conditions	condition	NOUN
ejde-390	38	14	on	on	ADP
ejde-390	38	15	the	the	DET
ejde-390	38	16	map	map	NOUN
ejde-390	38	17	a	a	PRON
ejde-390	38	18	(	(	PUNCT
ejde-390	38	19	·	·	PUNCT
ejde-390	38	20	)	)	PUNCT
ejde-390	38	21	are	be	AUX
ejde-390	38	22	more	more	ADV
ejde-390	38	23	restrictive	restrictive	ADJ
ejde-390	38	24	excluding	excluding	NOUN
ejde-390	38	25	,	,	PUNCT
ejde-390	38	26	for	for	ADP
ejde-390	38	27	example	example	NOUN
ejde-390	38	28	,	,	PUNCT
ejde-390	38	29	the	the	DET
ejde-390	38	30	important	important	ADJ
ejde-390	38	31	case	case	NOUN
ejde-390	38	32	of	of	ADP
ejde-390	38	33	the	the	DET
ejde-390	38	34	(	(	PUNCT
ejde-390	38	35	p	p	X
ejde-390	38	36	,	,	PUNCT
ejde-390	38	37	q)-laplacian	q)-laplacian	PROPN
ejde-390	38	38	.	.	PUNCT
ejde-390	39	1	also	also	ADV
ejde-390	39	2	ξ	ξ	X
ejde-390	39	3	≡	≡	PROPN
ejde-390	39	4	0	0	NUM
ejde-390	39	5	and	and	CCONJ
ejde-390	39	6	the	the	DET
ejde-390	39	7	authors	author	NOUN
ejde-390	39	8	do	do	AUX
ejde-390	39	9	not	not	PART
ejde-390	39	10	prove	prove	VERB
ejde-390	39	11	the	the	DET
ejde-390	39	12	precise	precise	ADJ
ejde-390	39	13	dependence	dependence	NOUN
ejde-390	39	14	on	on	ADP
ejde-390	39	15	λ	λ	PROPN
ejde-390	39	16	>	>	X
ejde-390	39	17	0	0	NUM
ejde-390	39	18	of	of	ADP
ejde-390	39	19	the	the	DET
ejde-390	39	20	set	set	NOUN
ejde-390	39	21	of	of	ADP
ejde-390	39	22	positive	positive	ADJ
ejde-390	39	23	solutions	solution	NOUN
ejde-390	39	24	(	(	PUNCT
ejde-390	39	25	bifurcation	bifurcation	NOUN
ejde-390	39	26	-	-	PUNCT
ejde-390	39	27	type	type	NOUN
ejde-390	39	28	result	result	NOUN
ejde-390	39	29	)	)	PUNCT
ejde-390	39	30	.	.	PUNCT
ejde-390	40	1	in	in	ADP
ejde-390	40	2	[	[	X
ejde-390	40	3	1	1	X
ejde-390	40	4	]	]	PUNCT
ejde-390	40	5	the	the	DET
ejde-390	40	6	differential	differential	ADJ
ejde-390	40	7	operator	operator	NOUN
ejde-390	40	8	is	be	AUX
ejde-390	40	9	the	the	DET
ejde-390	40	10	p	p	NOUN
ejde-390	40	11	-	-	PUNCT
ejde-390	40	12	laplacian	laplacian	ADJ
ejde-390	40	13	and	and	CCONJ
ejde-390	40	14	ξ	ξ	PRON
ejde-390	40	15	≡	≡	PROPN
ejde-390	40	16	0	0	NUM
ejde-390	40	17	.	.	PUNCT
ejde-390	41	1	the	the	DET
ejde-390	41	2	authors	author	NOUN
ejde-390	41	3	do	do	AUX
ejde-390	41	4	not	not	PART
ejde-390	41	5	prove	prove	VERB
ejde-390	41	6	the	the	DET
ejde-390	41	7	existence	existence	NOUN
ejde-390	41	8	of	of	ADP
ejde-390	41	9	nodal	nodal	ADJ
ejde-390	41	10	solutions	solution	NOUN
ejde-390	41	11	.	.	PUNCT
ejde-390	42	1	finally	finally	ADV
ejde-390	42	2	in	in	ADP
ejde-390	42	3	[	[	X
ejde-390	42	4	11	11	NUM
ejde-390	42	5	]	]	PUNCT
ejde-390	42	6	the	the	DET
ejde-390	42	7	equation	equation	NOUN
ejde-390	42	8	is	be	AUX
ejde-390	42	9	semilinear	semilinear	NOUN
ejde-390	42	10	driven	drive	VERB
ejde-390	42	11	by	by	ADP
ejde-390	42	12	the	the	DET
ejde-390	42	13	laplacian	laplacian	NOUN
ejde-390	42	14	,	,	PUNCT
ejde-390	42	15	but	but	CCONJ
ejde-390	42	16	the	the	DET
ejde-390	42	17	boundary	boundary	ADJ
ejde-390	42	18	condition	condition	NOUN
ejde-390	42	19	is	be	AUX
ejde-390	42	20	robin	robin	PROPN
ejde-390	42	21	.	.	PUNCT
ejde-390	43	1	it	it	PRON
ejde-390	43	2	is	be	AUX
ejde-390	43	3	an	an	DET
ejde-390	43	4	interesting	interesting	ADJ
ejde-390	43	5	open	open	ADJ
ejde-390	43	6	problem	problem	NOUN
ejde-390	43	7	whether	whether	SCONJ
ejde-390	43	8	we	we	PRON
ejde-390	43	9	can	can	AUX
ejde-390	43	10	extend	extend	VERB
ejde-390	43	11	our	our	PRON
ejde-390	43	12	work	work	NOUN
ejde-390	43	13	here	here	ADV
ejde-390	43	14	to	to	ADP
ejde-390	43	15	robin	robin	PROPN
ejde-390	43	16	boundary	boundary	ADJ
ejde-390	43	17	value	value	NOUN
ejde-390	43	18	problems	problem	NOUN
ejde-390	43	19	.	.	PUNCT
ejde-390	44	1	2	2	X
ejde-390	44	2	.	.	X
ejde-390	44	3	mathematical	mathematical	ADJ
ejde-390	44	4	background	background	NOUN
ejde-390	44	5	hypotheses	hypothesis	NOUN
ejde-390	44	6	in	in	ADP
ejde-390	44	7	the	the	DET
ejde-390	44	8	analysis	analysis	NOUN
ejde-390	44	9	of	of	ADP
ejde-390	44	10	problem	problem	NOUN
ejde-390	44	11	(	(	PUNCT
ejde-390	44	12	1.1	1.1	NUM
ejde-390	44	13	)	)	PUNCT
ejde-390	44	14	we	we	PRON
ejde-390	44	15	will	will	AUX
ejde-390	44	16	use	use	VERB
ejde-390	44	17	the	the	DET
ejde-390	44	18	sobolev	sobolev	NOUN
ejde-390	44	19	space	space	NOUN
ejde-390	44	20	w	w	PROPN
ejde-390	44	21	1,p(ω	1,p(ω	NUM
ejde-390	44	22	)	)	PUNCT
ejde-390	44	23	and	and	CCONJ
ejde-390	44	24	the	the	DET
ejde-390	44	25	banach	banach	NOUN
ejde-390	44	26	space	space	NOUN
ejde-390	44	27	c1(ω	c1(ω	NOUN
ejde-390	44	28	)	)	PUNCT
ejde-390	44	29	.	.	PUNCT
ejde-390	45	1	by	by	ADP
ejde-390	45	2	‖	‖	PROPN
ejde-390	45	3	·	·	PUNCT
ejde-390	45	4	‖	‖	PROPN
ejde-390	45	5	we	we	PRON
ejde-390	45	6	denote	denote	VERB
ejde-390	45	7	the	the	DET
ejde-390	45	8	norm	norm	NOUN
ejde-390	45	9	of	of	ADP
ejde-390	45	10	w	w	PROPN
ejde-390	45	11	1,p(ω	1,p(ω	PROPN
ejde-390	45	12	)	)	PUNCT
ejde-390	45	13	defined	define	VERB
ejde-390	45	14	by	by	ADP
ejde-390	45	15	‖u‖	‖u‖	PROPN
ejde-390	45	16	=	=	PUNCT
ejde-390	46	1	[	[	X
ejde-390	46	2	‖u‖pp	‖u‖pp	ADJ
ejde-390	46	3	+	+	ADJ
ejde-390	46	4	‖∇u‖pp]1	‖∇u‖pp]1	PROPN
ejde-390	46	5	/	/	SYM
ejde-390	46	6	p	p	NOUN
ejde-390	46	7	for	for	ADP
ejde-390	46	8	all	all	DET
ejde-390	46	9	u	u	NOUN
ejde-390	46	10	∈w	∈w	NOUN
ejde-390	46	11	1,p(ω	1,p(ω	NUM
ejde-390	46	12	)	)	PUNCT
ejde-390	46	13	.	.	PUNCT
ejde-390	47	1	the	the	DET
ejde-390	47	2	banach	banach	NOUN
ejde-390	47	3	space	space	NOUN
ejde-390	47	4	c1(ω	c1(ω	NOUN
ejde-390	47	5	)	)	PUNCT
ejde-390	47	6	is	be	AUX
ejde-390	47	7	ordered	order	VERB
ejde-390	47	8	with	with	ADP
ejde-390	47	9	positive	positive	ADJ
ejde-390	47	10	(	(	PUNCT
ejde-390	47	11	order	order	NOUN
ejde-390	47	12	)	)	PUNCT
ejde-390	47	13	cone	cone	NOUN
ejde-390	47	14	c+	c+	NOUN
ejde-390	47	15	=	=	PUNCT
ejde-390	47	16	{	{	PUNCT
ejde-390	47	17	u	u	NOUN
ejde-390	47	18	∈	∈	PROPN
ejde-390	47	19	c1(ω	c1(ω	PROPN
ejde-390	47	20	)	)	PUNCT
ejde-390	47	21	:	:	PUNCT
ejde-390	47	22	u(z	u(z	X
ejde-390	47	23	)	)	PUNCT
ejde-390	47	24	≥	≥	NOUN
ejde-390	47	25	0	0	NUM
ejde-390	47	26	for	for	ADP
ejde-390	47	27	all	all	DET
ejde-390	47	28	z	z	NOUN
ejde-390	47	29	∈	∈	PROPN
ejde-390	47	30	ω	ω	PROPN
ejde-390	47	31	}	}	PUNCT
ejde-390	47	32	.	.	PUNCT
ejde-390	48	1	this	this	DET
ejde-390	48	2	cone	cone	NOUN
ejde-390	48	3	has	have	VERB
ejde-390	48	4	a	a	DET
ejde-390	48	5	nonempty	nonempty	ADJ
ejde-390	48	6	interior	interior	NOUN
ejde-390	48	7	given	give	VERB
ejde-390	48	8	by	by	ADP
ejde-390	48	9	d+	d+	NOUN
ejde-390	48	10	=	=	SYM
ejde-390	48	11	{	{	PUNCT
ejde-390	48	12	u	u	X
ejde-390	48	13	∈	∈	PROPN
ejde-390	48	14	c1(ω	c1(ω	PROPN
ejde-390	48	15	)	)	PUNCT
ejde-390	48	16	:	:	PUNCT
ejde-390	48	17	u(z	u(z	X
ejde-390	48	18	)	)	PUNCT
ejde-390	48	19	>	>	X
ejde-390	48	20	0	0	PUNCT
ejde-390	48	21	for	for	ADP
ejde-390	48	22	all	all	DET
ejde-390	48	23	z	z	NOUN
ejde-390	48	24	∈	∈	PROPN
ejde-390	48	25	ω	ω	PROPN
ejde-390	48	26	}	}	PUNCT
ejde-390	48	27	.	.	PUNCT
ejde-390	49	1	we	we	PRON
ejde-390	49	2	will	will	AUX
ejde-390	49	3	also	also	ADV
ejde-390	49	4	consider	consider	VERB
ejde-390	49	5	another	another	DET
ejde-390	49	6	order	order	NOUN
ejde-390	49	7	cone	cone	NOUN
ejde-390	49	8	for	for	ADP
ejde-390	49	9	c1(ω	c1(ω	NOUN
ejde-390	49	10	)	)	PUNCT
ejde-390	49	11	,	,	PUNCT
ejde-390	49	12	namely	namely	ADV
ejde-390	49	13	the	the	DET
ejde-390	49	14	cone	cone	NOUN
ejde-390	49	15	ĉ+	ĉ+	PUNCT
ejde-390	49	16	=	=	PRON
ejde-390	49	17	{	{	PUNCT
ejde-390	49	18	u	u	NOUN
ejde-390	49	19	∈	∈	PROPN
ejde-390	49	20	c1(ω	c1(ω	PROPN
ejde-390	49	21	)	)	PUNCT
ejde-390	49	22	:	:	PUNCT
ejde-390	49	23	u(z	u(z	X
ejde-390	49	24	)	)	PUNCT
ejde-390	49	25	≥	≥	NOUN
ejde-390	49	26	0	0	NUM
ejde-390	49	27	for	for	ADP
ejde-390	49	28	all	all	DET
ejde-390	49	29	z	z	NOUN
ejde-390	49	30	∈	∈	PROPN
ejde-390	49	31	ω	ω	PROPN
ejde-390	49	32	,	,	PUNCT
ejde-390	49	33	∂u	∂u	PROPN
ejde-390	49	34	∂n	∂n	PROPN
ejde-390	49	35	∣∣	∣∣	NUM
ejde-390	49	36	∂ω∩u−1(0	∂ω∩u−1(0	NOUN
ejde-390	49	37	)	)	PUNCT
ejde-390	49	38	≤	≤	NOUN
ejde-390	49	39	0	0	NUM
ejde-390	49	40	}	}	PUNCT
ejde-390	49	41	.	.	PUNCT
ejde-390	50	1	this	this	DET
ejde-390	50	2	cone	cone	NOUN
ejde-390	50	3	too	too	ADV
ejde-390	50	4	has	have	VERB
ejde-390	50	5	a	a	DET
ejde-390	50	6	nonempty	nonempty	ADJ
ejde-390	50	7	interior	interior	ADJ
ejde-390	50	8	int	int	NOUN
ejde-390	50	9	ĉ+	ĉ+	PUNCT
ejde-390	51	1	=	=	PRON
ejde-390	51	2	{	{	PUNCT
ejde-390	51	3	u	u	NOUN
ejde-390	51	4	∈	∈	PROPN
ejde-390	51	5	ĉ+	ĉ+	X
ejde-390	51	6	:	:	PUNCT
ejde-390	51	7	u(z	u(z	X
ejde-390	51	8	)	)	PUNCT
ejde-390	51	9	>	>	X
ejde-390	51	10	0	0	PUNCT
ejde-390	52	1	for	for	ADP
ejde-390	52	2	all	all	DET
ejde-390	52	3	z	z	NOUN
ejde-390	52	4	∈	∈	PROPN
ejde-390	52	5	ω	ω	PROPN
ejde-390	52	6	,	,	PUNCT
ejde-390	52	7	∂u	∂u	PROPN
ejde-390	52	8	∂n	∂n	PROPN
ejde-390	52	9	∣∣	∣∣	NUM
ejde-390	52	10	∂ω∩u−1(0	∂ω∩u−1(0	NOUN
ejde-390	52	11	)	)	PUNCT
ejde-390	52	12	<	<	X
ejde-390	52	13	0	0	NUM
ejde-390	52	14	}	}	PUNCT
ejde-390	52	15	.	.	PUNCT
ejde-390	53	1	ejde-2020/12	ejde-2020/12	NOUN
ejde-390	53	2	positive	positive	ADJ
ejde-390	53	3	and	and	CCONJ
ejde-390	53	4	nodal	nodal	ADJ
ejde-390	53	5	solutions	solution	NOUN
ejde-390	53	6	3	3	NUM
ejde-390	53	7	given	give	VERB
ejde-390	53	8	x	x	PUNCT
ejde-390	53	9	∈	∈	PROPN
ejde-390	53	10	r	r	NOUN
ejde-390	53	11	,	,	PUNCT
ejde-390	53	12	we	we	PRON
ejde-390	53	13	set	set	VERB
ejde-390	53	14	x±	x±	PROPN
ejde-390	54	1	=	=	SYM
ejde-390	54	2	max{±x	max{±x	PROPN
ejde-390	54	3	,	,	PUNCT
ejde-390	54	4	0	0	NUM
ejde-390	54	5	}	}	PUNCT
ejde-390	54	6	.	.	PUNCT
ejde-390	55	1	for	for	ADP
ejde-390	55	2	any	any	DET
ejde-390	55	3	measurable	measurable	ADJ
ejde-390	55	4	function	function	NOUN
ejde-390	55	5	u	u	NOUN
ejde-390	55	6	:	:	PUNCT
ejde-390	55	7	ω	ω	PROPN
ejde-390	55	8	→	→	SYM
ejde-390	55	9	rn	rn	PROPN
ejde-390	55	10	,	,	PUNCT
ejde-390	55	11	we	we	PRON
ejde-390	55	12	define	define	VERB
ejde-390	55	13	u±(z	u±(z	NOUN
ejde-390	55	14	)	)	PUNCT
ejde-390	55	15	=	=	SYM
ejde-390	55	16	u(z)±	u(z)±	NOUN
ejde-390	55	17	for	for	ADP
ejde-390	55	18	all	all	DET
ejde-390	55	19	z	z	NOUN
ejde-390	55	20	∈	∈	PROPN
ejde-390	55	21	ω	ω	NOUN
ejde-390	55	22	.	.	PUNCT
ejde-390	56	1	if	if	SCONJ
ejde-390	56	2	u	u	PRON
ejde-390	56	3	∈w	∈w	VERB
ejde-390	56	4	1,p(ω	1,p(ω	NUM
ejde-390	56	5	)	)	PUNCT
ejde-390	56	6	,	,	PUNCT
ejde-390	56	7	then	then	ADV
ejde-390	56	8	u±	u±	PROPN
ejde-390	56	9	∈w	∈w	VERB
ejde-390	56	10	1,p(ω	1,p(ω	NUM
ejde-390	56	11	)	)	PUNCT
ejde-390	56	12	.	.	PUNCT
ejde-390	57	1	if	if	SCONJ
ejde-390	57	2	u	u	NOUN
ejde-390	57	3	,	,	PUNCT
ejde-390	57	4	v	v	ADP
ejde-390	57	5	∈w	∈w	NOUN
ejde-390	57	6	1,p(ω	1,p(ω	NUM
ejde-390	57	7	)	)	PUNCT
ejde-390	57	8	and	and	CCONJ
ejde-390	57	9	v	v	ADP
ejde-390	57	10	≤	≤	NUM
ejde-390	57	11	u	u	NOUN
ejde-390	57	12	,	,	PUNCT
ejde-390	57	13	we	we	PRON
ejde-390	57	14	define	define	VERB
ejde-390	57	15	[	[	X
ejde-390	57	16	v	v	NOUN
ejde-390	57	17	,	,	PUNCT
ejde-390	57	18	u	u	NOUN
ejde-390	57	19	]	]	X
ejde-390	57	20	=	=	SYM
ejde-390	57	21	{	{	PUNCT
ejde-390	57	22	h	h	NOUN
ejde-390	57	23	∈w	∈w	PROPN
ejde-390	57	24	1,p(ω	1,p(ω	NUM
ejde-390	57	25	)	)	PUNCT
ejde-390	57	26	:	:	PUNCT
ejde-390	58	1	v(z	v(z	NOUN
ejde-390	58	2	)	)	PUNCT
ejde-390	58	3	≤	≤	NUM
ejde-390	58	4	h(z	h(z	NOUN
ejde-390	58	5	)	)	PUNCT
ejde-390	58	6	≤	≤	NUM
ejde-390	58	7	u(z	u(z	NOUN
ejde-390	58	8	)	)	PUNCT
ejde-390	58	9	for	for	ADP
ejde-390	58	10	a.a	a.a	PROPN
ejde-390	58	11	.	.	PROPN
ejde-390	58	12	z	z	PROPN
ejde-390	58	13	∈	∈	PROPN
ejde-390	58	14	ω	ω	PROPN
ejde-390	58	15	}	}	PUNCT
ejde-390	58	16	,	,	PUNCT
ejde-390	59	1	[	[	X
ejde-390	59	2	v	v	NOUN
ejde-390	59	3	)	)	PUNCT
ejde-390	59	4	=	=	NOUN
ejde-390	59	5	{	{	PUNCT
ejde-390	59	6	h	h	NOUN
ejde-390	59	7	∈w	∈w	PROPN
ejde-390	59	8	1,p(ω	1,p(ω	NUM
ejde-390	59	9	)	)	PUNCT
ejde-390	59	10	:	:	PUNCT
ejde-390	60	1	v(z	v(z	NOUN
ejde-390	60	2	)	)	PUNCT
ejde-390	60	3	≤	≤	NUM
ejde-390	60	4	h(z	h(z	NOUN
ejde-390	60	5	)	)	PUNCT
ejde-390	60	6	for	for	ADP
ejde-390	60	7	a.a	a.a	PROPN
ejde-390	60	8	.	.	PROPN
ejde-390	60	9	z	z	PROPN
ejde-390	60	10	∈	∈	PROPN
ejde-390	60	11	ω	ω	PROPN
ejde-390	60	12	}	}	PUNCT
ejde-390	60	13	.	.	PUNCT
ejde-390	61	1	by	by	ADP
ejde-390	61	2	intc1(ω)[v	intc1(ω)[v	PROPN
ejde-390	61	3	,	,	PUNCT
ejde-390	61	4	u	u	NOUN
ejde-390	61	5	]	]	X
ejde-390	62	1	we	we	PRON
ejde-390	62	2	denote	denote	VERB
ejde-390	62	3	the	the	DET
ejde-390	62	4	interior	interior	NOUN
ejde-390	62	5	in	in	ADP
ejde-390	62	6	c1(ω	c1(ω	NOUN
ejde-390	62	7	)	)	PUNCT
ejde-390	62	8	of	of	ADP
ejde-390	62	9	[	[	X
ejde-390	62	10	v	v	NOUN
ejde-390	62	11	,	,	PUNCT
ejde-390	62	12	u	u	NOUN
ejde-390	62	13	]	]	X
ejde-390	62	14	∩	∩	X
ejde-390	62	15	c1(ω	c1(ω	X
ejde-390	62	16	)	)	PUNCT
ejde-390	62	17	.	.	PUNCT
ejde-390	63	1	let	let	VERB
ejde-390	63	2	x	x	PRON
ejde-390	63	3	be	be	AUX
ejde-390	63	4	a	a	DET
ejde-390	63	5	banach	banach	NOUN
ejde-390	63	6	space	space	NOUN
ejde-390	63	7	,	,	PUNCT
ejde-390	63	8	ϕ	ϕ	PROPN
ejde-390	63	9	∈	∈	PROPN
ejde-390	63	10	c1(x	c1(x	NOUN
ejde-390	63	11	,	,	PUNCT
ejde-390	63	12	r	r	NOUN
ejde-390	63	13	)	)	PUNCT
ejde-390	63	14	and	and	CCONJ
ejde-390	63	15	c	c	PROPN
ejde-390	63	16	∈	∈	PROPN
ejde-390	63	17	r.	r.	PROPN
ejde-390	63	18	we	we	PRON
ejde-390	63	19	define	define	VERB
ejde-390	63	20	kϕ	kϕ	X
ejde-390	63	21	=	=	SYM
ejde-390	63	22	{	{	PUNCT
ejde-390	63	23	x	x	PUNCT
ejde-390	63	24	∈	∈	PROPN
ejde-390	63	25	x	x	X
ejde-390	63	26	:	:	PUNCT
ejde-390	63	27	ϕ′(x	ϕ′(x	X
ejde-390	63	28	)	)	PUNCT
ejde-390	64	1	=	=	SYM
ejde-390	64	2	0	0	X
ejde-390	64	3	}	}	PUNCT
ejde-390	64	4	(	(	PUNCT
ejde-390	64	5	the	the	DET
ejde-390	64	6	critical	critical	ADJ
ejde-390	64	7	set	set	NOUN
ejde-390	64	8	of	of	ADP
ejde-390	64	9	ϕ	ϕ	NOUN
ejde-390	64	10	)	)	PUNCT
ejde-390	64	11	,	,	PUNCT
ejde-390	65	1	ϕc	ϕc	NOUN
ejde-390	65	2	=	=	PRON
ejde-390	65	3	{	{	PUNCT
ejde-390	65	4	x	x	PUNCT
ejde-390	65	5	∈	∈	PROPN
ejde-390	65	6	x	x	X
ejde-390	65	7	:	:	PUNCT
ejde-390	65	8	ϕ(x	ϕ(x	X
ejde-390	65	9	)	)	PUNCT
ejde-390	65	10	≤	≤	NOUN
ejde-390	66	1	c	c	X
ejde-390	66	2	}	}	PUNCT
ejde-390	66	3	(	(	PUNCT
ejde-390	66	4	the	the	DET
ejde-390	66	5	sublevel	sublevel	NOUN
ejde-390	66	6	set	set	NOUN
ejde-390	66	7	of	of	ADP
ejde-390	66	8	ϕ	ϕ	NOUN
ejde-390	66	9	at	at	ADP
ejde-390	66	10	c	c	NOUN
ejde-390	66	11	)	)	PUNCT
ejde-390	66	12	.	.	PUNCT
ejde-390	67	1	let	let	AUX
ejde-390	67	2	(	(	PUNCT
ejde-390	67	3	a	a	DET
ejde-390	67	4	,	,	PUNCT
ejde-390	67	5	b	b	NOUN
ejde-390	67	6	)	)	PUNCT
ejde-390	67	7	be	be	AUX
ejde-390	67	8	a	a	DET
ejde-390	67	9	topological	topological	ADJ
ejde-390	67	10	pair	pair	NOUN
ejde-390	67	11	such	such	ADJ
ejde-390	67	12	that	that	SCONJ
ejde-390	67	13	b	b	ADP
ejde-390	67	14	⊆	⊆	NUM
ejde-390	67	15	a	a	DET
ejde-390	67	16	⊆	⊆	NUM
ejde-390	67	17	x.	x.	NOUN
ejde-390	67	18	by	by	ADP
ejde-390	67	19	hk(a	hk(a	X
ejde-390	67	20	,	,	PUNCT
ejde-390	67	21	b	b	NOUN
ejde-390	67	22	)	)	PUNCT
ejde-390	67	23	,	,	PUNCT
ejde-390	67	24	k	k	PROPN
ejde-390	67	25	∈	∈	PROPN
ejde-390	67	26	n0	n0	PROPN
ejde-390	67	27	,	,	PUNCT
ejde-390	67	28	we	we	PRON
ejde-390	67	29	denote	denote	VERB
ejde-390	67	30	the	the	DET
ejde-390	67	31	kth	kth	PROPN
ejde-390	67	32	-	-	PUNCT
ejde-390	67	33	relative	relative	ADJ
ejde-390	67	34	singular	singular	PROPN
ejde-390	67	35	homology	homology	NOUN
ejde-390	67	36	group	group	NOUN
ejde-390	67	37	for	for	ADP
ejde-390	67	38	the	the	DET
ejde-390	67	39	pair	pair	NOUN
ejde-390	67	40	(	(	PUNCT
ejde-390	67	41	a	a	DET
ejde-390	67	42	,	,	PUNCT
ejde-390	67	43	b	b	NOUN
ejde-390	67	44	)	)	PUNCT
ejde-390	67	45	with	with	ADP
ejde-390	67	46	integer	integer	NOUN
ejde-390	67	47	coefficients	coefficient	NOUN
ejde-390	67	48	.	.	PUNCT
ejde-390	68	1	if	if	SCONJ
ejde-390	68	2	u	u	PROPN
ejde-390	68	3	∈	∈	PROPN
ejde-390	68	4	kϕ	kϕ	PROPN
ejde-390	68	5	is	be	AUX
ejde-390	68	6	isolated	isolate	VERB
ejde-390	68	7	and	and	CCONJ
ejde-390	68	8	ϕ(u	ϕ(u	NOUN
ejde-390	68	9	)	)	PUNCT
ejde-390	69	1	=	=	SYM
ejde-390	69	2	c	c	X
ejde-390	69	3	,	,	PUNCT
ejde-390	69	4	then	then	ADV
ejde-390	69	5	the	the	DET
ejde-390	69	6	critical	critical	ADJ
ejde-390	69	7	groups	group	NOUN
ejde-390	69	8	of	of	ADP
ejde-390	69	9	ϕ	ϕ	NOUN
ejde-390	69	10	at	at	ADP
ejde-390	69	11	u	u	NOUN
ejde-390	69	12	are	be	AUX
ejde-390	69	13	defined	define	VERB
ejde-390	69	14	by	by	ADP
ejde-390	69	15	ck(ϕ	ck(ϕ	NOUN
ejde-390	69	16	,	,	PUNCT
ejde-390	69	17	u	u	NOUN
ejde-390	69	18	)	)	PUNCT
ejde-390	69	19	=	=	SYM
ejde-390	69	20	hk(ϕc	hk(ϕc	PROPN
ejde-390	69	21	∩	∩	NOUN
ejde-390	69	22	u,ϕc	u,ϕc	NUM
ejde-390	69	23	∩	∩	ADJ
ejde-390	69	24	u	u	NOUN
ejde-390	69	25	\	\	PROPN
ejde-390	69	26	{	{	PUNCT
ejde-390	69	27	u	u	NOUN
ejde-390	69	28	}	}	PUNCT
ejde-390	69	29	)	)	PUNCT
ejde-390	69	30	for	for	ADP
ejde-390	69	31	all	all	DET
ejde-390	69	32	k	k	PROPN
ejde-390	69	33	∈	∈	PROPN
ejde-390	69	34	n0	n0	PROPN
ejde-390	69	35	,	,	PUNCT
ejde-390	69	36	with	with	ADP
ejde-390	69	37	u	u	NOUN
ejde-390	69	38	being	be	AUX
ejde-390	69	39	a	a	DET
ejde-390	69	40	neighborhood	neighborhood	NOUN
ejde-390	69	41	of	of	ADP
ejde-390	69	42	u	u	PRON
ejde-390	69	43	such	such	ADJ
ejde-390	69	44	that	that	SCONJ
ejde-390	69	45	kϕ	kϕ	PROPN
ejde-390	69	46	∩	∩	NOUN
ejde-390	69	47	ϕc	ϕc	ADP
ejde-390	69	48	∩	∩	ADJ
ejde-390	69	49	u	u	NOUN
ejde-390	69	50	=	=	PUNCT
ejde-390	69	51	{	{	PUNCT
ejde-390	69	52	u	u	NOUN
ejde-390	69	53	}	}	PUNCT
ejde-390	69	54	.	.	PUNCT
ejde-390	70	1	the	the	DET
ejde-390	70	2	excision	excision	NOUN
ejde-390	70	3	property	property	NOUN
ejde-390	70	4	of	of	ADP
ejde-390	70	5	singular	singular	ADJ
ejde-390	70	6	homology	homology	NOUN
ejde-390	70	7	,	,	PUNCT
ejde-390	70	8	implies	imply	VERB
ejde-390	70	9	that	that	SCONJ
ejde-390	70	10	this	this	DET
ejde-390	70	11	definition	definition	NOUN
ejde-390	70	12	is	be	AUX
ejde-390	70	13	independent	independent	ADJ
ejde-390	70	14	of	of	ADP
ejde-390	70	15	the	the	DET
ejde-390	70	16	isolating	isolate	VERB
ejde-390	70	17	neighborhood	neighborhood	NOUN
ejde-390	70	18	.	.	PUNCT
ejde-390	71	1	let	let	VERB
ejde-390	71	2	x∗	x∗	PROPN
ejde-390	71	3	be	be	AUX
ejde-390	71	4	the	the	DET
ejde-390	71	5	topological	topological	ADJ
ejde-390	71	6	dual	dual	ADJ
ejde-390	71	7	of	of	ADP
ejde-390	71	8	x	x	PUNCT
ejde-390	71	9	and	and	CCONJ
ejde-390	71	10	denote	denote	VERB
ejde-390	71	11	by	by	ADP
ejde-390	71	12	〈	〈	PROPN
ejde-390	71	13	·	·	PROPN
ejde-390	71	14	,	,	PUNCT
ejde-390	71	15	·	·	PUNCT
ejde-390	71	16	〉	〉	NOUN
ejde-390	71	17	the	the	DET
ejde-390	71	18	duality	duality	NOUN
ejde-390	71	19	brackets	bracket	NOUN
ejde-390	71	20	of	of	ADP
ejde-390	71	21	the	the	DET
ejde-390	71	22	pair	pair	NOUN
ejde-390	71	23	(	(	PUNCT
ejde-390	71	24	x∗	x∗	PROPN
ejde-390	71	25	,	,	PUNCT
ejde-390	71	26	x	x	NOUN
ejde-390	71	27	)	)	PUNCT
ejde-390	71	28	.	.	PUNCT
ejde-390	72	1	a	a	DET
ejde-390	72	2	map	map	NOUN
ejde-390	72	3	a	a	PRON
ejde-390	72	4	:	:	PUNCT
ejde-390	72	5	x	x	SYM
ejde-390	72	6	→	→	SYM
ejde-390	72	7	x∗	x∗	PROPN
ejde-390	72	8	is	be	AUX
ejde-390	72	9	said	say	VERB
ejde-390	72	10	to	to	PART
ejde-390	72	11	be	be	AUX
ejde-390	72	12	of	of	ADP
ejde-390	72	13	type	type	NOUN
ejde-390	72	14	(	(	PUNCT
ejde-390	72	15	s)+	s)+	VERB
ejde-390	72	16	if	if	SCONJ
ejde-390	72	17	it	it	PRON
ejde-390	72	18	has	have	VERB
ejde-390	72	19	the	the	DET
ejde-390	72	20	following	follow	VERB
ejde-390	72	21	property	property	NOUN
ejde-390	72	22	:	:	PUNCT
ejde-390	72	23	un	un	AUX
ejde-390	72	24	w−→	w−→	PROPN
ejde-390	72	25	u	u	PROPN
ejde-390	72	26	in	in	ADP
ejde-390	72	27	x	x	X
ejde-390	72	28	and	and	CCONJ
ejde-390	72	29	lim	lim	PROPN
ejde-390	72	30	sup	sup	PROPN
ejde-390	72	31	n→+∞	n→+∞	PROPN
ejde-390	72	32	〈	〈	PROPN
ejde-390	72	33	a(un	a(un	PROPN
ejde-390	72	34	)	)	PUNCT
ejde-390	72	35	,	,	PUNCT
ejde-390	72	36	un	un	PROPN
ejde-390	72	37	−	−	PROPN
ejde-390	72	38	u	u	PROPN
ejde-390	72	39	〉	〉	PROPN
ejde-390	72	40	≤	≤	NUM
ejde-390	72	41	0	0	NUM
ejde-390	72	42	⇒	⇒	PROPN
ejde-390	72	43	un	un	PROPN
ejde-390	72	44	→	→	SYM
ejde-390	72	45	u	u	PROPN
ejde-390	72	46	in	in	ADP
ejde-390	72	47	x.	x.	NOUN
ejde-390	72	48	also	also	ADV
ejde-390	72	49	,	,	PUNCT
ejde-390	72	50	we	we	PRON
ejde-390	72	51	say	say	VERB
ejde-390	72	52	that	that	SCONJ
ejde-390	72	53	ϕ	ϕ	PROPN
ejde-390	72	54	∈	∈	PROPN
ejde-390	72	55	c1(x	c1(x	NOUN
ejde-390	72	56	,	,	PUNCT
ejde-390	72	57	r	r	NOUN
ejde-390	72	58	)	)	PUNCT
ejde-390	72	59	satisfies	satisfy	VERB
ejde-390	72	60	the	the	DET
ejde-390	72	61	“	"	PUNCT
ejde-390	72	62	c	c	NOUN
ejde-390	72	63	-	-	PUNCT
ejde-390	72	64	condition	condition	NOUN
ejde-390	72	65	”	"	PUNCT
ejde-390	72	66	,	,	PUNCT
ejde-390	72	67	if	if	SCONJ
ejde-390	72	68	the	the	DET
ejde-390	72	69	following	follow	VERB
ejde-390	72	70	property	property	NOUN
ejde-390	72	71	holds	hold	VERB
ejde-390	72	72	:	:	PUNCT
ejde-390	72	73	every	every	DET
ejde-390	72	74	sequence	sequence	NOUN
ejde-390	72	75	{	{	PUNCT
ejde-390	72	76	un}n≥1	un}n≥1	NOUN
ejde-390	72	77	⊆	⊆	NUM
ejde-390	72	78	x	x	SYM
ejde-390	72	79	such	such	ADJ
ejde-390	72	80	that	that	SCONJ
ejde-390	72	81	{	{	PUNCT
ejde-390	72	82	ϕ(un)}n≥1	ϕ(un)}n≥1	NOUN
ejde-390	72	83	⊆	⊆	NUM
ejde-390	72	84	r	r	NOUN
ejde-390	72	85	is	be	AUX
ejde-390	72	86	bounded	bound	VERB
ejde-390	72	87	and	and	CCONJ
ejde-390	72	88	(	(	PUNCT
ejde-390	72	89	1	1	NUM
ejde-390	72	90	+	+	CCONJ
ejde-390	72	91	‖un‖x)ϕ′(un)→	‖un‖x)ϕ′(un)→	NOUN
ejde-390	72	92	0	0	NUM
ejde-390	72	93	in	in	ADP
ejde-390	72	94	x∗	x∗	PROPN
ejde-390	72	95	as	as	ADP
ejde-390	72	96	n	n	PROPN
ejde-390	72	97	→	→	SYM
ejde-390	72	98	+	+	PROPN
ejde-390	72	99	∞	∞	PROPN
ejde-390	72	100	,	,	PUNCT
ejde-390	72	101	admits	admit	VERB
ejde-390	72	102	a	a	DET
ejde-390	72	103	strongly	strongly	ADV
ejde-390	72	104	convergent	convergent	ADJ
ejde-390	72	105	subsequence	subsequence	NOUN
ejde-390	72	106	.	.	PUNCT
ejde-390	73	1	if	if	SCONJ
ejde-390	73	2	h1	h1	PROPN
ejde-390	73	3	,	,	PUNCT
ejde-390	73	4	h2	h2	PROPN
ejde-390	73	5	∈	∈	PROPN
ejde-390	73	6	l∞(ω	l∞(ω	NOUN
ejde-390	73	7	)	)	PUNCT
ejde-390	73	8	,	,	PUNCT
ejde-390	73	9	then	then	ADV
ejde-390	73	10	we	we	PRON
ejde-390	73	11	write	write	VERB
ejde-390	73	12	h1	h1	PROPN
ejde-390	73	13	�	�	PROPN
ejde-390	73	14	h2	h2	PROPN
ejde-390	73	15	when	when	SCONJ
ejde-390	73	16	we	we	PRON
ejde-390	73	17	have	have	VERB
ejde-390	73	18	h1(z	h1(z	NOUN
ejde-390	73	19	)	)	PUNCT
ejde-390	73	20	≤	≤	NOUN
ejde-390	73	21	h2(z	h2(z	X
ejde-390	73	22	)	)	PUNCT
ejde-390	73	23	for	for	ADP
ejde-390	73	24	a.a	a.a	PROPN
ejde-390	73	25	.	.	PROPN
ejde-390	73	26	z	z	PROPN
ejde-390	73	27	∈	∈	PROPN
ejde-390	73	28	ω	ω	PROPN
ejde-390	73	29	and	and	CCONJ
ejde-390	73	30	the	the	DET
ejde-390	73	31	above	above	ADJ
ejde-390	73	32	inequality	inequality	NOUN
ejde-390	73	33	is	be	AUX
ejde-390	73	34	strict	strict	ADJ
ejde-390	73	35	on	on	ADP
ejde-390	73	36	a	a	DET
ejde-390	73	37	set	set	NOUN
ejde-390	73	38	of	of	ADP
ejde-390	73	39	positive	positive	ADJ
ejde-390	73	40	measure	measure	NOUN
ejde-390	73	41	.	.	PUNCT
ejde-390	74	1	finally	finally	ADV
ejde-390	74	2	for	for	ADP
ejde-390	74	3	any	any	DET
ejde-390	74	4	measurable	measurable	ADJ
ejde-390	74	5	function	function	NOUN
ejde-390	74	6	f	f	NOUN
ejde-390	74	7	:	:	PUNCT
ejde-390	74	8	ω	ω	NUM
ejde-390	74	9	×	×	NOUN
ejde-390	74	10	r	r	NOUN
ejde-390	74	11	→	→	SYM
ejde-390	74	12	r	r	NOUN
ejde-390	74	13	,	,	PUNCT
ejde-390	74	14	by	by	ADP
ejde-390	74	15	nf	nf	INTJ
ejde-390	74	16	(	(	PUNCT
ejde-390	74	17	·	·	PUNCT
ejde-390	74	18	)	)	PUNCT
ejde-390	74	19	we	we	PRON
ejde-390	74	20	denote	denote	VERB
ejde-390	74	21	the	the	DET
ejde-390	74	22	nemytskii	nemytskii	ADJ
ejde-390	74	23	operator	operator	NOUN
ejde-390	74	24	corresponding	correspond	VERB
ejde-390	74	25	to	to	ADP
ejde-390	74	26	f	f	PROPN
ejde-390	74	27	,	,	PUNCT
ejde-390	74	28	that	that	ADV
ejde-390	74	29	is	is	ADV
ejde-390	74	30	,	,	PUNCT
ejde-390	74	31	nf	nf	INTJ
ejde-390	74	32	(	(	PUNCT
ejde-390	74	33	u	u	NOUN
ejde-390	74	34	)	)	PUNCT
ejde-390	74	35	(	(	PUNCT
ejde-390	74	36	·	·	PUNCT
ejde-390	74	37	)	)	PUNCT
ejde-390	75	1	=	=	SYM
ejde-390	75	2	f	f	X
ejde-390	75	3	(	(	PUNCT
ejde-390	75	4	·	·	PUNCT
ejde-390	75	5	,	,	PUNCT
ejde-390	75	6	u	u	NOUN
ejde-390	75	7	(	(	PUNCT
ejde-390	75	8	·	·	PUNCT
ejde-390	75	9	)	)	PUNCT
ejde-390	75	10	)	)	PUNCT
ejde-390	75	11	for	for	ADP
ejde-390	75	12	every	every	DET
ejde-390	75	13	u	u	NOUN
ejde-390	75	14	:	:	PUNCT
ejde-390	75	15	ω→	ω→	PUNCT
ejde-390	75	16	r	r	NOUN
ejde-390	75	17	measurable	measurable	NOUN
ejde-390	75	18	,	,	PUNCT
ejde-390	75	19	and	and	CCONJ
ejde-390	75	20	by	by	ADP
ejde-390	75	21	|	|	ADV
ejde-390	75	22	·	·	PUNCT
ejde-390	75	23	|n	|n	NOUN
ejde-390	75	24	we	we	PRON
ejde-390	75	25	denote	denote	VERB
ejde-390	75	26	the	the	DET
ejde-390	75	27	lebesgue	lebesgue	ADJ
ejde-390	75	28	measure	measure	NOUN
ejde-390	75	29	on	on	ADP
ejde-390	75	30	rn	rn	PROPN
ejde-390	75	31	.	.	PUNCT
ejde-390	76	1	let	let	VERB
ejde-390	76	2	ϑ	ϑ	X
ejde-390	76	3	∈	∈	NOUN
ejde-390	76	4	c1(0,+∞	c1(0,+∞	PROPN
ejde-390	76	5	)	)	PUNCT
ejde-390	76	6	with	with	ADP
ejde-390	76	7	ϑ(t	ϑ(t	NOUN
ejde-390	76	8	)	)	PUNCT
ejde-390	76	9	>	>	X
ejde-390	76	10	0	0	PUNCT
ejde-390	77	1	for	for	ADP
ejde-390	77	2	all	all	DET
ejde-390	77	3	t	t	PROPN
ejde-390	77	4	>	>	X
ejde-390	77	5	0	0	X
ejde-390	77	6	.	.	PUNCT
ejde-390	78	1	we	we	PRON
ejde-390	78	2	assume	assume	VERB
ejde-390	78	3	that	that	SCONJ
ejde-390	78	4	0	0	PUNCT
ejde-390	78	5	<	<	X
ejde-390	78	6	ĉ	ĉ	X
ejde-390	78	7	≤	≤	X
ejde-390	78	8	ϑ′(t)t	ϑ′(t)t	PROPN
ejde-390	78	9	ϑ(t	ϑ(t	X
ejde-390	78	10	)	)	PUNCT
ejde-390	78	11	≤	≤	NUM
ejde-390	78	12	c0	c0	NOUN
ejde-390	78	13	and	and	CCONJ
ejde-390	78	14	c1	c1	PROPN
ejde-390	78	15	t	t	PROPN
ejde-390	78	16	p−1	p−1	PROPN
ejde-390	78	17	≤	≤	PROPN
ejde-390	78	18	ϑ(t	ϑ(t	NOUN
ejde-390	78	19	)	)	PUNCT
ejde-390	78	20	≤	≤	NUM
ejde-390	78	21	c2[ts−1	c2[ts−1	NOUN
ejde-390	78	22	+	+	CCONJ
ejde-390	78	23	tp−1	tp−1	PROPN
ejde-390	78	24	]	]	PUNCT
ejde-390	78	25	for	for	ADP
ejde-390	78	26	all	all	DET
ejde-390	78	27	t	t	PROPN
ejde-390	78	28	>	>	X
ejde-390	78	29	0	0	NUM
ejde-390	78	30	,	,	PUNCT
ejde-390	78	31	with	with	SCONJ
ejde-390	78	32	1	1	NUM
ejde-390	78	33	≤	≤	NOUN
ejde-390	78	34	s	s	PART
ejde-390	78	35	<	<	X
ejde-390	78	36	p	p	X
ejde-390	78	37	<	<	X
ejde-390	78	38	+	+	PROPN
ejde-390	78	39	∞	∞	PROPN
ejde-390	78	40	,	,	PUNCT
ejde-390	78	41	c1	c1	PROPN
ejde-390	78	42	,	,	PUNCT
ejde-390	78	43	c2	c2	PROPN
ejde-390	78	44	>	>	X
ejde-390	78	45	0	0	PROPN
ejde-390	78	46	.	.	PUNCT
ejde-390	79	1	the	the	DET
ejde-390	79	2	hypotheses	hypothesis	NOUN
ejde-390	79	3	on	on	ADP
ejde-390	79	4	the	the	DET
ejde-390	79	5	map	map	NOUN
ejde-390	79	6	a	a	PRON
ejde-390	79	7	(	(	PUNCT
ejde-390	79	8	·	·	PUNCT
ejde-390	79	9	)	)	PUNCT
ejde-390	79	10	are	be	AUX
ejde-390	79	11	as	as	SCONJ
ejde-390	79	12	follows	follow	VERB
ejde-390	79	13	:	:	PUNCT
ejde-390	79	14	(	(	PUNCT
ejde-390	79	15	h1	h1	NOUN
ejde-390	79	16	)	)	PUNCT
ejde-390	79	17	a(y	a(y	PROPN
ejde-390	79	18	)	)	PUNCT
ejde-390	80	1	=	=	SYM
ejde-390	80	2	a0(|y|)y	a0(|y|)y	VERB
ejde-390	80	3	for	for	ADP
ejde-390	80	4	all	all	DET
ejde-390	80	5	y	y	PROPN
ejde-390	80	6	∈	∈	PROPN
ejde-390	80	7	rn	rn	PROPN
ejde-390	80	8	with	with	ADP
ejde-390	80	9	a0(t	a0(t	PROPN
ejde-390	80	10	)	)	PUNCT
ejde-390	80	11	>	>	X
ejde-390	80	12	0	0	PUNCT
ejde-390	80	13	for	for	ADP
ejde-390	80	14	all	all	DET
ejde-390	80	15	t	t	PROPN
ejde-390	80	16	>	>	X
ejde-390	80	17	0	0	NUM
ejde-390	80	18	,	,	PUNCT
ejde-390	80	19	and	and	CCONJ
ejde-390	80	20	(	(	PUNCT
ejde-390	80	21	i	i	NOUN
ejde-390	80	22	)	)	PUNCT
ejde-390	80	23	a0	a0	PROPN
ejde-390	80	24	∈	∈	PROPN
ejde-390	80	25	c1(0,+∞	c1(0,+∞	PROPN
ejde-390	80	26	)	)	PUNCT
ejde-390	80	27	,	,	PUNCT
ejde-390	80	28	t	t	PROPN
ejde-390	80	29	→	→	SYM
ejde-390	80	30	a0(t)t	a0(t)t	PRON
ejde-390	80	31	is	be	AUX
ejde-390	80	32	strictly	strictly	ADV
ejde-390	80	33	increasing	increase	VERB
ejde-390	80	34	on	on	ADP
ejde-390	80	35	(	(	PUNCT
ejde-390	80	36	0,+∞	0,+∞	NUM
ejde-390	80	37	)	)	PUNCT
ejde-390	80	38	,	,	PUNCT
ejde-390	80	39	a0(t)t→	a0(t)t→	NOUN
ejde-390	80	40	0	0	PUNCT
ejde-390	81	1	+	+	CCONJ
ejde-390	81	2	as	as	ADP
ejde-390	81	3	t→	t→	X
ejde-390	81	4	0	0	NUM
ejde-390	81	5	+	+	NUM
ejde-390	81	6	and	and	CCONJ
ejde-390	81	7	limt→0	limt→0	PROPN
ejde-390	81	8	+	+	CCONJ
ejde-390	82	1	a′0(t)t	a′0(t)t	PROPN
ejde-390	82	2	a0(t	a0(t	PROPN
ejde-390	82	3	)	)	PUNCT
ejde-390	82	4	>	>	X
ejde-390	82	5	−1	−1	NOUN
ejde-390	82	6	;	;	PUNCT
ejde-390	82	7	4	4	NUM
ejde-390	82	8	n.	n.	NOUN
ejde-390	82	9	s.	s.	PROPN
ejde-390	82	10	papageorgiou	papageorgiou	PROPN
ejde-390	82	11	,	,	PUNCT
ejde-390	82	12	c.	c.	PROPN
ejde-390	82	13	vetro	vetro	PROPN
ejde-390	82	14	,	,	PUNCT
ejde-390	82	15	f.	f.	PROPN
ejde-390	82	16	vetro	vetro	PROPN
ejde-390	82	17	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	82	18	(	(	PUNCT
ejde-390	82	19	ii	ii	NOUN
ejde-390	82	20	)	)	PUNCT
ejde-390	82	21	there	there	PRON
ejde-390	82	22	exists	exist	VERB
ejde-390	82	23	c3	c3	PROPN
ejde-390	82	24	>	>	X
ejde-390	82	25	0	0	NUM
ejde-390	83	1	such	such	ADJ
ejde-390	83	2	that	that	SCONJ
ejde-390	83	3	|∇a(y)|	|∇a(y)|	NOUN
ejde-390	83	4	≤	≤	NOUN
ejde-390	83	5	c3	c3	PROPN
ejde-390	83	6	ϑ(|y|	ϑ(|y|	PROPN
ejde-390	83	7	)	)	PUNCT
ejde-390	83	8	|y|	|y|	NOUN
ejde-390	83	9	for	for	ADP
ejde-390	83	10	all	all	DET
ejde-390	83	11	y	y	PROPN
ejde-390	83	12	∈	∈	PROPN
ejde-390	83	13	rn	rn	PROPN
ejde-390	83	14	\	\	PROPN
ejde-390	83	15	{	{	PUNCT
ejde-390	83	16	0	0	NUM
ejde-390	83	17	}	}	PUNCT
ejde-390	83	18	;	;	PUNCT
ejde-390	83	19	(	(	PUNCT
ejde-390	83	20	iii	iii	X
ejde-390	83	21	)	)	PUNCT
ejde-390	83	22	(	(	PUNCT
ejde-390	83	23	∇a(y)ξ	∇a(y)ξ	PROPN
ejde-390	83	24	,	,	PUNCT
ejde-390	83	25	ξ)rn	ξ)rn	PROPN
ejde-390	83	26	≥	≥	NOUN
ejde-390	83	27	ϑ(|y|	ϑ(|y|	NOUN
ejde-390	83	28	)	)	PUNCT
ejde-390	83	29	|y|	|y|	NOUN
ejde-390	83	30	|ξ|	|ξ|	NOUN
ejde-390	83	31	2	2	NUM
ejde-390	83	32	for	for	ADP
ejde-390	83	33	all	all	DET
ejde-390	83	34	y	y	PROPN
ejde-390	83	35	∈	∈	PROPN
ejde-390	83	36	rn	rn	PROPN
ejde-390	83	37	\	\	PROPN
ejde-390	83	38	{	{	PUNCT
ejde-390	83	39	0	0	NUM
ejde-390	83	40	}	}	PUNCT
ejde-390	83	41	,	,	PUNCT
ejde-390	83	42	ξ	ξ	PROPN
ejde-390	83	43	∈	∈	PROPN
ejde-390	83	44	rn	rn	PROPN
ejde-390	83	45	;	;	PUNCT
ejde-390	83	46	(	(	PUNCT
ejde-390	83	47	iv	iv	X
ejde-390	83	48	)	)	PUNCT
ejde-390	83	49	if	if	SCONJ
ejde-390	83	50	g0(t	g0(t	NOUN
ejde-390	83	51	)	)	PUNCT
ejde-390	83	52	=	=	SYM
ejde-390	84	1	∫	∫	PROPN
ejde-390	84	2	t	t	NOUN
ejde-390	84	3	0	0	NUM
ejde-390	85	1	a0(s)sds	a0(s)sds	NUM
ejde-390	85	2	,	,	PUNCT
ejde-390	85	3	then	then	ADV
ejde-390	85	4	there	there	PRON
ejde-390	85	5	exist	exist	VERB
ejde-390	85	6	q	q	PROPN
ejde-390	85	7	∈	∈	PROPN
ejde-390	85	8	(	(	PUNCT
ejde-390	85	9	1	1	NUM
ejde-390	85	10	,	,	PUNCT
ejde-390	85	11	p	p	NOUN
ejde-390	85	12	)	)	PUNCT
ejde-390	85	13	and	and	CCONJ
ejde-390	85	14	c∗	c∗	PROPN
ejde-390	85	15	,	,	PUNCT
ejde-390	85	16	c4	c4	NOUN
ejde-390	85	17	>	>	X
ejde-390	85	18	0	0	NUM
ejde-390	86	1	such	such	ADJ
ejde-390	86	2	that	that	SCONJ
ejde-390	86	3	lim	lim	PROPN
ejde-390	86	4	sup	sup	NOUN
ejde-390	86	5	t→0	t→0	PROPN
ejde-390	86	6	+	+	CCONJ
ejde-390	86	7	qg0(t	qg0(t	PROPN
ejde-390	86	8	)	)	PUNCT
ejde-390	86	9	tq	tq	ADV
ejde-390	86	10	≤	≤	NUM
ejde-390	86	11	c∗	c∗	NOUN
ejde-390	86	12	,	,	PUNCT
ejde-390	86	13	t→	t→	PRON
ejde-390	86	14	g0(t1	g0(t1	NOUN
ejde-390	86	15	/	/	SYM
ejde-390	86	16	q	q	NOUN
ejde-390	86	17	)	)	PUNCT
ejde-390	86	18	is	be	AUX
ejde-390	86	19	convex	convex	NOUN
ejde-390	86	20	,	,	PUNCT
ejde-390	86	21	c4	c4	NOUN
ejde-390	86	22	t	t	PROPN
ejde-390	86	23	p	p	NOUN
ejde-390	86	24	≤	≤	PROPN
ejde-390	86	25	a0(t)t2	a0(t)t2	NOUN
ejde-390	87	1	−	−	PROPN
ejde-390	87	2	qg0(t	qg0(t	PROPN
ejde-390	87	3	)	)	PUNCT
ejde-390	87	4	for	for	ADP
ejde-390	87	5	all	all	DET
ejde-390	87	6	t	t	PROPN
ejde-390	87	7	>	>	X
ejde-390	87	8	0	0	NUM
ejde-390	87	9	,	,	PUNCT
ejde-390	87	10	0	0	NUM
ejde-390	87	11	≤	≤	NUM
ejde-390	87	12	pg0(t)−	pg0(t)−	PROPN
ejde-390	87	13	a0(t)t2	a0(t)t2	NOUN
ejde-390	87	14	for	for	ADP
ejde-390	87	15	all	all	DET
ejde-390	87	16	t	t	PROPN
ejde-390	87	17	>	>	X
ejde-390	87	18	0	0	X
ejde-390	87	19	.	.	PUNCT
ejde-390	88	1	remark	remark	PROPN
ejde-390	88	2	2.1	2.1	NUM
ejde-390	88	3	.	.	PUNCT
ejde-390	89	1	hypotheses	hypothesis	NOUN
ejde-390	89	2	(	(	PUNCT
ejde-390	89	3	h1)(i)(ii)(iii	h1)(i)(ii)(iii	NOUN
ejde-390	89	4	)	)	PUNCT
ejde-390	89	5	are	be	AUX
ejde-390	89	6	dictated	dictate	VERB
ejde-390	89	7	by	by	ADP
ejde-390	89	8	the	the	DET
ejde-390	89	9	nonlinear	nonlinear	ADJ
ejde-390	89	10	regularity	regularity	NOUN
ejde-390	89	11	theory	theory	NOUN
ejde-390	89	12	of	of	ADP
ejde-390	89	13	lieberman	lieberman	PROPN
ejde-390	90	1	[	[	X
ejde-390	90	2	7	7	NUM
ejde-390	90	3	]	]	PUNCT
ejde-390	90	4	and	and	CCONJ
ejde-390	90	5	the	the	DET
ejde-390	90	6	nonlinear	nonlinear	ADJ
ejde-390	90	7	maximum	maximum	ADJ
ejde-390	90	8	principle	principle	NOUN
ejde-390	90	9	of	of	ADP
ejde-390	90	10	pucci	pucci	NOUN
ejde-390	90	11	-	-	PUNCT
ejde-390	90	12	serrin	serrin	NOUN
ejde-390	90	13	[	[	X
ejde-390	90	14	15	15	NUM
ejde-390	90	15	]	]	PUNCT
ejde-390	90	16	.	.	PUNCT
ejde-390	91	1	hypothesis	hypothesis	NOUN
ejde-390	91	2	(	(	PUNCT
ejde-390	91	3	h1)(iv	h1)(iv	PROPN
ejde-390	91	4	)	)	PUNCT
ejde-390	91	5	is	be	AUX
ejde-390	91	6	motivated	motivate	VERB
ejde-390	91	7	by	by	ADP
ejde-390	91	8	the	the	DET
ejde-390	91	9	particular	particular	ADJ
ejde-390	91	10	needs	need	NOUN
ejde-390	91	11	of	of	ADP
ejde-390	91	12	our	our	PRON
ejde-390	91	13	problem	problem	NOUN
ejde-390	91	14	.	.	PUNCT
ejde-390	92	1	however	however	ADV
ejde-390	92	2	,	,	PUNCT
ejde-390	92	3	as	as	ADP
ejde-390	92	4	the	the	DET
ejde-390	92	5	examples	example	NOUN
ejde-390	92	6	below	below	ADP
ejde-390	92	7	illustrate	illustrate	NOUN
ejde-390	92	8	,	,	PUNCT
ejde-390	92	9	it	it	PRON
ejde-390	92	10	is	be	AUX
ejde-390	92	11	not	not	PART
ejde-390	92	12	restrictive	restrictive	ADJ
ejde-390	92	13	and	and	CCONJ
ejde-390	92	14	it	it	PRON
ejde-390	92	15	is	be	AUX
ejde-390	92	16	satisfied	satisfied	ADJ
ejde-390	92	17	in	in	ADP
ejde-390	92	18	all	all	DET
ejde-390	92	19	cases	case	NOUN
ejde-390	92	20	of	of	ADP
ejde-390	92	21	interest	interest	NOUN
ejde-390	92	22	.	.	PUNCT
ejde-390	93	1	from	from	ADP
ejde-390	93	2	the	the	DET
ejde-390	93	3	above	above	ADJ
ejde-390	93	4	hypotheses	hypothesis	NOUN
ejde-390	93	5	we	we	PRON
ejde-390	93	6	see	see	VERB
ejde-390	93	7	that	that	SCONJ
ejde-390	93	8	the	the	DET
ejde-390	93	9	primitive	primitive	ADJ
ejde-390	93	10	g0	g0	NOUN
ejde-390	93	11	(	(	PUNCT
ejde-390	93	12	·	·	PUNCT
ejde-390	93	13	)	)	PUNCT
ejde-390	93	14	is	be	AUX
ejde-390	93	15	strictly	strictly	ADV
ejde-390	93	16	convex	convex	ADJ
ejde-390	93	17	and	and	CCONJ
ejde-390	93	18	strictly	strictly	ADV
ejde-390	93	19	increasing	increase	VERB
ejde-390	93	20	.	.	PUNCT
ejde-390	94	1	we	we	PRON
ejde-390	94	2	set	set	VERB
ejde-390	94	3	g(y	g(y	PROPN
ejde-390	94	4	)	)	PUNCT
ejde-390	94	5	=	=	PUNCT
ejde-390	94	6	g0(|y|	g0(|y|	NOUN
ejde-390	94	7	)	)	PUNCT
ejde-390	94	8	for	for	ADP
ejde-390	94	9	all	all	DET
ejde-390	94	10	y	y	PROPN
ejde-390	94	11	∈	∈	PROPN
ejde-390	94	12	rn	rn	PROPN
ejde-390	94	13	.	.	PUNCT
ejde-390	95	1	then	then	ADV
ejde-390	95	2	g	g	PROPN
ejde-390	95	3	(	(	PUNCT
ejde-390	95	4	·	·	PUNCT
ejde-390	95	5	)	)	PUNCT
ejde-390	95	6	is	be	AUX
ejde-390	95	7	convex	convex	ADJ
ejde-390	95	8	and	and	CCONJ
ejde-390	95	9	∇g(y	∇g(y	NOUN
ejde-390	95	10	)	)	PUNCT
ejde-390	95	11	=	=	SYM
ejde-390	95	12	g′0(|y|	g′0(|y|	PROPN
ejde-390	95	13	)	)	PUNCT
ejde-390	96	1	y	y	PROPN
ejde-390	96	2	|y|	|y|	ADJ
ejde-390	96	3	=	=	PUNCT
ejde-390	96	4	a0(|y|)y	a0(|y|)y	PROPN
ejde-390	96	5	=	=	SYM
ejde-390	96	6	a(y	a(y	PROPN
ejde-390	96	7	)	)	PUNCT
ejde-390	96	8	for	for	ADP
ejde-390	96	9	all	all	DET
ejde-390	96	10	y	y	PROPN
ejde-390	96	11	∈	∈	PROPN
ejde-390	96	12	rn	rn	PROPN
ejde-390	96	13	\	\	PROPN
ejde-390	96	14	{	{	PUNCT
ejde-390	96	15	0	0	NUM
ejde-390	96	16	}	}	PUNCT
ejde-390	96	17	.	.	PUNCT
ejde-390	97	1	so	so	ADV
ejde-390	97	2	,	,	PUNCT
ejde-390	97	3	g	g	PROPN
ejde-390	97	4	(	(	PUNCT
ejde-390	97	5	·	·	PUNCT
ejde-390	97	6	)	)	PUNCT
ejde-390	97	7	is	be	AUX
ejde-390	97	8	the	the	DET
ejde-390	97	9	primitive	primitive	NOUN
ejde-390	97	10	of	of	ADP
ejde-390	97	11	a	a	PRON
ejde-390	97	12	(	(	PUNCT
ejde-390	97	13	·	·	PUNCT
ejde-390	97	14	)	)	PUNCT
ejde-390	97	15	.	.	PUNCT
ejde-390	98	1	this	this	DET
ejde-390	98	2	fact	fact	NOUN
ejde-390	98	3	and	and	CCONJ
ejde-390	98	4	the	the	DET
ejde-390	98	5	convexity	convexity	NOUN
ejde-390	98	6	of	of	ADP
ejde-390	98	7	g	g	PROPN
ejde-390	98	8	(	(	PUNCT
ejde-390	98	9	·	·	PUNCT
ejde-390	98	10	)	)	PUNCT
ejde-390	98	11	imply	imply	VERB
ejde-390	98	12	that	that	SCONJ
ejde-390	98	13	g(y	g(y	NOUN
ejde-390	98	14	)	)	PUNCT
ejde-390	98	15	≤	≤	NOUN
ejde-390	98	16	(	(	PUNCT
ejde-390	98	17	a(y	a(y	PROPN
ejde-390	98	18	)	)	PUNCT
ejde-390	98	19	,	,	PUNCT
ejde-390	98	20	y)rn	y)rn	PROPN
ejde-390	98	21	for	for	ADP
ejde-390	98	22	all	all	DET
ejde-390	98	23	y	y	PROPN
ejde-390	98	24	∈	∈	PROPN
ejde-390	98	25	rn	rn	PROPN
ejde-390	98	26	.	.	PUNCT
ejde-390	99	1	(	(	PUNCT
ejde-390	99	2	2.1	2.1	NUM
ejde-390	99	3	)	)	PUNCT
ejde-390	99	4	hypotheses	hypothesis	NOUN
ejde-390	99	5	(	(	PUNCT
ejde-390	99	6	h1	h1	NOUN
ejde-390	99	7	)	)	PUNCT
ejde-390	99	8	lead	lead	NOUN
ejde-390	99	9	to	to	ADP
ejde-390	99	10	the	the	DET
ejde-390	99	11	following	follow	VERB
ejde-390	99	12	lemma	lemma	PROPN
ejde-390	99	13	summarizing	summarize	VERB
ejde-390	99	14	the	the	DET
ejde-390	99	15	main	main	ADJ
ejde-390	99	16	properties	property	NOUN
ejde-390	99	17	of	of	ADP
ejde-390	99	18	the	the	DET
ejde-390	99	19	map	map	NOUN
ejde-390	99	20	y	y	PROPN
ejde-390	99	21	→	→	SYM
ejde-390	99	22	a(y	a(y	PROPN
ejde-390	99	23	)	)	PUNCT
ejde-390	99	24	(	(	PUNCT
ejde-390	99	25	see	see	VERB
ejde-390	99	26	papageorgiou	papageorgiou	NOUN
ejde-390	99	27	-	-	PUNCT
ejde-390	99	28	rǎdulescu	rǎdulescu	NOUN
ejde-390	100	1	[	[	X
ejde-390	100	2	9	9	NUM
ejde-390	100	3	]	]	NUM
ejde-390	100	4	)	)	PUNCT
ejde-390	100	5	.	.	PUNCT
ejde-390	101	1	lemma	lemma	PROPN
ejde-390	101	2	2.2	2.2	NUM
ejde-390	101	3	.	.	PUNCT
ejde-390	102	1	if	if	SCONJ
ejde-390	102	2	hypotheses	hypothesis	NOUN
ejde-390	102	3	(	(	PUNCT
ejde-390	102	4	h1)(i)(ii)(iii	h1)(i)(ii)(iii	NOUN
ejde-390	102	5	)	)	PUNCT
ejde-390	102	6	hold	hold	NOUN
ejde-390	102	7	,	,	PUNCT
ejde-390	102	8	then	then	ADV
ejde-390	102	9	(	(	PUNCT
ejde-390	102	10	a	a	X
ejde-390	102	11	)	)	PUNCT
ejde-390	102	12	a	a	PRON
ejde-390	102	13	(	(	PUNCT
ejde-390	102	14	·	·	PUNCT
ejde-390	102	15	)	)	PUNCT
ejde-390	102	16	is	be	AUX
ejde-390	102	17	continuous	continuous	ADJ
ejde-390	102	18	,	,	PUNCT
ejde-390	102	19	strictly	strictly	ADV
ejde-390	102	20	monotone	monotone	ADJ
ejde-390	102	21	,	,	PUNCT
ejde-390	102	22	hence	hence	ADV
ejde-390	102	23	maximal	maximal	ADJ
ejde-390	102	24	monotone	monotone	NOUN
ejde-390	102	25	;	;	PUNCT
ejde-390	102	26	(	(	PUNCT
ejde-390	102	27	b	b	X
ejde-390	102	28	)	)	PUNCT
ejde-390	102	29	there	there	PRON
ejde-390	102	30	exists	exist	VERB
ejde-390	102	31	c5	c5	PROPN
ejde-390	102	32	>	>	X
ejde-390	102	33	0	0	NUM
ejde-390	103	1	such	such	ADJ
ejde-390	103	2	that	that	SCONJ
ejde-390	103	3	|a(y)|	|a(y)|	PROPN
ejde-390	103	4	≤	≤	NUM
ejde-390	103	5	c5[|y|s−1	c5[|y|s−1	PROPN
ejde-390	103	6	+	+	CCONJ
ejde-390	103	7	|y|p−1	|y|p−1	NUM
ejde-390	103	8	]	]	X
ejde-390	103	9	for	for	ADP
ejde-390	103	10	all	all	DET
ejde-390	103	11	y	y	PROPN
ejde-390	103	12	∈	∈	PROPN
ejde-390	103	13	rn	rn	PROPN
ejde-390	103	14	;	;	PUNCT
ejde-390	103	15	(	(	PUNCT
ejde-390	103	16	c	c	X
ejde-390	103	17	)	)	PUNCT
ejde-390	103	18	(	(	PUNCT
ejde-390	103	19	a(y	a(y	PROPN
ejde-390	103	20	)	)	PUNCT
ejde-390	103	21	,	,	PUNCT
ejde-390	103	22	y)rn	y)rn	PROPN
ejde-390	103	23	≥	≥	PROPN
ejde-390	103	24	c1	c1	PROPN
ejde-390	103	25	p−1	p−1	PROPN
ejde-390	103	26	|y|	|y|	PROPN
ejde-390	103	27	p	p	NOUN
ejde-390	103	28	for	for	ADP
ejde-390	103	29	all	all	DET
ejde-390	103	30	y	y	PROPN
ejde-390	103	31	∈	∈	PROPN
ejde-390	103	32	rn	rn	PROPN
ejde-390	103	33	.	.	PUNCT
ejde-390	104	1	this	this	DET
ejde-390	104	2	lemma	lemma	PROPN
ejde-390	104	3	and	and	CCONJ
ejde-390	104	4	(	(	PUNCT
ejde-390	104	5	2.1	2.1	NUM
ejde-390	104	6	)	)	PUNCT
ejde-390	104	7	lead	lead	NOUN
ejde-390	104	8	to	to	ADP
ejde-390	104	9	the	the	DET
ejde-390	104	10	following	follow	VERB
ejde-390	104	11	growth	growth	NOUN
ejde-390	104	12	estimates	estimate	NOUN
ejde-390	104	13	for	for	ADP
ejde-390	104	14	the	the	DET
ejde-390	104	15	primitive	primitive	ADJ
ejde-390	104	16	g	g	NOUN
ejde-390	104	17	(	(	PUNCT
ejde-390	104	18	·	·	PUNCT
ejde-390	104	19	)	)	PUNCT
ejde-390	104	20	.	.	PUNCT
ejde-390	105	1	corollary	corollary	ADJ
ejde-390	105	2	2.3	2.3	NUM
ejde-390	105	3	.	.	PUNCT
ejde-390	106	1	if	if	SCONJ
ejde-390	106	2	hypotheses	hypothesis	NOUN
ejde-390	106	3	(	(	PUNCT
ejde-390	106	4	h1)(i)(ii)(iii	h1)(i)(ii)(iii	NOUN
ejde-390	106	5	)	)	PUNCT
ejde-390	106	6	hold	hold	NOUN
ejde-390	106	7	,	,	PUNCT
ejde-390	106	8	then	then	ADV
ejde-390	106	9	there	there	PRON
ejde-390	106	10	exists	exist	VERB
ejde-390	106	11	c6	c6	PROPN
ejde-390	106	12	>	>	X
ejde-390	106	13	0	0	PUNCT
ejde-390	107	1	such	such	ADJ
ejde-390	107	2	that	that	DET
ejde-390	107	3	c1	c1	PROPN
ejde-390	107	4	p(p−1	p(p−1	PROPN
ejde-390	107	5	)	)	PUNCT
ejde-390	107	6	|y|	|y|	NOUN
ejde-390	107	7	p	p	ADJ
ejde-390	107	8	≤	≤	ADJ
ejde-390	107	9	g(y	g(y	NOUN
ejde-390	107	10	)	)	PUNCT
ejde-390	107	11	≤	≤	NOUN
ejde-390	107	12	c6[1	c6[1	NOUN
ejde-390	107	13	+	+	CCONJ
ejde-390	107	14	|y|p	|y|p	NOUN
ejde-390	107	15	]	]	X
ejde-390	107	16	for	for	ADP
ejde-390	107	17	all	all	DET
ejde-390	107	18	y	y	PROPN
ejde-390	107	19	∈	∈	PROPN
ejde-390	107	20	rn	rn	PROPN
ejde-390	107	21	.	.	PUNCT
ejde-390	108	1	the	the	DET
ejde-390	108	2	following	follow	VERB
ejde-390	108	3	examples	example	NOUN
ejde-390	108	4	show	show	VERB
ejde-390	108	5	that	that	SCONJ
ejde-390	108	6	the	the	DET
ejde-390	108	7	framework	framework	NOUN
ejde-390	108	8	provided	provide	VERB
ejde-390	108	9	by	by	ADP
ejde-390	108	10	hypotheses	hypothesis	NOUN
ejde-390	108	11	(	(	PUNCT
ejde-390	108	12	h1	h1	NOUN
ejde-390	108	13	)	)	PUNCT
ejde-390	108	14	is	be	AUX
ejde-390	108	15	broad	broad	ADJ
ejde-390	108	16	.	.	PUNCT
ejde-390	108	17	example	example	NOUN
ejde-390	109	1	2.4	2.4	NUM
ejde-390	109	2	.	.	PUNCT
ejde-390	110	1	the	the	DET
ejde-390	110	2	following	follow	VERB
ejde-390	110	3	maps	map	NOUN
ejde-390	110	4	satisfy	satisfy	VERB
ejde-390	110	5	hypotheses	hypothesis	NOUN
ejde-390	110	6	(	(	PUNCT
ejde-390	110	7	h1	h1	NOUN
ejde-390	110	8	)	)	PUNCT
ejde-390	110	9	(	(	PUNCT
ejde-390	110	10	see	see	VERB
ejde-390	110	11	[	[	X
ejde-390	110	12	9	9	NUM
ejde-390	110	13	]	]	SYM
ejde-390	110	14	):	):	PUNCT
ejde-390	110	15	(	(	PUNCT
ejde-390	110	16	a	a	X
ejde-390	110	17	)	)	PUNCT
ejde-390	110	18	a(y	a(y	PROPN
ejde-390	110	19	)	)	PUNCT
ejde-390	110	20	=	=	SYM
ejde-390	110	21	|y|p−2y	|y|p−2y	PROPN
ejde-390	110	22	with	with	ADP
ejde-390	110	23	1	1	NUM
ejde-390	110	24	<	<	X
ejde-390	110	25	p	p	X
ejde-390	110	26	<	<	X
ejde-390	110	27	+	+	PROPN
ejde-390	110	28	∞.	∞.	PROPN
ejde-390	110	29	this	this	DET
ejde-390	110	30	map	map	NOUN
ejde-390	110	31	corresponds	correspond	VERB
ejde-390	110	32	to	to	ADP
ejde-390	110	33	the	the	DET
ejde-390	110	34	p	p	PROPN
ejde-390	110	35	-	-	PUNCT
ejde-390	110	36	laplacian	laplacian	ADJ
ejde-390	110	37	differential	differential	NOUN
ejde-390	110	38	operator	operator	NOUN
ejde-390	110	39	.	.	PUNCT
ejde-390	111	1	(	(	PUNCT
ejde-390	111	2	b	b	X
ejde-390	111	3	)	)	PUNCT
ejde-390	111	4	a(y	a(y	PROPN
ejde-390	111	5	)	)	PUNCT
ejde-390	112	1	=	=	PUNCT
ejde-390	112	2	|y|p−2y	|y|p−2y	PROPN
ejde-390	112	3	+	+	CCONJ
ejde-390	112	4	|y|q−2y	|y|q−2y	PROPN
ejde-390	112	5	with	with	ADP
ejde-390	112	6	1	1	NUM
ejde-390	112	7	<	<	X
ejde-390	112	8	q	q	X
ejde-390	112	9	<	<	X
ejde-390	112	10	p	p	X
ejde-390	112	11	<	<	X
ejde-390	112	12	+	+	PROPN
ejde-390	112	13	∞.	∞.	PROPN
ejde-390	112	14	this	this	DET
ejde-390	112	15	map	map	NOUN
ejde-390	112	16	corresponds	correspond	VERB
ejde-390	112	17	to	to	ADP
ejde-390	112	18	the	the	DET
ejde-390	112	19	(	(	PUNCT
ejde-390	112	20	p	p	X
ejde-390	112	21	,	,	PUNCT
ejde-390	112	22	q)-laplacian	q)-laplacian	PUNCT
ejde-390	112	23	differential	differential	NOUN
ejde-390	112	24	operator	operator	NOUN
ejde-390	112	25	,	,	PUNCT
ejde-390	112	26	that	that	ADV
ejde-390	112	27	is	is	ADV
ejde-390	112	28	,	,	PUNCT
ejde-390	112	29	the	the	DET
ejde-390	112	30	sum	sum	NOUN
ejde-390	112	31	of	of	ADP
ejde-390	112	32	a	a	DET
ejde-390	112	33	p	p	NOUN
ejde-390	112	34	-	-	PUNCT
ejde-390	112	35	laplacian	laplacian	NOUN
ejde-390	112	36	and	and	CCONJ
ejde-390	112	37	of	of	ADP
ejde-390	112	38	a	a	DET
ejde-390	112	39	q	q	NOUN
ejde-390	112	40	-	-	PUNCT
ejde-390	112	41	laplacian	laplacian	NOUN
ejde-390	112	42	.	.	PUNCT
ejde-390	113	1	such	such	ADJ
ejde-390	113	2	operators	operator	NOUN
ejde-390	113	3	arise	arise	VERB
ejde-390	113	4	in	in	ADP
ejde-390	113	5	many	many	ADJ
ejde-390	113	6	problems	problem	NOUN
ejde-390	113	7	of	of	ADP
ejde-390	113	8	mathematical	mathematical	ADJ
ejde-390	113	9	physics	physics	NOUN
ejde-390	113	10	and	and	CCONJ
ejde-390	113	11	correspond	correspond	VERB
ejde-390	113	12	to	to	ADP
ejde-390	113	13	the	the	DET
ejde-390	113	14	so	so	ADV
ejde-390	113	15	-	-	PUNCT
ejde-390	113	16	called	call	VERB
ejde-390	113	17	double	double	ADJ
ejde-390	113	18	phase	phase	NOUN
ejde-390	113	19	equations	equation	NOUN
ejde-390	113	20	.	.	PUNCT
ejde-390	114	1	in	in	ADP
ejde-390	114	2	this	this	DET
ejde-390	114	3	direction	direction	NOUN
ejde-390	114	4	we	we	PRON
ejde-390	114	5	mention	mention	VERB
ejde-390	114	6	the	the	DET
ejde-390	114	7	works	work	NOUN
ejde-390	114	8	of	of	ADP
ejde-390	114	9	cherfils	cherfil	NOUN
ejde-390	114	10	-	-	PUNCT
ejde-390	114	11	il’yasov	il’yasov	NOUN
ejde-390	114	12	[	[	X
ejde-390	114	13	2	2	NUM
ejde-390	114	14	]	]	PUNCT
ejde-390	114	15	(	(	PUNCT
ejde-390	114	16	reaction	reaction	NOUN
ejde-390	114	17	-	-	PUNCT
ejde-390	114	18	diffusion	diffusion	NOUN
ejde-390	114	19	systems	system	NOUN
ejde-390	114	20	)	)	PUNCT
ejde-390	114	21	and	and	CCONJ
ejde-390	114	22	of	of	ADP
ejde-390	114	23	zhikov	zhikov	PROPN
ejde-390	114	24	[	[	X
ejde-390	114	25	16	16	NUM
ejde-390	114	26	]	]	PUNCT
ejde-390	114	27	(	(	PUNCT
ejde-390	114	28	problems	problem	NOUN
ejde-390	114	29	in	in	ADP
ejde-390	114	30	elasticity	elasticity	NOUN
ejde-390	114	31	theory	theory	NOUN
ejde-390	114	32	)	)	PUNCT
ejde-390	114	33	.	.	PUNCT
ejde-390	115	1	(	(	PUNCT
ejde-390	115	2	c	c	X
ejde-390	115	3	)	)	PUNCT
ejde-390	115	4	a(y	a(y	PROPN
ejde-390	115	5	)	)	PUNCT
ejde-390	115	6	=	=	PUNCT
ejde-390	116	1	[	[	X
ejde-390	116	2	1	1	NUM
ejde-390	116	3	+	+	SYM
ejde-390	116	4	|y|2	|y|2	ADJ
ejde-390	116	5	]	]	X
ejde-390	116	6	p−2	p−2	PROPN
ejde-390	116	7	2	2	NUM
ejde-390	116	8	y	y	NOUN
ejde-390	116	9	with	with	ADP
ejde-390	116	10	1	1	NUM
ejde-390	116	11	<	<	X
ejde-390	116	12	p	p	X
ejde-390	116	13	<	<	X
ejde-390	116	14	+	+	PROPN
ejde-390	116	15	∞.	∞.	PROPN
ejde-390	116	16	this	this	DET
ejde-390	116	17	map	map	NOUN
ejde-390	116	18	corresponds	correspond	VERB
ejde-390	116	19	to	to	ADP
ejde-390	116	20	the	the	DET
ejde-390	116	21	extended	extended	ADJ
ejde-390	116	22	capillary	capillary	ADJ
ejde-390	116	23	differential	differential	NOUN
ejde-390	116	24	operator	operator	NOUN
ejde-390	116	25	.	.	PUNCT
ejde-390	117	1	ejde-2020/12	ejde-2020/12	NOUN
ejde-390	117	2	positive	positive	ADJ
ejde-390	117	3	and	and	CCONJ
ejde-390	117	4	nodal	nodal	ADJ
ejde-390	117	5	solutions	solution	NOUN
ejde-390	117	6	5	5	NUM
ejde-390	117	7	(	(	PUNCT
ejde-390	117	8	d	d	NOUN
ejde-390	117	9	)	)	PUNCT
ejde-390	117	10	a(y	a(y	PROPN
ejde-390	117	11	)	)	PUNCT
ejde-390	117	12	=	=	PUNCT
ejde-390	118	1	[	[	X
ejde-390	118	2	1	1	NUM
ejde-390	118	3	+	+	NUM
ejde-390	118	4	1	1	NUM
ejde-390	118	5	1+|y|p	1+|y|p	NUM
ejde-390	118	6	]	]	X
ejde-390	118	7	|y|p−2y	|y|p−2y	PROPN
ejde-390	118	8	with	with	ADP
ejde-390	118	9	1	1	NUM
ejde-390	118	10	<	<	X
ejde-390	118	11	p	p	X
ejde-390	118	12	<	<	X
ejde-390	118	13	+	+	PROPN
ejde-390	118	14	∞.	∞.	PROPN
ejde-390	118	15	this	this	DET
ejde-390	118	16	map	map	NOUN
ejde-390	118	17	corresponds	correspond	VERB
ejde-390	118	18	to	to	ADP
ejde-390	118	19	a	a	DET
ejde-390	118	20	differential	differential	ADJ
ejde-390	118	21	operator	operator	NOUN
ejde-390	118	22	which	which	PRON
ejde-390	118	23	arises	arise	VERB
ejde-390	118	24	in	in	ADP
ejde-390	118	25	problems	problem	NOUN
ejde-390	118	26	of	of	ADP
ejde-390	118	27	plasticity	plasticity	NOUN
ejde-390	118	28	theory	theory	NOUN
ejde-390	118	29	(	(	PUNCT
ejde-390	118	30	see	see	VERB
ejde-390	118	31	fuchs	fuchs	PROPN
ejde-390	118	32	-	-	PUNCT
ejde-390	118	33	li	li	NOUN
ejde-390	119	1	[	[	X
ejde-390	119	2	3	3	NUM
ejde-390	119	3	]	]	PUNCT
ejde-390	119	4	)	)	PUNCT
ejde-390	119	5	.	.	PUNCT
ejde-390	120	1	let	let	VERB
ejde-390	120	2	a	a	DET
ejde-390	120	3	:	:	PUNCT
ejde-390	120	4	w	w	ADP
ejde-390	120	5	1,p(ω)→w	1,p(ω)→w	NUM
ejde-390	120	6	1,p(ω)∗	1,p(ω)∗	NUM
ejde-390	120	7	be	be	AUX
ejde-390	120	8	the	the	DET
ejde-390	120	9	nonlinear	nonlinear	ADJ
ejde-390	120	10	operator	operator	NOUN
ejde-390	120	11	defined	define	VERB
ejde-390	120	12	by	by	ADP
ejde-390	120	13	〈	〈	PROPN
ejde-390	120	14	a(u	a(u	PROPN
ejde-390	120	15	)	)	PUNCT
ejde-390	120	16	,	,	PUNCT
ejde-390	121	1	h	h	NOUN
ejde-390	121	2	〉	〉	NUM
ejde-390	121	3	=	=	SYM
ejde-390	121	4	∫	∫	PROPN
ejde-390	121	5	ω	ω	PROPN
ejde-390	121	6	(	(	PUNCT
ejde-390	121	7	a(∇u),∇h)rndz	a(∇u),∇h)rndz	ADV
ejde-390	121	8	for	for	ADP
ejde-390	121	9	all	all	DET
ejde-390	121	10	u	u	NOUN
ejde-390	121	11	,	,	PUNCT
ejde-390	121	12	h	h	PROPN
ejde-390	121	13	∈w	∈w	NOUN
ejde-390	121	14	1,p(ω	1,p(ω	NUM
ejde-390	121	15	)	)	PUNCT
ejde-390	121	16	.	.	PUNCT
ejde-390	122	1	from	from	ADP
ejde-390	122	2	gasiński	gasiński	ADJ
ejde-390	122	3	-	-	PUNCT
ejde-390	122	4	papageorgiou	papageorgiou	NOUN
ejde-390	122	5	[	[	X
ejde-390	122	6	4	4	NUM
ejde-390	122	7	]	]	PUNCT
ejde-390	122	8	(	(	PUNCT
ejde-390	122	9	problem	problem	NOUN
ejde-390	122	10	2.192	2.192	NUM
ejde-390	122	11	,	,	PUNCT
ejde-390	122	12	p.	p.	NOUN
ejde-390	122	13	279	279	NUM
ejde-390	122	14	)	)	PUNCT
ejde-390	122	15	,	,	PUNCT
ejde-390	122	16	we	we	PRON
ejde-390	122	17	have	have	VERB
ejde-390	122	18	the	the	DET
ejde-390	122	19	following	follow	VERB
ejde-390	122	20	result	result	NOUN
ejde-390	122	21	.	.	PUNCT
ejde-390	123	1	proposition	proposition	NOUN
ejde-390	123	2	2.5	2.5	NUM
ejde-390	123	3	.	.	PUNCT
ejde-390	124	1	if	if	SCONJ
ejde-390	124	2	hypotheses	hypothesis	NOUN
ejde-390	124	3	(	(	PUNCT
ejde-390	124	4	h1	h1	NOUN
ejde-390	124	5	)	)	PUNCT
ejde-390	124	6	hold	hold	NOUN
ejde-390	124	7	,	,	PUNCT
ejde-390	124	8	then	then	ADV
ejde-390	124	9	the	the	DET
ejde-390	124	10	map	map	NOUN
ejde-390	124	11	a	a	PRON
ejde-390	124	12	(	(	PUNCT
ejde-390	124	13	·	·	PUNCT
ejde-390	124	14	)	)	PUNCT
ejde-390	124	15	is	be	AUX
ejde-390	124	16	continuous	continuous	ADJ
ejde-390	124	17	,	,	PUNCT
ejde-390	124	18	monotone	monotone	ADJ
ejde-390	124	19	(	(	PUNCT
ejde-390	124	20	hence	hence	ADV
ejde-390	124	21	maximal	maximal	ADJ
ejde-390	124	22	monotone	monotone	NOUN
ejde-390	124	23	too	too	ADV
ejde-390	124	24	)	)	PUNCT
ejde-390	124	25	and	and	CCONJ
ejde-390	124	26	of	of	ADP
ejde-390	124	27	type	type	NOUN
ejde-390	124	28	(	(	PUNCT
ejde-390	124	29	s)+	s)+	PROPN
ejde-390	124	30	.	.	PUNCT
ejde-390	125	1	the	the	DET
ejde-390	125	2	following	follow	VERB
ejde-390	125	3	strong	strong	ADJ
ejde-390	125	4	comparison	comparison	NOUN
ejde-390	125	5	principle	principle	NOUN
ejde-390	125	6	by	by	ADP
ejde-390	125	7	papageorgiou	papageorgiou	NOUN
ejde-390	125	8	-	-	PUNCT
ejde-390	125	9	rǎdulescu	rǎdulescu	NUM
ejde-390	125	10	-	-	PUNCT
ejde-390	125	11	repovš	repovš	NOUN
ejde-390	125	12	[	[	X
ejde-390	125	13	13	13	NUM
ejde-390	125	14	]	]	PUNCT
ejde-390	125	15	,	,	PUNCT
ejde-390	125	16	will	will	AUX
ejde-390	125	17	be	be	AUX
ejde-390	125	18	useful	useful	ADJ
ejde-390	125	19	in	in	ADP
ejde-390	125	20	our	our	PRON
ejde-390	125	21	analysis	analysis	NOUN
ejde-390	125	22	of	of	ADP
ejde-390	125	23	problem	problem	NOUN
ejde-390	125	24	(	(	PUNCT
ejde-390	125	25	1.1	1.1	NUM
ejde-390	125	26	)	)	PUNCT
ejde-390	125	27	.	.	PUNCT
ejde-390	126	1	proposition	proposition	NOUN
ejde-390	126	2	2.6	2.6	NUM
ejde-390	126	3	.	.	PUNCT
ejde-390	127	1	if	if	SCONJ
ejde-390	127	2	hypotheses	hypothesis	NOUN
ejde-390	127	3	(	(	PUNCT
ejde-390	127	4	h1	h1	NOUN
ejde-390	127	5	)	)	PUNCT
ejde-390	127	6	hold	hold	NOUN
ejde-390	127	7	,	,	PUNCT
ejde-390	127	8	ξ̂	ξ̂	NUM
ejde-390	127	9	∈	∈	PROPN
ejde-390	127	10	l∞(ω	l∞(ω	NOUN
ejde-390	127	11	)	)	PUNCT
ejde-390	127	12	with	with	ADP
ejde-390	127	13	ξ̂(z	ξ̂(z	NOUN
ejde-390	127	14	)	)	PUNCT
ejde-390	127	15	≥	≥	NOUN
ejde-390	127	16	0	0	NUM
ejde-390	127	17	for	for	ADP
ejde-390	127	18	a.a	a.a	PROPN
ejde-390	127	19	.	.	PROPN
ejde-390	127	20	z	z	PROPN
ejde-390	127	21	∈	∈	PROPN
ejde-390	127	22	ω	ω	PROPN
ejde-390	127	23	,	,	PUNCT
ejde-390	127	24	h1	h1	PROPN
ejde-390	127	25	,	,	PUNCT
ejde-390	127	26	h2	h2	PROPN
ejde-390	127	27	∈	∈	PROPN
ejde-390	127	28	l∞(ω	l∞(ω	NOUN
ejde-390	127	29	)	)	PUNCT
ejde-390	127	30	with	with	ADP
ejde-390	127	31	0	0	NUM
ejde-390	127	32	<	<	X
ejde-390	127	33	η	η	PROPN
ejde-390	127	34	≤	≤	X
ejde-390	127	35	h2(z)−	h2(z)−	X
ejde-390	127	36	h1(z	h1(z	X
ejde-390	127	37	)	)	PUNCT
ejde-390	127	38	for	for	ADP
ejde-390	127	39	a.a	a.a	PROPN
ejde-390	127	40	.	.	PROPN
ejde-390	127	41	z	z	PROPN
ejde-390	127	42	∈	∈	PROPN
ejde-390	127	43	ω	ω	PROPN
ejde-390	127	44	and	and	CCONJ
ejde-390	127	45	u	u	NOUN
ejde-390	127	46	,	,	PUNCT
ejde-390	127	47	v	v	NOUN
ejde-390	127	48	∈	∈	NOUN
ejde-390	127	49	c1,α(ω	c1,α(ω	NOUN
ejde-390	127	50	)	)	PUNCT
ejde-390	127	51	with	with	ADP
ejde-390	127	52	α	α	PROPN
ejde-390	127	53	∈	∈	PROPN
ejde-390	127	54	(	(	PUNCT
ejde-390	127	55	0	0	NUM
ejde-390	127	56	,	,	PUNCT
ejde-390	127	57	1	1	NUM
ejde-390	127	58	]	]	PUNCT
ejde-390	127	59	,	,	PUNCT
ejde-390	127	60	v	v	ADJ
ejde-390	127	61	≤	≤	NOUN
ejde-390	127	62	u	u	NOUN
ejde-390	127	63	and	and	CCONJ
ejde-390	127	64	−	−	PROPN
ejde-390	127	65	div	div	X
ejde-390	127	66	a(∇v(z	a(∇v(z	PROPN
ejde-390	127	67	)	)	PUNCT
ejde-390	127	68	)	)	PUNCT
ejde-390	128	1	+	+	CCONJ
ejde-390	128	2	ξ̂(z)|v(z)|p−2v(z	ξ̂(z)|v(z)|p−2v(z	NOUN
ejde-390	128	3	)	)	PUNCT
ejde-390	128	4	=	=	SYM
ejde-390	128	5	h1(z	h1(z	NOUN
ejde-390	128	6	)	)	PUNCT
ejde-390	128	7	for	for	ADP
ejde-390	128	8	a.a	a.a	PROPN
ejde-390	128	9	.	.	PROPN
ejde-390	128	10	z	z	PROPN
ejde-390	128	11	∈	∈	PROPN
ejde-390	128	12	ω	ω	PROPN
ejde-390	128	13	,	,	PUNCT
ejde-390	128	14	−	−	PROPN
ejde-390	128	15	div	div	PROPN
ejde-390	128	16	a(∇u(z	a(∇u(z	NOUN
ejde-390	128	17	)	)	PUNCT
ejde-390	128	18	)	)	PUNCT
ejde-390	129	1	+	+	CCONJ
ejde-390	129	2	ξ̂(z)|u(z)|p−2u(z	ξ̂(z)|u(z)|p−2u(z	ADJ
ejde-390	129	3	)	)	PUNCT
ejde-390	129	4	=	=	SYM
ejde-390	129	5	h2(z	h2(z	X
ejde-390	129	6	)	)	PUNCT
ejde-390	129	7	for	for	ADP
ejde-390	129	8	a.a	a.a	PROPN
ejde-390	129	9	.	.	PROPN
ejde-390	129	10	z	z	PROPN
ejde-390	129	11	∈	∈	PROPN
ejde-390	129	12	ω	ω	PROPN
ejde-390	129	13	,	,	PUNCT
ejde-390	129	14	then	then	ADV
ejde-390	129	15	u−	u−	PROPN
ejde-390	129	16	v	v	NUM
ejde-390	129	17	∈	∈	PROPN
ejde-390	129	18	int	int	NOUN
ejde-390	129	19	ĉ+	ĉ+	PROPN
ejde-390	129	20	.	.	PUNCT
ejde-390	130	1	next	next	ADV
ejde-390	130	2	we	we	PRON
ejde-390	130	3	introduce	introduce	VERB
ejde-390	130	4	hypotheses	hypothesis	NOUN
ejde-390	130	5	on	on	ADP
ejde-390	130	6	the	the	DET
ejde-390	130	7	potential	potential	ADJ
ejde-390	130	8	function	function	NOUN
ejde-390	130	9	ξ(z	ξ(z	NOUN
ejde-390	130	10	)	)	PUNCT
ejde-390	130	11	and	and	CCONJ
ejde-390	130	12	on	on	ADP
ejde-390	130	13	the	the	DET
ejde-390	130	14	reaction	reaction	NOUN
ejde-390	130	15	term	term	NOUN
ejde-390	130	16	f(z	f(z	PROPN
ejde-390	130	17	,	,	PUNCT
ejde-390	130	18	x	x	NOUN
ejde-390	130	19	)	)	PUNCT
ejde-390	130	20	.	.	PUNCT
ejde-390	131	1	(	(	PUNCT
ejde-390	131	2	h2	h2	NOUN
ejde-390	131	3	)	)	PUNCT
ejde-390	131	4	ξ	ξ	PROPN
ejde-390	131	5	∈	∈	PROPN
ejde-390	131	6	l∞(ω	l∞(ω	NOUN
ejde-390	131	7	)	)	PUNCT
ejde-390	131	8	.	.	PUNCT
ejde-390	132	1	(	(	PUNCT
ejde-390	132	2	h3	h3	NOUN
ejde-390	132	3	)	)	PUNCT
ejde-390	132	4	f	f	NOUN
ejde-390	132	5	:	:	PUNCT
ejde-390	132	6	ω	ω	NUM
ejde-390	132	7	×	×	NOUN
ejde-390	132	8	r	r	NOUN
ejde-390	132	9	→	→	SYM
ejde-390	132	10	r	r	NOUN
ejde-390	132	11	is	be	AUX
ejde-390	132	12	a	a	DET
ejde-390	132	13	carathéodory	carathéodory	NOUN
ejde-390	132	14	function	function	NOUN
ejde-390	132	15	such	such	ADJ
ejde-390	132	16	that	that	DET
ejde-390	132	17	f(z	f(z	PROPN
ejde-390	132	18	,	,	PUNCT
ejde-390	132	19	0	0	NUM
ejde-390	132	20	)	)	PUNCT
ejde-390	132	21	=	=	SYM
ejde-390	132	22	0	0	NUM
ejde-390	132	23	for	for	ADP
ejde-390	132	24	a.a	a.a	PROPN
ejde-390	132	25	.	.	PROPN
ejde-390	132	26	z	z	PROPN
ejde-390	132	27	∈	∈	PROPN
ejde-390	132	28	ω	ω	PROPN
ejde-390	132	29	and	and	CCONJ
ejde-390	132	30	(	(	PUNCT
ejde-390	132	31	i	i	NOUN
ejde-390	132	32	)	)	PUNCT
ejde-390	132	33	η(z)xp−1	η(z)xp−1	PROPN
ejde-390	132	34	≤	≤	PROPN
ejde-390	132	35	f(z	f(z	PROPN
ejde-390	132	36	,	,	PUNCT
ejde-390	132	37	x	x	NOUN
ejde-390	132	38	)	)	PUNCT
ejde-390	132	39	≤	≤	PUNCT
ejde-390	132	40	α(z)[1	α(z)[1	PRON
ejde-390	133	1	+	+	CCONJ
ejde-390	133	2	xr−1	xr−1	PROPN
ejde-390	133	3	]	]	PUNCT
ejde-390	133	4	for	for	ADP
ejde-390	133	5	a.a	a.a	PROPN
ejde-390	133	6	.	.	PROPN
ejde-390	133	7	z	z	PROPN
ejde-390	133	8	∈	∈	PROPN
ejde-390	133	9	ω	ω	PROPN
ejde-390	133	10	,	,	PUNCT
ejde-390	133	11	all	all	PRON
ejde-390	133	12	x	x	PRON
ejde-390	133	13	≥	≥	NOUN
ejde-390	133	14	0	0	NUM
ejde-390	133	15	,	,	PUNCT
ejde-390	133	16	with	with	ADP
ejde-390	133	17	η	η	PROPN
ejde-390	133	18	,	,	PUNCT
ejde-390	133	19	α	α	PROPN
ejde-390	133	20	∈	∈	PROPN
ejde-390	133	21	l∞(ω	l∞(ω	NOUN
ejde-390	133	22	)	)	PUNCT
ejde-390	133	23	,	,	PUNCT
ejde-390	133	24	ξ+	ξ+	NUM
ejde-390	133	25	�	�	PROPN
ejde-390	133	26	η	η	PROPN
ejde-390	133	27	and	and	CCONJ
ejde-390	133	28	p	p	X
ejde-390	133	29	<	<	X
ejde-390	133	30	r	r	NOUN
ejde-390	133	31	<	<	X
ejde-390	133	32	p∗	p∗	NOUN
ejde-390	133	33	=	=	X
ejde-390	133	34	{	{	PUNCT
ejde-390	133	35	np	np	INTJ
ejde-390	133	36	n−p	n−p	PROPN
ejde-390	133	37	if	if	SCONJ
ejde-390	133	38	n	n	ADP
ejde-390	133	39	>	>	X
ejde-390	133	40	p	p	PROPN
ejde-390	134	1	+	+	PROPN
ejde-390	134	2	∞	∞	PROPN
ejde-390	134	3	if	if	SCONJ
ejde-390	134	4	p	p	PROPN
ejde-390	134	5	≥	≥	NOUN
ejde-390	134	6	n	n	NOUN
ejde-390	134	7	;	;	PUNCT
ejde-390	134	8	(	(	PUNCT
ejde-390	134	9	ii	ii	NOUN
ejde-390	134	10	)	)	PUNCT
ejde-390	134	11	if	if	SCONJ
ejde-390	134	12	f	f	PROPN
ejde-390	134	13	(	(	PUNCT
ejde-390	134	14	z	z	NOUN
ejde-390	134	15	,	,	PUNCT
ejde-390	134	16	x	x	NOUN
ejde-390	134	17	)	)	PUNCT
ejde-390	134	18	=	=	SYM
ejde-390	135	1	∫	∫	PROPN
ejde-390	135	2	x	x	SYM
ejde-390	135	3	0	0	NUM
ejde-390	135	4	f(z	f(z	PROPN
ejde-390	135	5	,	,	PUNCT
ejde-390	135	6	s)ds	s)ds	PROPN
ejde-390	135	7	,	,	PUNCT
ejde-390	135	8	then	then	ADV
ejde-390	135	9	limx→+∞	limx→+∞	ADP
ejde-390	136	1	f	f	X
ejde-390	136	2	(	(	PUNCT
ejde-390	136	3	z	z	NOUN
ejde-390	136	4	,	,	PUNCT
ejde-390	136	5	x	x	NOUN
ejde-390	136	6	)	)	PUNCT
ejde-390	136	7	xp	xp	NOUN
ejde-390	137	1	=	=	PUNCT
ejde-390	138	1	+	+	NOUN
ejde-390	138	2	∞	∞	NOUN
ejde-390	138	3	uniformly	uniformly	ADJ
ejde-390	138	4	for	for	ADP
ejde-390	138	5	a.a	a.a	PROPN
ejde-390	138	6	.	.	PROPN
ejde-390	138	7	z	z	PROPN
ejde-390	138	8	∈	∈	PROPN
ejde-390	138	9	ω	ω	PROPN
ejde-390	138	10	;	;	PUNCT
ejde-390	138	11	(	(	PUNCT
ejde-390	138	12	iii	iii	X
ejde-390	138	13	)	)	PUNCT
ejde-390	138	14	if	if	SCONJ
ejde-390	138	15	d(z	d(z	NOUN
ejde-390	138	16	,	,	PUNCT
ejde-390	138	17	x	x	NOUN
ejde-390	138	18	)	)	PUNCT
ejde-390	138	19	=	=	SYM
ejde-390	138	20	f(z	f(z	PROPN
ejde-390	138	21	,	,	PUNCT
ejde-390	138	22	x)x−	x)x−	NOUN
ejde-390	138	23	pf	pf	PROPN
ejde-390	138	24	(	(	PUNCT
ejde-390	138	25	z	z	PROPN
ejde-390	138	26	,	,	PUNCT
ejde-390	138	27	x	x	NOUN
ejde-390	138	28	)	)	PUNCT
ejde-390	138	29	,	,	PUNCT
ejde-390	138	30	then	then	ADV
ejde-390	138	31	there	there	PRON
ejde-390	138	32	exists	exist	VERB
ejde-390	138	33	e	e	PROPN
ejde-390	138	34	∈	∈	PROPN
ejde-390	138	35	l1(ω	l1(ω	PROPN
ejde-390	138	36	)	)	PUNCT
ejde-390	139	1	such	such	ADJ
ejde-390	139	2	that	that	SCONJ
ejde-390	139	3	d(z	d(z	PROPN
ejde-390	139	4	,	,	PUNCT
ejde-390	139	5	x	x	NOUN
ejde-390	139	6	)	)	PUNCT
ejde-390	139	7	≤	≤	NOUN
ejde-390	139	8	d(z	d(z	PROPN
ejde-390	139	9	,	,	PUNCT
ejde-390	139	10	y	y	NOUN
ejde-390	139	11	)	)	PUNCT
ejde-390	139	12	+	+	PUNCT
ejde-390	139	13	e(z	e(z	NOUN
ejde-390	139	14	)	)	PUNCT
ejde-390	139	15	for	for	ADP
ejde-390	139	16	a.a	a.a	PROPN
ejde-390	139	17	.	.	PROPN
ejde-390	139	18	z	z	PROPN
ejde-390	139	19	∈	∈	PROPN
ejde-390	139	20	ω	ω	PROPN
ejde-390	139	21	,	,	PUNCT
ejde-390	139	22	all	all	PRON
ejde-390	139	23	0	0	NUM
ejde-390	139	24	≤	≤	NUM
ejde-390	139	25	x	x	PUNCT
ejde-390	139	26	≤	≤	ADJ
ejde-390	139	27	y	y	PROPN
ejde-390	139	28	and	and	CCONJ
ejde-390	139	29	d(z	d(z	PROPN
ejde-390	139	30	,	,	PUNCT
ejde-390	139	31	x)→	x)→	PUNCT
ejde-390	140	1	+	+	ADJ
ejde-390	140	2	∞	∞	PROPN
ejde-390	140	3	for	for	ADP
ejde-390	140	4	a.a	a.a	PROPN
ejde-390	140	5	.	.	PROPN
ejde-390	140	6	z	z	PROPN
ejde-390	140	7	∈	∈	PROPN
ejde-390	140	8	ω	ω	PROPN
ejde-390	140	9	as	as	ADP
ejde-390	140	10	x→	x→	PROPN
ejde-390	140	11	+	+	NOUN
ejde-390	140	12	∞	∞	PROPN
ejde-390	140	13	;	;	PUNCT
ejde-390	140	14	(	(	PUNCT
ejde-390	140	15	iv	iv	X
ejde-390	140	16	)	)	PUNCT
ejde-390	140	17	with	with	ADP
ejde-390	140	18	q	q	PROPN
ejde-390	140	19	∈	∈	PROPN
ejde-390	140	20	(	(	PUNCT
ejde-390	140	21	1	1	NUM
ejde-390	140	22	,	,	PUNCT
ejde-390	140	23	p	p	NOUN
ejde-390	140	24	)	)	PUNCT
ejde-390	140	25	as	as	ADP
ejde-390	140	26	in	in	ADP
ejde-390	140	27	hypothesis	hypothesis	NOUN
ejde-390	140	28	(	(	PUNCT
ejde-390	140	29	h1)(iv	h1)(iv	PROPN
ejde-390	140	30	)	)	PUNCT
ejde-390	140	31	,	,	PUNCT
ejde-390	140	32	we	we	PRON
ejde-390	140	33	have	have	VERB
ejde-390	140	34	limx→0	limx→0	ADV
ejde-390	140	35	+	+	VERB
ejde-390	140	36	f(z	f(z	NOUN
ejde-390	140	37	,	,	PUNCT
ejde-390	140	38	x	x	NOUN
ejde-390	140	39	)	)	PUNCT
ejde-390	140	40	xq−1	xq−1	NOUN
ejde-390	140	41	=	=	PUNCT
ejde-390	141	1	+	+	PUNCT
ejde-390	141	2	∞	∞	NOUN
ejde-390	141	3	uniformly	uniformly	ADJ
ejde-390	141	4	for	for	ADP
ejde-390	141	5	a.a	a.a	PROPN
ejde-390	141	6	.	.	PROPN
ejde-390	141	7	z	z	PROPN
ejde-390	141	8	∈	∈	PROPN
ejde-390	141	9	ω	ω	PROPN
ejde-390	141	10	;	;	PUNCT
ejde-390	141	11	(	(	PUNCT
ejde-390	141	12	v	v	NOUN
ejde-390	141	13	)	)	PUNCT
ejde-390	141	14	for	for	ADP
ejde-390	141	15	each	each	DET
ejde-390	141	16	ρ	ρ	PROPN
ejde-390	141	17	>	>	X
ejde-390	141	18	0	0	PUNCT
ejde-390	141	19	there	there	PRON
ejde-390	141	20	exists	exist	VERB
ejde-390	141	21	ξ̂ρ	ξ̂ρ	NOUN
ejde-390	141	22	>	>	X
ejde-390	141	23	0	0	NUM
ejde-390	141	24	such	such	ADJ
ejde-390	141	25	that	that	PRON
ejde-390	141	26	for	for	ADP
ejde-390	141	27	a.a	a.a	PROPN
ejde-390	141	28	.	.	PROPN
ejde-390	141	29	z	z	PROPN
ejde-390	141	30	∈	∈	PROPN
ejde-390	141	31	ω	ω	NUM
ejde-390	141	32	the	the	DET
ejde-390	141	33	function	function	NOUN
ejde-390	141	34	x→	x→	PUNCT
ejde-390	141	35	f(z	f(z	PROPN
ejde-390	141	36	,	,	PUNCT
ejde-390	141	37	x	x	NOUN
ejde-390	141	38	)	)	PUNCT
ejde-390	142	1	+	+	CCONJ
ejde-390	142	2	ξ̂ρx	ξ̂ρx	ADJ
ejde-390	142	3	p−1	p−1	PROPN
ejde-390	142	4	is	be	AUX
ejde-390	142	5	nondecreasing	nondecrease	VERB
ejde-390	142	6	on	on	ADP
ejde-390	142	7	[	[	X
ejde-390	142	8	0	0	NUM
ejde-390	142	9	,	,	PUNCT
ejde-390	142	10	ρ	ρ	NOUN
ejde-390	142	11	]	]	PUNCT
ejde-390	142	12	.	.	PUNCT
ejde-390	143	1	remark	remark	PROPN
ejde-390	143	2	2.7	2.7	NUM
ejde-390	143	3	.	.	PUNCT
ejde-390	144	1	since	since	SCONJ
ejde-390	144	2	initially	initially	ADV
ejde-390	144	3	(	(	PUNCT
ejde-390	144	4	section	section	NOUN
ejde-390	144	5	3	3	NUM
ejde-390	144	6	)	)	PUNCT
ejde-390	144	7	our	our	PRON
ejde-390	144	8	aim	aim	NOUN
ejde-390	144	9	is	be	AUX
ejde-390	144	10	to	to	PART
ejde-390	144	11	produce	produce	VERB
ejde-390	144	12	positive	positive	ADJ
ejde-390	144	13	solutions	solution	NOUN
ejde-390	144	14	for	for	ADP
ejde-390	144	15	problem	problem	NOUN
ejde-390	144	16	(	(	PUNCT
ejde-390	144	17	1.1	1.1	NUM
ejde-390	144	18	)	)	PUNCT
ejde-390	144	19	and	and	CCONJ
ejde-390	144	20	all	all	DET
ejde-390	144	21	the	the	DET
ejde-390	144	22	above	above	ADJ
ejde-390	144	23	conditions	condition	NOUN
ejde-390	144	24	of	of	ADP
ejde-390	144	25	f(z	f(z	PROPN
ejde-390	144	26	,	,	PUNCT
ejde-390	144	27	·	·	PUNCT
ejde-390	144	28	)	)	PUNCT
ejde-390	144	29	concern	concern	NOUN
ejde-390	144	30	the	the	DET
ejde-390	144	31	positive	positive	ADJ
ejde-390	144	32	semiaxis	semiaxis	NOUN
ejde-390	144	33	r+	r+	PUNCT
ejde-390	144	34	=	=	PUNCT
ejde-390	145	1	[	[	X
ejde-390	145	2	0,+∞	0,+∞	NUM
ejde-390	145	3	)	)	PUNCT
ejde-390	145	4	,	,	PUNCT
ejde-390	145	5	without	without	ADP
ejde-390	145	6	any	any	DET
ejde-390	145	7	loss	loss	NOUN
ejde-390	145	8	of	of	ADP
ejde-390	145	9	generality	generality	NOUN
ejde-390	145	10	we	we	PRON
ejde-390	145	11	may	may	AUX
ejde-390	145	12	assume	assume	VERB
ejde-390	145	13	that	that	SCONJ
ejde-390	145	14	f(z	f(z	NOUN
ejde-390	145	15	,	,	PUNCT
ejde-390	145	16	x	x	NOUN
ejde-390	145	17	)	)	PUNCT
ejde-390	145	18	=	=	SYM
ejde-390	145	19	0	0	NUM
ejde-390	145	20	for	for	ADP
ejde-390	145	21	a.a	a.a	PROPN
ejde-390	145	22	.	.	PROPN
ejde-390	145	23	z	z	PROPN
ejde-390	145	24	∈	∈	PROPN
ejde-390	145	25	ω	ω	PROPN
ejde-390	145	26	,	,	PUNCT
ejde-390	145	27	all	all	PRON
ejde-390	145	28	x	x	SYM
ejde-390	145	29	≤	≤	ADV
ejde-390	145	30	0	0	NUM
ejde-390	145	31	.	.	PUNCT
ejde-390	146	1	(	(	PUNCT
ejde-390	146	2	2.2	2.2	NUM
ejde-390	146	3	)	)	PUNCT
ejde-390	146	4	hypotheses	hypothesis	NOUN
ejde-390	146	5	(	(	PUNCT
ejde-390	146	6	h3)(ii)(iii	h3)(ii)(iii	NUM
ejde-390	146	7	)	)	PUNCT
ejde-390	146	8	imply	imply	VERB
ejde-390	146	9	that	that	SCONJ
ejde-390	146	10	lim	lim	PROPN
ejde-390	146	11	x→+∞	x→+∞	PROPN
ejde-390	146	12	f(z	f(z	PROPN
ejde-390	146	13	,	,	PUNCT
ejde-390	146	14	x	x	X
ejde-390	146	15	)	)	PUNCT
ejde-390	146	16	xp−1	xp−1	PUNCT
ejde-390	147	1	=	=	PUNCT
ejde-390	148	1	+	+	NUM
ejde-390	148	2	∞	∞	NOUN
ejde-390	148	3	uniformly	uniformly	ADJ
ejde-390	148	4	for	for	ADP
ejde-390	148	5	a.a	a.a	PROPN
ejde-390	148	6	.	.	PROPN
ejde-390	148	7	z	z	PROPN
ejde-390	148	8	∈	∈	PROPN
ejde-390	148	9	ω	ω	PROPN
ejde-390	148	10	.	.	PROPN
ejde-390	148	11	6	6	NUM
ejde-390	148	12	n.	n.	PROPN
ejde-390	148	13	s.	s.	PROPN
ejde-390	148	14	papageorgiou	papageorgiou	PROPN
ejde-390	148	15	,	,	PUNCT
ejde-390	148	16	c.	c.	PROPN
ejde-390	148	17	vetro	vetro	PROPN
ejde-390	148	18	,	,	PUNCT
ejde-390	148	19	f.	f.	PROPN
ejde-390	148	20	vetro	vetro	PROPN
ejde-390	148	21	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	148	22	therefore	therefore	ADV
ejde-390	148	23	the	the	DET
ejde-390	148	24	reaction	reaction	NOUN
ejde-390	148	25	f(z	f(z	PROPN
ejde-390	148	26	,	,	PUNCT
ejde-390	148	27	·	·	PUNCT
ejde-390	148	28	)	)	PUNCT
ejde-390	148	29	is	be	AUX
ejde-390	148	30	(	(	PUNCT
ejde-390	148	31	p	p	X
ejde-390	148	32	−	−	PROPN
ejde-390	148	33	1)-superlinear	1)-superlinear	NUM
ejde-390	148	34	near	near	ADP
ejde-390	148	35	+	+	PROPN
ejde-390	148	36	∞.	∞.	PROPN
ejde-390	148	37	usually	usually	ADV
ejde-390	148	38	such	such	ADJ
ejde-390	148	39	problems	problem	NOUN
ejde-390	148	40	are	be	AUX
ejde-390	148	41	treated	treat	VERB
ejde-390	148	42	using	use	VERB
ejde-390	148	43	the	the	DET
ejde-390	148	44	ar	ar	NOUN
ejde-390	148	45	-	-	NOUN
ejde-390	148	46	condition	condition	NOUN
ejde-390	148	47	which	which	PRON
ejde-390	148	48	leads	lead	VERB
ejde-390	148	49	to	to	ADP
ejde-390	148	50	an	an	DET
ejde-390	148	51	easy	easy	ADJ
ejde-390	148	52	verification	verification	NOUN
ejde-390	148	53	of	of	ADP
ejde-390	148	54	the	the	DET
ejde-390	148	55	c	c	NOUN
ejde-390	148	56	-	-	PUNCT
ejde-390	148	57	condition	condition	NOUN
ejde-390	148	58	for	for	ADP
ejde-390	148	59	the	the	DET
ejde-390	148	60	energy	energy	NOUN
ejde-390	148	61	(	(	PUNCT
ejde-390	148	62	euler	euler	NOUN
ejde-390	148	63	)	)	PUNCT
ejde-390	148	64	functional	functional	ADJ
ejde-390	148	65	of	of	ADP
ejde-390	148	66	the	the	DET
ejde-390	148	67	problem	problem	NOUN
ejde-390	148	68	.	.	PUNCT
ejde-390	149	1	we	we	PRON
ejde-390	149	2	recall	recall	VERB
ejde-390	149	3	that	that	SCONJ
ejde-390	149	4	the	the	DET
ejde-390	149	5	ar	ar	NOUN
ejde-390	149	6	-	-	NOUN
ejde-390	149	7	condition	condition	NOUN
ejde-390	149	8	(	(	PUNCT
ejde-390	149	9	unilateral	unilateral	ADJ
ejde-390	149	10	version	version	NOUN
ejde-390	149	11	due	due	ADP
ejde-390	149	12	to	to	ADP
ejde-390	149	13	(	(	PUNCT
ejde-390	149	14	2.2	2.2	NUM
ejde-390	149	15	)	)	PUNCT
ejde-390	149	16	)	)	PUNCT
ejde-390	149	17	,	,	PUNCT
ejde-390	149	18	says	say	VERB
ejde-390	149	19	that	that	SCONJ
ejde-390	149	20	there	there	PRON
ejde-390	149	21	exist	exist	VERB
ejde-390	149	22	ϑ	ϑ	X
ejde-390	149	23	>	>	X
ejde-390	149	24	p	p	PROPN
ejde-390	149	25	and	and	CCONJ
ejde-390	149	26	m	m	PROPN
ejde-390	149	27	>	>	X
ejde-390	149	28	0	0	NUM
ejde-390	149	29	such	such	ADJ
ejde-390	149	30	that	that	SCONJ
ejde-390	149	31	0	0	NUM
ejde-390	149	32	<	<	X
ejde-390	149	33	ϑf	ϑf	ADP
ejde-390	149	34	(	(	PUNCT
ejde-390	149	35	z	z	NOUN
ejde-390	149	36	,	,	PUNCT
ejde-390	149	37	x	x	NOUN
ejde-390	149	38	)	)	PUNCT
ejde-390	149	39	≤	≤	NUM
ejde-390	149	40	f(z	f(z	PROPN
ejde-390	149	41	,	,	PUNCT
ejde-390	149	42	x)x	x)x	PUNCT
ejde-390	149	43	for	for	ADP
ejde-390	149	44	a.a	a.a	PROPN
ejde-390	149	45	.	.	PROPN
ejde-390	149	46	z	z	PROPN
ejde-390	149	47	∈	∈	PROPN
ejde-390	149	48	ω	ω	PROPN
ejde-390	149	49	,	,	PUNCT
ejde-390	149	50	all	all	PRON
ejde-390	149	51	x	x	NOUN
ejde-390	149	52	≥m	≥m	NOUN
ejde-390	149	53	,	,	PUNCT
ejde-390	149	54	(	(	PUNCT
ejde-390	149	55	2.3	2.3	NUM
ejde-390	149	56	)	)	PUNCT
ejde-390	149	57	0	0	PUNCT
ejde-390	150	1	<	<	X
ejde-390	150	2	ess	ess	PROPN
ejde-390	150	3	infω	infω	ADJ
ejde-390	150	4	f	f	PROPN
ejde-390	150	5	(	(	PUNCT
ejde-390	150	6	·	·	PUNCT
ejde-390	150	7	,	,	PUNCT
ejde-390	150	8	m	m	NOUN
ejde-390	150	9	)	)	PUNCT
ejde-390	150	10	.	.	PUNCT
ejde-390	151	1	(	(	PUNCT
ejde-390	151	2	2.4	2.4	NUM
ejde-390	151	3	)	)	PUNCT
ejde-390	151	4	integrating	integrating	NOUN
ejde-390	151	5	(	(	PUNCT
ejde-390	151	6	2.3	2.3	NUM
ejde-390	151	7	)	)	PUNCT
ejde-390	151	8	and	and	CCONJ
ejde-390	151	9	using	use	VERB
ejde-390	151	10	(	(	PUNCT
ejde-390	151	11	2.4	2.4	NUM
ejde-390	151	12	)	)	PUNCT
ejde-390	151	13	,	,	PUNCT
ejde-390	151	14	we	we	PRON
ejde-390	151	15	obtain	obtain	VERB
ejde-390	151	16	the	the	DET
ejde-390	151	17	following	follow	VERB
ejde-390	151	18	weaker	weak	ADJ
ejde-390	151	19	condition	condition	NOUN
ejde-390	151	20	c7x	c7x	PUNCT
ejde-390	151	21	ϑ	ϑ	X
ejde-390	151	22	≤	≤	PROPN
ejde-390	151	23	f	f	X
ejde-390	151	24	(	(	PUNCT
ejde-390	151	25	z	z	NOUN
ejde-390	151	26	,	,	PUNCT
ejde-390	151	27	x	x	NOUN
ejde-390	151	28	)	)	PUNCT
ejde-390	151	29	for	for	ADP
ejde-390	151	30	a.a	a.a	PROPN
ejde-390	151	31	.	.	PROPN
ejde-390	151	32	z	z	PROPN
ejde-390	151	33	∈	∈	PROPN
ejde-390	151	34	ω	ω	PROPN
ejde-390	151	35	,	,	PUNCT
ejde-390	151	36	all	all	PRON
ejde-390	151	37	x	x	NOUN
ejde-390	151	38	≥m	≥m	NOUN
ejde-390	151	39	,	,	PUNCT
ejde-390	151	40	some	some	DET
ejde-390	151	41	c7	c7	PROPN
ejde-390	151	42	>	>	X
ejde-390	151	43	0	0	PROPN
ejde-390	151	44	,	,	PUNCT
ejde-390	151	45	⇒	⇒	NOUN
ejde-390	151	46	c7x	c7x	PROPN
ejde-390	151	47	ϑ−1	ϑ−1	PROPN
ejde-390	151	48	≤	≤	PROPN
ejde-390	151	49	f(z	f(z	PROPN
ejde-390	151	50	,	,	PUNCT
ejde-390	151	51	x	x	NOUN
ejde-390	151	52	)	)	PUNCT
ejde-390	151	53	for	for	ADP
ejde-390	151	54	a.a	a.a	PROPN
ejde-390	151	55	.	.	PROPN
ejde-390	151	56	z	z	PROPN
ejde-390	151	57	∈	∈	PROPN
ejde-390	151	58	ω	ω	PROPN
ejde-390	151	59	,	,	PUNCT
ejde-390	151	60	all	all	PRON
ejde-390	151	61	x	x	NOUN
ejde-390	151	62	≥m	≥m	NOUN
ejde-390	151	63	,	,	PUNCT
ejde-390	151	64	(	(	PUNCT
ejde-390	151	65	see	see	VERB
ejde-390	151	66	(	(	PUNCT
ejde-390	151	67	2.3	2.3	NUM
ejde-390	151	68	)	)	PUNCT
ejde-390	151	69	)	)	PUNCT
ejde-390	151	70	.	.	PUNCT
ejde-390	152	1	(	(	PUNCT
ejde-390	152	2	2.5	2.5	NUM
ejde-390	152	3	)	)	PUNCT
ejde-390	152	4	from	from	ADP
ejde-390	152	5	(	(	PUNCT
ejde-390	152	6	2.5	2.5	NUM
ejde-390	152	7	)	)	PUNCT
ejde-390	152	8	we	we	PRON
ejde-390	152	9	see	see	VERB
ejde-390	152	10	that	that	SCONJ
ejde-390	152	11	the	the	DET
ejde-390	152	12	ar	ar	NOUN
ejde-390	152	13	-	-	PUNCT
ejde-390	152	14	condition	condition	NOUN
ejde-390	152	15	implies	imply	VERB
ejde-390	152	16	that	that	SCONJ
ejde-390	152	17	f(z	f(z	PROPN
ejde-390	152	18	,	,	PUNCT
ejde-390	152	19	·	·	PUNCT
ejde-390	152	20	)	)	PUNCT
ejde-390	152	21	has	have	VERB
ejde-390	152	22	at	at	ADV
ejde-390	152	23	least	least	ADJ
ejde-390	152	24	(	(	PUNCT
ejde-390	152	25	ϑ−1)polynomial	ϑ−1)polynomial	ADJ
ejde-390	152	26	growth	growth	NOUN
ejde-390	152	27	.	.	PUNCT
ejde-390	153	1	in	in	ADP
ejde-390	153	2	this	this	DET
ejde-390	153	3	work	work	NOUN
ejde-390	153	4	,	,	PUNCT
ejde-390	153	5	we	we	PRON
ejde-390	153	6	replace	replace	VERB
ejde-390	153	7	the	the	DET
ejde-390	153	8	ar	ar	NOUN
ejde-390	153	9	-	-	NOUN
ejde-390	153	10	condition	condition	NOUN
ejde-390	153	11	by	by	ADP
ejde-390	153	12	the	the	DET
ejde-390	153	13	quasimonotonicity	quasimonotonicity	NOUN
ejde-390	153	14	condition	condition	NOUN
ejde-390	153	15	on	on	ADP
ejde-390	153	16	d(z	d(z	PROPN
ejde-390	153	17	,	,	PUNCT
ejde-390	153	18	·	·	PUNCT
ejde-390	153	19	)	)	PUNCT
ejde-390	153	20	stated	state	VERB
ejde-390	153	21	in	in	ADP
ejde-390	153	22	hypothesis	hypothesis	NOUN
ejde-390	153	23	(	(	PUNCT
ejde-390	153	24	h3)(iii	h3)(iii	NOUN
ejde-390	153	25	)	)	PUNCT
ejde-390	153	26	.	.	PUNCT
ejde-390	154	1	this	this	DET
ejde-390	154	2	hypothesis	hypothesis	NOUN
ejde-390	154	3	is	be	AUX
ejde-390	154	4	a	a	DET
ejde-390	154	5	slight	slight	ADJ
ejde-390	154	6	generalization	generalization	NOUN
ejde-390	154	7	of	of	ADP
ejde-390	154	8	a	a	DET
ejde-390	154	9	condition	condition	NOUN
ejde-390	154	10	used	use	VERB
ejde-390	154	11	by	by	ADP
ejde-390	154	12	li	li	PROPN
ejde-390	154	13	-	-	PROPN
ejde-390	154	14	yang	yang	PROPN
ejde-390	155	1	[	[	X
ejde-390	155	2	6	6	NUM
ejde-390	155	3	]	]	PUNCT
ejde-390	155	4	.	.	PUNCT
ejde-390	156	1	this	this	DET
ejde-390	156	2	condition	condition	NOUN
ejde-390	156	3	is	be	AUX
ejde-390	156	4	satisfied	satisfied	ADJ
ejde-390	156	5	if	if	SCONJ
ejde-390	156	6	there	there	PRON
ejde-390	156	7	exists	exist	VERB
ejde-390	156	8	m	m	VERB
ejde-390	156	9	>	>	X
ejde-390	156	10	0	0	NUM
ejde-390	156	11	such	such	ADJ
ejde-390	156	12	that	that	PRON
ejde-390	156	13	for	for	ADP
ejde-390	156	14	a.a	a.a	PROPN
ejde-390	156	15	.	.	PROPN
ejde-390	156	16	z	z	PROPN
ejde-390	156	17	∈	∈	PROPN
ejde-390	156	18	ω	ω	NUM
ejde-390	156	19	the	the	DET
ejde-390	156	20	function	function	NOUN
ejde-390	156	21	x→	x→	PUNCT
ejde-390	156	22	f(z	f(z	PROPN
ejde-390	156	23	,	,	PUNCT
ejde-390	156	24	x	x	X
ejde-390	156	25	)	)	PUNCT
ejde-390	156	26	xp−1	xp−1	PRON
ejde-390	156	27	is	be	AUX
ejde-390	156	28	nondecreasing	nondecrease	VERB
ejde-390	156	29	on	on	ADP
ejde-390	156	30	[	[	X
ejde-390	156	31	m,+∞	m,+∞	NUM
ejde-390	156	32	)	)	PUNCT
ejde-390	156	33	.	.	PUNCT
ejde-390	157	1	hence	hence	ADV
ejde-390	157	2	from	from	ADP
ejde-390	157	3	(	(	PUNCT
ejde-390	157	4	2.5	2.5	NUM
ejde-390	157	5	)	)	PUNCT
ejde-390	157	6	we	we	PRON
ejde-390	157	7	infer	infer	VERB
ejde-390	157	8	that	that	SCONJ
ejde-390	157	9	the	the	DET
ejde-390	157	10	quasimonotonicity	quasimonotonicity	NOUN
ejde-390	157	11	condition	condition	NOUN
ejde-390	157	12	on	on	ADP
ejde-390	157	13	d(z	d(z	PROPN
ejde-390	157	14	,	,	PUNCT
ejde-390	157	15	·	·	PUNCT
ejde-390	157	16	)	)	PUNCT
ejde-390	157	17	is	be	AUX
ejde-390	157	18	more	more	ADV
ejde-390	157	19	general	general	ADJ
ejde-390	157	20	than	than	ADP
ejde-390	157	21	the	the	DET
ejde-390	157	22	ar	ar	NOUN
ejde-390	157	23	-	-	NOUN
ejde-390	157	24	condition	condition	NOUN
ejde-390	157	25	.	.	PUNCT
ejde-390	158	1	it	it	PRON
ejde-390	158	2	permits	permit	VERB
ejde-390	158	3	the	the	DET
ejde-390	158	4	consideration	consideration	NOUN
ejde-390	158	5	of	of	ADP
ejde-390	158	6	superlinear	superlinear	ADJ
ejde-390	158	7	nonlinearities	nonlinearitie	NOUN
ejde-390	158	8	with	with	ADP
ejde-390	158	9	“	"	PUNCT
ejde-390	158	10	slower	slow	ADJ
ejde-390	158	11	”	"	PUNCT
ejde-390	158	12	growth	growth	NOUN
ejde-390	158	13	near	near	ADP
ejde-390	158	14	+	+	PROPN
ejde-390	158	15	∞.	∞.	PROPN
ejde-390	158	16	to	to	PART
ejde-390	158	17	see	see	VERB
ejde-390	158	18	this	this	PRON
ejde-390	158	19	,	,	PUNCT
ejde-390	158	20	consider	consider	VERB
ejde-390	158	21	the	the	DET
ejde-390	158	22	following	follow	VERB
ejde-390	158	23	function	function	NOUN
ejde-390	158	24	f(z	f(z	PROPN
ejde-390	158	25	,	,	PUNCT
ejde-390	158	26	x	x	NOUN
ejde-390	158	27	)	)	PUNCT
ejde-390	159	1	=	=	PRON
ejde-390	159	2	{	{	PUNCT
ejde-390	159	3	η(z)(x+)q−1	η(z)(x+)q−1	NOUN
ejde-390	159	4	if	if	SCONJ
ejde-390	159	5	x	x	SYM
ejde-390	159	6	≤	≤	NUM
ejde-390	159	7	1	1	NUM
ejde-390	159	8	,	,	PUNCT
ejde-390	159	9	xp−1	xp−1	NOUN
ejde-390	160	1	lnx+	lnx+	PROPN
ejde-390	160	2	η(z)xτ−1	η(z)xτ−1	NOUN
ejde-390	160	3	if	if	SCONJ
ejde-390	160	4	1	1	NUM
ejde-390	160	5	<	<	X
ejde-390	160	6	x	x	X
ejde-390	160	7	,	,	PUNCT
ejde-390	160	8	with	with	ADP
ejde-390	160	9	η	η	PROPN
ejde-390	160	10	∈	∈	PROPN
ejde-390	160	11	l∞(ω	l∞(ω	NOUN
ejde-390	160	12	)	)	PUNCT
ejde-390	160	13	,	,	PUNCT
ejde-390	160	14	ξ+	ξ+	NUM
ejde-390	160	15	�	�	PROPN
ejde-390	160	16	η	η	PROPN
ejde-390	160	17	and	and	CCONJ
ejde-390	160	18	1	1	NUM
ejde-390	160	19	<	<	X
ejde-390	160	20	τ	τ	PROPN
ejde-390	160	21	,	,	PUNCT
ejde-390	160	22	q	q	X
ejde-390	160	23	<	<	X
ejde-390	160	24	p.	p.	NOUN
ejde-390	160	25	this	this	DET
ejde-390	160	26	function	function	NOUN
ejde-390	160	27	satisfies	satisfy	VERB
ejde-390	160	28	hypotheses	hypothesis	NOUN
ejde-390	160	29	(	(	PUNCT
ejde-390	160	30	h3	h3	NOUN
ejde-390	160	31	)	)	PUNCT
ejde-390	160	32	but	but	CCONJ
ejde-390	160	33	fails	fail	VERB
ejde-390	160	34	to	to	PART
ejde-390	160	35	satisfy	satisfy	VERB
ejde-390	160	36	the	the	DET
ejde-390	160	37	ar	ar	NOUN
ejde-390	160	38	-	-	NOUN
ejde-390	160	39	condition	condition	NOUN
ejde-390	160	40	(	(	PUNCT
ejde-390	160	41	see	see	VERB
ejde-390	160	42	(	(	PUNCT
ejde-390	160	43	2.3	2.3	NUM
ejde-390	160	44	)	)	PUNCT
ejde-390	160	45	,	,	PUNCT
ejde-390	160	46	(	(	PUNCT
ejde-390	160	47	2.4	2.4	NUM
ejde-390	160	48	)	)	PUNCT
ejde-390	160	49	)	)	PUNCT
ejde-390	160	50	.	.	PUNCT
ejde-390	161	1	in	in	ADP
ejde-390	161	2	what	what	PRON
ejde-390	161	3	follows	follow	VERB
ejde-390	161	4	γ	γ	X
ejde-390	161	5	:	:	PUNCT
ejde-390	161	6	w	w	PROPN
ejde-390	161	7	1,p(ω)→	1,p(ω)→	NUM
ejde-390	161	8	r	r	NOUN
ejde-390	161	9	is	be	AUX
ejde-390	161	10	the	the	DET
ejde-390	161	11	c1	c1	NOUN
ejde-390	161	12	-	-	PUNCT
ejde-390	161	13	functional	functional	ADJ
ejde-390	161	14	defined	define	VERB
ejde-390	161	15	by	by	ADP
ejde-390	161	16	γ(u	γ(u	PROPN
ejde-390	161	17	)	)	PUNCT
ejde-390	162	1	=	=	SYM
ejde-390	162	2	∫	∫	PROPN
ejde-390	163	1	ω	ω	NUM
ejde-390	163	2	pg(∇u)dz	pg(∇u)dz	PROPN
ejde-390	163	3	+	+	CCONJ
ejde-390	163	4	∫	∫	PROPN
ejde-390	163	5	ω	ω	NUM
ejde-390	163	6	ξ(z)|u|pdz	ξ(z)|u|pdz	NOUN
ejde-390	163	7	for	for	ADP
ejde-390	163	8	all	all	DET
ejde-390	163	9	u	u	NOUN
ejde-390	163	10	∈w	∈w	NOUN
ejde-390	163	11	1,p(ω	1,p(ω	NUM
ejde-390	163	12	)	)	PUNCT
ejde-390	163	13	.	.	PUNCT
ejde-390	164	1	3	3	X
ejde-390	164	2	.	.	X
ejde-390	164	3	positive	positive	ADJ
ejde-390	164	4	solutions	solution	NOUN
ejde-390	164	5	in	in	ADP
ejde-390	164	6	this	this	DET
ejde-390	164	7	section	section	NOUN
ejde-390	164	8	we	we	PRON
ejde-390	164	9	study	study	VERB
ejde-390	164	10	the	the	DET
ejde-390	164	11	dependence	dependence	NOUN
ejde-390	164	12	on	on	ADP
ejde-390	164	13	the	the	DET
ejde-390	164	14	parameter	parameter	NOUN
ejde-390	165	1	λ	λ	PROPN
ejde-390	165	2	>	>	X
ejde-390	165	3	0	0	NUM
ejde-390	165	4	of	of	ADP
ejde-390	165	5	the	the	DET
ejde-390	165	6	set	set	NOUN
ejde-390	165	7	of	of	ADP
ejde-390	165	8	positive	positive	ADJ
ejde-390	165	9	solutions	solution	NOUN
ejde-390	165	10	.	.	PUNCT
ejde-390	166	1	so	so	ADV
ejde-390	166	2	,	,	PUNCT
ejde-390	166	3	we	we	PRON
ejde-390	166	4	introduce	introduce	VERB
ejde-390	166	5	the	the	DET
ejde-390	166	6	following	follow	VERB
ejde-390	166	7	two	two	NUM
ejde-390	166	8	sets	set	NOUN
ejde-390	166	9	:	:	PUNCT
ejde-390	166	10	l	l	NOUN
ejde-390	166	11	=	=	PUNCT
ejde-390	166	12	{	{	PUNCT
ejde-390	166	13	λ	λ	X
ejde-390	166	14	>	>	X
ejde-390	166	15	0	0	PUNCT
ejde-390	166	16	:	:	PUNCT
ejde-390	166	17	problem	problem	NOUN
ejde-390	166	18	(	(	PUNCT
ejde-390	166	19	1.1	1.1	NUM
ejde-390	166	20	)	)	PUNCT
ejde-390	166	21	has	have	VERB
ejde-390	166	22	a	a	DET
ejde-390	166	23	positive	positive	ADJ
ejde-390	166	24	solution	solution	NOUN
ejde-390	166	25	}	}	PUNCT
ejde-390	166	26	,	,	PUNCT
ejde-390	166	27	sλ	sλ	NOUN
ejde-390	166	28	=	=	SYM
ejde-390	166	29	set	set	NOUN
ejde-390	166	30	of	of	ADP
ejde-390	166	31	positive	positive	ADJ
ejde-390	166	32	solutions	solution	NOUN
ejde-390	166	33	of	of	ADP
ejde-390	166	34	(	(	PUNCT
ejde-390	166	35	1.1	1.1	NUM
ejde-390	166	36	)	)	PUNCT
ejde-390	166	37	.	.	PUNCT
ejde-390	167	1	we	we	PRON
ejde-390	167	2	start	start	VERB
ejde-390	167	3	with	with	ADP
ejde-390	167	4	the	the	DET
ejde-390	167	5	following	follow	VERB
ejde-390	167	6	result	result	NOUN
ejde-390	167	7	about	about	ADP
ejde-390	167	8	these	these	DET
ejde-390	167	9	two	two	NUM
ejde-390	167	10	sets	set	NOUN
ejde-390	167	11	.	.	PUNCT
ejde-390	168	1	proposition	proposition	NOUN
ejde-390	168	2	3.1	3.1	NUM
ejde-390	168	3	.	.	PUNCT
ejde-390	169	1	if	if	SCONJ
ejde-390	169	2	hypotheses	hypothesis	NOUN
ejde-390	169	3	(	(	PUNCT
ejde-390	169	4	h1)–(h3	h1)–(h3	NOUN
ejde-390	169	5	)	)	PUNCT
ejde-390	169	6	hold	hold	VERB
ejde-390	169	7	,	,	PUNCT
ejde-390	169	8	then	then	ADV
ejde-390	169	9	l	l	NOUN
ejde-390	169	10	6=	6=	NOUN
ejde-390	169	11	∅	∅	NOUN
ejde-390	169	12	and	and	CCONJ
ejde-390	169	13	,	,	PUNCT
ejde-390	169	14	for	for	ADP
ejde-390	169	15	every	every	DET
ejde-390	169	16	λ	λ	PROPN
ejde-390	169	17	∈	∈	PROPN
ejde-390	169	18	l	l	NOUN
ejde-390	169	19	,	,	PUNCT
ejde-390	169	20	∅	∅	NOUN
ejde-390	169	21	6=	6=	X
ejde-390	169	22	sλ	sλ	ADP
ejde-390	169	23	⊆	⊆	NUM
ejde-390	169	24	d+	d+	NOUN
ejde-390	169	25	.	.	PUNCT
ejde-390	170	1	proof	proof	NOUN
ejde-390	170	2	.	.	PUNCT
ejde-390	171	1	let	let	VERB
ejde-390	171	2	µ	µ	X
ejde-390	171	3	>	>	X
ejde-390	171	4	‖ξ‖∞	‖ξ‖∞	PROPN
ejde-390	171	5	(	(	PUNCT
ejde-390	171	6	see	see	VERB
ejde-390	171	7	hypothesis	hypothesis	NOUN
ejde-390	171	8	(	(	PUNCT
ejde-390	171	9	h2	h2	NOUN
ejde-390	171	10	)	)	PUNCT
ejde-390	171	11	)	)	PUNCT
ejde-390	171	12	and	and	CCONJ
ejde-390	171	13	consider	consider	VERB
ejde-390	171	14	the	the	DET
ejde-390	171	15	following	follow	VERB
ejde-390	171	16	auxiliary	auxiliary	ADJ
ejde-390	171	17	neumann	neumann	PROPN
ejde-390	171	18	problem	problem	PROPN
ejde-390	171	19	−div	−div	X
ejde-390	171	20	a(∇u(z	a(∇u(z	NOUN
ejde-390	171	21	)	)	PUNCT
ejde-390	171	22	)	)	PUNCT
ejde-390	172	1	+	+	CCONJ
ejde-390	172	2	[	[	X
ejde-390	172	3	ξ(z	ξ(z	NOUN
ejde-390	172	4	)	)	PUNCT
ejde-390	172	5	+	+	CCONJ
ejde-390	172	6	µ]u(z)p−1	µ]u(z)p−1	NOUN
ejde-390	172	7	=	=	SYM
ejde-390	172	8	1	1	NUM
ejde-390	172	9	in	in	ADP
ejde-390	172	10	ω	ω	NUM
ejde-390	172	11	,	,	PUNCT
ejde-390	172	12	∂u	∂u	PROPN
ejde-390	172	13	∂n	∂n	PROPN
ejde-390	172	14	=	=	PUNCT
ejde-390	172	15	0	0	NUM
ejde-390	172	16	on	on	ADP
ejde-390	172	17	∂ω	∂ω	PROPN
ejde-390	172	18	.	.	PUNCT
ejde-390	173	1	(	(	PUNCT
ejde-390	173	2	3.1	3.1	NUM
ejde-390	173	3	)	)	PUNCT
ejde-390	173	4	using	use	VERB
ejde-390	173	5	lemma	lemma	PROPN
ejde-390	173	6	2.2	2.2	NUM
ejde-390	173	7	,	,	PUNCT
ejde-390	173	8	proposition	proposition	NOUN
ejde-390	173	9	2.5	2.5	NUM
ejde-390	173	10	and	and	CCONJ
ejde-390	173	11	the	the	DET
ejde-390	173	12	fact	fact	NOUN
ejde-390	173	13	that	that	SCONJ
ejde-390	173	14	µ	µ	X
ejde-390	173	15	>	>	X
ejde-390	173	16	‖ξ‖∞	‖ξ‖∞	PROPN
ejde-390	173	17	,	,	PUNCT
ejde-390	173	18	we	we	PRON
ejde-390	173	19	see	see	VERB
ejde-390	173	20	that	that	SCONJ
ejde-390	173	21	the	the	DET
ejde-390	173	22	left	left	ADJ
ejde-390	173	23	hand	hand	NOUN
ejde-390	173	24	side	side	NOUN
ejde-390	173	25	of	of	ADP
ejde-390	173	26	(	(	PUNCT
ejde-390	173	27	3.1	3.1	NUM
ejde-390	173	28	)	)	PUNCT
ejde-390	173	29	is	be	AUX
ejde-390	173	30	continuous	continuous	ADJ
ejde-390	173	31	,	,	PUNCT
ejde-390	173	32	strictly	strictly	ADV
ejde-390	173	33	monotone	monotone	ADJ
ejde-390	173	34	and	and	CCONJ
ejde-390	173	35	coercive	coercive	ADJ
ejde-390	173	36	.	.	PUNCT
ejde-390	174	1	therefore	therefore	ADV
ejde-390	174	2	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	174	3	positive	positive	ADJ
ejde-390	174	4	and	and	CCONJ
ejde-390	174	5	nodal	nodal	ADJ
ejde-390	174	6	solutions	solution	NOUN
ejde-390	174	7	7	7	NUM
ejde-390	174	8	problem	problem	NOUN
ejde-390	174	9	(	(	PUNCT
ejde-390	174	10	3.1	3.1	NUM
ejde-390	174	11	)	)	PUNCT
ejde-390	174	12	admits	admit	VERB
ejde-390	174	13	a	a	DET
ejde-390	174	14	unique	unique	ADJ
ejde-390	174	15	solution	solution	NOUN
ejde-390	174	16	u	u	NOUN
ejde-390	174	17	∈	∈	PROPN
ejde-390	174	18	w	w	PROPN
ejde-390	174	19	1,p(ω	1,p(ω	NUM
ejde-390	174	20	)	)	PUNCT
ejde-390	174	21	,	,	PUNCT
ejde-390	174	22	u	u	PROPN
ejde-390	174	23	6=	6=	PROPN
ejde-390	174	24	0	0	NUM
ejde-390	174	25	.	.	PUNCT
ejde-390	175	1	moreover	moreover	ADV
ejde-390	175	2	,	,	PUNCT
ejde-390	175	3	the	the	DET
ejde-390	175	4	nonlinear	nonlinear	ADJ
ejde-390	175	5	regularity	regularity	NOUN
ejde-390	175	6	theory	theory	NOUN
ejde-390	175	7	(	(	PUNCT
ejde-390	175	8	see	see	VERB
ejde-390	175	9	[	[	X
ejde-390	175	10	7	7	NUM
ejde-390	175	11	]	]	PUNCT
ejde-390	175	12	)	)	PUNCT
ejde-390	175	13	and	and	CCONJ
ejde-390	175	14	the	the	DET
ejde-390	175	15	nonlinear	nonlinear	ADJ
ejde-390	175	16	maximum	maximum	ADJ
ejde-390	175	17	principle	principle	NOUN
ejde-390	175	18	(	(	PUNCT
ejde-390	175	19	see	see	VERB
ejde-390	175	20	[	[	X
ejde-390	175	21	15	15	NUM
ejde-390	175	22	]	]	NUM
ejde-390	175	23	)	)	PUNCT
ejde-390	175	24	,	,	PUNCT
ejde-390	175	25	imply	imply	VERB
ejde-390	175	26	that	that	SCONJ
ejde-390	175	27	u	u	PROPN
ejde-390	175	28	∈	∈	PROPN
ejde-390	175	29	d+	d+	PUNCT
ejde-390	175	30	.	.	PUNCT
ejde-390	176	1	we	we	PRON
ejde-390	176	2	set	set	VERB
ejde-390	176	3	m0	m0	NOUN
ejde-390	176	4	=	=	SYM
ejde-390	176	5	‖nf	‖nf	NUM
ejde-390	176	6	(	(	PUNCT
ejde-390	176	7	u)‖∞	u)‖∞	ADJ
ejde-390	176	8	(	(	PUNCT
ejde-390	176	9	see	see	VERB
ejde-390	176	10	hypothesis	hypothesis	NOUN
ejde-390	176	11	(	(	PUNCT
ejde-390	176	12	h3	h3	NOUN
ejde-390	176	13	)	)	PUNCT
ejde-390	176	14	(	(	PUNCT
ejde-390	176	15	i	i	NOUN
ejde-390	176	16	)	)	PUNCT
ejde-390	176	17	)	)	PUNCT
ejde-390	176	18	,	,	PUNCT
ejde-390	176	19	m0	m0	NOUN
ejde-390	176	20	=	=	SYM
ejde-390	176	21	min	min	PROPN
ejde-390	176	22	ω	ω	NUM
ejde-390	176	23	u	u	NOUN
ejde-390	176	24	>	>	X
ejde-390	176	25	0	0	PUNCT
ejde-390	176	26	(	(	PUNCT
ejde-390	176	27	recall	recall	VERB
ejde-390	176	28	that	that	SCONJ
ejde-390	176	29	u	u	PROPN
ejde-390	176	30	∈	∈	PROPN
ejde-390	176	31	d+	d+	PUNCT
ejde-390	176	32	)	)	PUNCT
ejde-390	176	33	,	,	PUNCT
ejde-390	176	34	λ	λ	X
ejde-390	176	35	=	=	SYM
ejde-390	176	36	µ+	µ+	PUNCT
ejde-390	176	37	m0	m0	NOUN
ejde-390	176	38	mp−1	mp−1	X
ejde-390	176	39	0	0	NUM
ejde-390	176	40	>	>	X
ejde-390	176	41	0	0	X
ejde-390	176	42	.	.	PUNCT
ejde-390	177	1	we	we	PRON
ejde-390	177	2	have	have	VERB
ejde-390	177	3	−	−	VERB
ejde-390	177	4	div	div	PROPN
ejde-390	177	5	a(∇u(z	a(∇u(z	NOUN
ejde-390	177	6	)	)	PUNCT
ejde-390	177	7	)	)	PUNCT
ejde-390	178	1	+	+	CCONJ
ejde-390	178	2	[	[	X
ejde-390	178	3	ξ(z	ξ(z	NOUN
ejde-390	178	4	)	)	PUNCT
ejde-390	178	5	+	+	NOUN
ejde-390	178	6	λ]u(z)p−1	λ]u(z)p−1	NOUN
ejde-390	178	7	=	=	SYM
ejde-390	178	8	−div	−div	NOUN
ejde-390	178	9	a(∇u(z	a(∇u(z	NOUN
ejde-390	178	10	)	)	PUNCT
ejde-390	178	11	)	)	PUNCT
ejde-390	179	1	+	+	CCONJ
ejde-390	179	2	[	[	X
ejde-390	179	3	ξ(z	ξ(z	NOUN
ejde-390	179	4	)	)	PUNCT
ejde-390	179	5	+	+	CCONJ
ejde-390	179	6	µ]u(z)p−1	µ]u(z)p−1	NOUN
ejde-390	179	7	+	+	PROPN
ejde-390	179	8	m0	m0	PROPN
ejde-390	179	9	(	(	PUNCT
ejde-390	179	10	u(z	u(z	NOUN
ejde-390	179	11	)	)	PUNCT
ejde-390	179	12	m0	m0	NOUN
ejde-390	179	13	)	)	PUNCT
ejde-390	180	1	p−1	p−1	PROPN
ejde-390	180	2	≥	≥	NOUN
ejde-390	180	3	1	1	NUM
ejde-390	180	4	+	+	NUM
ejde-390	180	5	m0	m0	NOUN
ejde-390	180	6	(	(	PUNCT
ejde-390	180	7	see	see	VERB
ejde-390	180	8	(	(	PUNCT
ejde-390	180	9	3.1	3.1	NUM
ejde-390	180	10	)	)	PUNCT
ejde-390	180	11	and	and	CCONJ
ejde-390	180	12	recall	recall	VERB
ejde-390	180	13	that	that	PRON
ejde-390	180	14	u(z	u(z	NOUN
ejde-390	180	15	)	)	PUNCT
ejde-390	180	16	≥	≥	NOUN
ejde-390	180	17	m0	m0	NOUN
ejde-390	180	18	for	for	ADP
ejde-390	180	19	all	all	DET
ejde-390	180	20	z	z	NOUN
ejde-390	180	21	∈	∈	PROPN
ejde-390	180	22	ω	ω	PROPN
ejde-390	180	23	)	)	PUNCT
ejde-390	180	24	>	>	X
ejde-390	180	25	f(z	f(z	PROPN
ejde-390	180	26	,	,	PUNCT
ejde-390	180	27	u(z	u(z	NOUN
ejde-390	180	28	)	)	PUNCT
ejde-390	180	29	)	)	PUNCT
ejde-390	180	30	for	for	ADP
ejde-390	180	31	a.a	a.a	PROPN
ejde-390	180	32	.	.	PROPN
ejde-390	180	33	z	z	PROPN
ejde-390	180	34	∈	∈	PROPN
ejde-390	180	35	ω	ω	PROPN
ejde-390	180	36	.	.	PUNCT
ejde-390	181	1	(	(	PUNCT
ejde-390	181	2	3.2	3.2	NUM
ejde-390	181	3	)	)	PUNCT
ejde-390	181	4	we	we	PRON
ejde-390	181	5	introduce	introduce	VERB
ejde-390	181	6	the	the	DET
ejde-390	181	7	carathéodory	carathéodory	NOUN
ejde-390	181	8	function	function	NOUN
ejde-390	181	9	f̂(z	f̂(z	NOUN
ejde-390	181	10	,	,	PUNCT
ejde-390	181	11	x	x	NOUN
ejde-390	181	12	)	)	PUNCT
ejde-390	181	13	=	=	SYM
ejde-390	181	14	{	{	PUNCT
ejde-390	181	15	f(z	f(z	PROPN
ejde-390	181	16	,	,	PUNCT
ejde-390	181	17	x+	x+	PUNCT
ejde-390	181	18	)	)	PUNCT
ejde-390	181	19	if	if	SCONJ
ejde-390	181	20	x	x	SYM
ejde-390	181	21	≤	≤	NUM
ejde-390	181	22	u(z	u(z	NOUN
ejde-390	181	23	)	)	PUNCT
ejde-390	181	24	,	,	PUNCT
ejde-390	181	25	f(z	f(z	PROPN
ejde-390	181	26	,	,	PUNCT
ejde-390	181	27	u(z	u(z	NOUN
ejde-390	181	28	)	)	PUNCT
ejde-390	181	29	)	)	PUNCT
ejde-390	182	1	if	if	SCONJ
ejde-390	182	2	u(z	u(z	NOUN
ejde-390	182	3	)	)	PUNCT
ejde-390	182	4	<	<	X
ejde-390	182	5	x.	x.	X
ejde-390	182	6	(	(	PUNCT
ejde-390	182	7	3.3	3.3	NUM
ejde-390	182	8	)	)	PUNCT
ejde-390	182	9	(	(	PUNCT
ejde-390	182	10	see	see	VERB
ejde-390	182	11	(	(	PUNCT
ejde-390	182	12	2.2	2.2	NUM
ejde-390	182	13	)	)	PUNCT
ejde-390	182	14	)	)	PUNCT
ejde-390	182	15	.	.	PUNCT
ejde-390	183	1	we	we	PRON
ejde-390	183	2	set	set	VERB
ejde-390	183	3	f̂	f̂	PROPN
ejde-390	183	4	(	(	PUNCT
ejde-390	183	5	z	z	NOUN
ejde-390	183	6	,	,	PUNCT
ejde-390	183	7	x	x	NOUN
ejde-390	183	8	)	)	PUNCT
ejde-390	183	9	=	=	SYM
ejde-390	184	1	∫	∫	PROPN
ejde-390	184	2	x	x	SYM
ejde-390	184	3	0	0	NUM
ejde-390	184	4	f̂(z	f̂(z	NOUN
ejde-390	184	5	,	,	PUNCT
ejde-390	184	6	s)ds	s)ds	PROPN
ejde-390	184	7	and	and	CCONJ
ejde-390	184	8	consider	consider	VERB
ejde-390	184	9	the	the	DET
ejde-390	184	10	c1	c1	NOUN
ejde-390	184	11	-	-	PUNCT
ejde-390	184	12	functional	functional	ADJ
ejde-390	184	13	ϕ̂	ϕ̂	PUNCT
ejde-390	184	14	:	:	PUNCT
ejde-390	184	15	w	w	PROPN
ejde-390	184	16	1,p(ω	1,p(ω	NUM
ejde-390	184	17	)	)	PUNCT
ejde-390	184	18	→	→	SYM
ejde-390	184	19	r	r	NOUN
ejde-390	184	20	defined	define	VERB
ejde-390	184	21	by	by	ADP
ejde-390	184	22	ϕ̂(u	ϕ̂(u	ADP
ejde-390	184	23	)	)	PUNCT
ejde-390	184	24	=	=	SYM
ejde-390	185	1	1	1	NUM
ejde-390	185	2	p	p	NOUN
ejde-390	185	3	γ(u	γ(u	PROPN
ejde-390	185	4	)	)	PUNCT
ejde-390	186	1	+	+	NUM
ejde-390	186	2	λ	λ	AUX
ejde-390	186	3	p	p	NOUN
ejde-390	186	4	‖u‖pp	‖u‖pp	NOUN
ejde-390	186	5	−	−	PROPN
ejde-390	186	6	∫	∫	PROPN
ejde-390	186	7	ω	ω	PROPN
ejde-390	186	8	f̂	f̂	X
ejde-390	186	9	(	(	PUNCT
ejde-390	186	10	z	z	NOUN
ejde-390	186	11	,	,	PUNCT
ejde-390	186	12	u)dz	u)dz	PROPN
ejde-390	186	13	for	for	ADP
ejde-390	186	14	all	all	DET
ejde-390	186	15	u	u	NOUN
ejde-390	186	16	∈w	∈w	NOUN
ejde-390	186	17	1,p(ω	1,p(ω	NUM
ejde-390	186	18	)	)	PUNCT
ejde-390	186	19	.	.	PUNCT
ejde-390	187	1	from	from	ADP
ejde-390	187	2	(	(	PUNCT
ejde-390	187	3	3.3	3.3	NUM
ejde-390	187	4	)	)	PUNCT
ejde-390	187	5	and	and	CCONJ
ejde-390	187	6	since	since	SCONJ
ejde-390	187	7	λ	λ	PROPN
ejde-390	187	8	>	>	X
ejde-390	187	9	µ	µ	X
ejde-390	187	10	>	>	X
ejde-390	187	11	‖ξ‖∞	‖ξ‖∞	PROPN
ejde-390	187	12	,	,	PUNCT
ejde-390	187	13	we	we	PRON
ejde-390	187	14	see	see	VERB
ejde-390	187	15	that	that	SCONJ
ejde-390	187	16	ϕ̂	ϕ̂	PROPN
ejde-390	187	17	(	(	PUNCT
ejde-390	187	18	·	·	PUNCT
ejde-390	187	19	)	)	PUNCT
ejde-390	187	20	is	be	AUX
ejde-390	187	21	coercive	coercive	ADJ
ejde-390	187	22	.	.	PUNCT
ejde-390	188	1	also	also	ADV
ejde-390	188	2	using	use	VERB
ejde-390	188	3	the	the	DET
ejde-390	188	4	sobolev	sobolev	NOUN
ejde-390	188	5	embedding	embed	VERB
ejde-390	188	6	theorem	theorem	VERB
ejde-390	188	7	,	,	PUNCT
ejde-390	188	8	we	we	PRON
ejde-390	188	9	show	show	VERB
ejde-390	188	10	that	that	SCONJ
ejde-390	188	11	ϕ̂	ϕ̂	PROPN
ejde-390	188	12	(	(	PUNCT
ejde-390	188	13	·	·	PUNCT
ejde-390	188	14	)	)	PUNCT
ejde-390	188	15	is	be	AUX
ejde-390	188	16	sequentially	sequentially	ADV
ejde-390	188	17	weakly	weakly	ADV
ejde-390	188	18	lower	low	ADJ
ejde-390	188	19	semicontinuous	semicontinuous	ADJ
ejde-390	188	20	.	.	PUNCT
ejde-390	189	1	so	so	ADV
ejde-390	189	2	,	,	PUNCT
ejde-390	189	3	by	by	ADP
ejde-390	189	4	the	the	DET
ejde-390	189	5	weierstrass	weierstrass	NOUN
ejde-390	189	6	-	-	PUNCT
ejde-390	189	7	tonelli	tonelli	NOUN
ejde-390	189	8	theorem	theorem	PROPN
ejde-390	189	9	,	,	PUNCT
ejde-390	189	10	we	we	PRON
ejde-390	189	11	can	can	AUX
ejde-390	189	12	find	find	VERB
ejde-390	189	13	u0	u0	ADJ
ejde-390	189	14	∈w	∈w	NOUN
ejde-390	189	15	1,p(ω	1,p(ω	NUM
ejde-390	189	16	)	)	PUNCT
ejde-390	189	17	such	such	ADJ
ejde-390	189	18	that	that	DET
ejde-390	189	19	ϕ̂(u0	ϕ̂(u0	NOUN
ejde-390	189	20	)	)	PUNCT
ejde-390	189	21	=	=	SYM
ejde-390	189	22	inf[ϕ̂(u	inf[ϕ̂(u	PROPN
ejde-390	189	23	)	)	PUNCT
ejde-390	189	24	:	:	PUNCT
ejde-390	190	1	u	u	NOUN
ejde-390	190	2	∈w	∈w	VERB
ejde-390	190	3	1,p(ω	1,p(ω	NUM
ejde-390	190	4	)	)	PUNCT
ejde-390	190	5	]	]	PUNCT
ejde-390	190	6	.	.	PUNCT
ejde-390	191	1	(	(	PUNCT
ejde-390	191	2	3.4	3.4	NUM
ejde-390	191	3	)	)	PUNCT
ejde-390	191	4	hypotheses	hypothesis	NOUN
ejde-390	191	5	(	(	PUNCT
ejde-390	191	6	h1)(iv	h1)(iv	NOUN
ejde-390	191	7	)	)	PUNCT
ejde-390	191	8	and	and	CCONJ
ejde-390	191	9	(	(	PUNCT
ejde-390	191	10	h3)(iv	h3)(iv	NOUN
ejde-390	191	11	)	)	PUNCT
ejde-390	191	12	imply	imply	VERB
ejde-390	191	13	that	that	SCONJ
ejde-390	191	14	given	give	VERB
ejde-390	191	15	η	η	PROPN
ejde-390	191	16	>	>	X
ejde-390	191	17	c∗0	c∗0	PROPN
ejde-390	191	18	>	>	X
ejde-390	191	19	c∗	c∗	PROPN
ejde-390	191	20	,	,	PUNCT
ejde-390	191	21	we	we	PRON
ejde-390	191	22	can	can	AUX
ejde-390	191	23	find	find	VERB
ejde-390	191	24	δ	δ	PROPN
ejde-390	191	25	∈	∈	PROPN
ejde-390	191	26	(	(	PUNCT
ejde-390	191	27	0,m0	0,m0	X
ejde-390	191	28	]	]	X
ejde-390	191	29	such	such	ADJ
ejde-390	191	30	that	that	SCONJ
ejde-390	191	31	g(y	g(y	NOUN
ejde-390	191	32	)	)	PUNCT
ejde-390	191	33	≤	≤	NUM
ejde-390	191	34	c∗0	c∗0	NOUN
ejde-390	191	35	q	q	PROPN
ejde-390	192	1	|y|q	|y|q	PROPN
ejde-390	192	2	for	for	ADP
ejde-390	192	3	all	all	DET
ejde-390	192	4	|y|	|y|	PROPN
ejde-390	192	5	≤	≤	PROPN
ejde-390	192	6	δ	δ	PROPN
ejde-390	192	7	,	,	PUNCT
ejde-390	192	8	f	f	PROPN
ejde-390	192	9	(	(	PUNCT
ejde-390	192	10	z	z	PROPN
ejde-390	192	11	,	,	PUNCT
ejde-390	192	12	x	x	NOUN
ejde-390	192	13	)	)	PUNCT
ejde-390	192	14	≥	≥	PROPN
ejde-390	192	15	η	η	PROPN
ejde-390	192	16	q	q	PROPN
ejde-390	192	17	xq	xq	PROPN
ejde-390	192	18	for	for	ADP
ejde-390	192	19	a.a	a.a	PROPN
ejde-390	192	20	.	.	PROPN
ejde-390	192	21	z	z	PROPN
ejde-390	192	22	∈	∈	PROPN
ejde-390	192	23	ω	ω	PROPN
ejde-390	192	24	,	,	PUNCT
ejde-390	192	25	all	all	PRON
ejde-390	192	26	x	x	SYM
ejde-390	192	27	∈	∈	PROPN
ejde-390	193	1	[	[	X
ejde-390	193	2	0	0	NUM
ejde-390	193	3	,	,	PUNCT
ejde-390	193	4	δ	δ	PROPN
ejde-390	193	5	]	]	X
ejde-390	193	6	.	.	PUNCT
ejde-390	194	1	(	(	PUNCT
ejde-390	194	2	3.5	3.5	NUM
ejde-390	194	3	)	)	PUNCT
ejde-390	194	4	given	give	VERB
ejde-390	194	5	u	u	NOUN
ejde-390	194	6	∈	∈	PROPN
ejde-390	194	7	d+	d+	PUNCT
ejde-390	194	8	,	,	PUNCT
ejde-390	194	9	we	we	PRON
ejde-390	194	10	choose	choose	VERB
ejde-390	194	11	t	t	PROPN
ejde-390	194	12	∈	∈	PROPN
ejde-390	194	13	(	(	PUNCT
ejde-390	194	14	0	0	NUM
ejde-390	194	15	,	,	PUNCT
ejde-390	194	16	1	1	X
ejde-390	194	17	)	)	PUNCT
ejde-390	194	18	small	small	ADJ
ejde-390	194	19	such	such	ADJ
ejde-390	194	20	that	that	DET
ejde-390	194	21	t|∇u(z)|	t|∇u(z)|	ADJ
ejde-390	194	22	≤	≤	ADJ
ejde-390	194	23	δ	δ	PROPN
ejde-390	194	24	and	and	CCONJ
ejde-390	194	25	tu(z	tu(z	NUM
ejde-390	194	26	)	)	PUNCT
ejde-390	194	27	≤	≤	NUM
ejde-390	195	1	δ	δ	PROPN
ejde-390	195	2	for	for	ADP
ejde-390	195	3	all	all	DET
ejde-390	195	4	z	z	NOUN
ejde-390	195	5	∈	∈	PROPN
ejde-390	195	6	ω	ω	PROPN
ejde-390	195	7	.	.	PUNCT
ejde-390	196	1	(	(	PUNCT
ejde-390	196	2	3.6	3.6	NUM
ejde-390	196	3	)	)	PUNCT
ejde-390	196	4	using	use	VERB
ejde-390	196	5	(	(	PUNCT
ejde-390	196	6	3.5	3.5	NUM
ejde-390	196	7	)	)	PUNCT
ejde-390	196	8	and	and	CCONJ
ejde-390	196	9	(	(	PUNCT
ejde-390	196	10	3.6	3.6	NUM
ejde-390	196	11	)	)	PUNCT
ejde-390	196	12	,	,	PUNCT
ejde-390	196	13	we	we	PRON
ejde-390	196	14	have	have	VERB
ejde-390	196	15	ϕ̂(tu	ϕ̂(tu	NOUN
ejde-390	196	16	)	)	PUNCT
ejde-390	196	17	≤	≤	NUM
ejde-390	197	1	c∗0	c∗0	NOUN
ejde-390	197	2	q	q	PROPN
ejde-390	198	1	tq‖∇u‖qq	tq‖∇u‖qq	NOUN
ejde-390	199	1	+	+	CCONJ
ejde-390	199	2	tp	tp	X
ejde-390	199	3	p	p	NOUN
ejde-390	200	1	[	[	X
ejde-390	200	2	‖ξ‖∞	‖ξ‖∞	X
ejde-390	200	3	+	+	NUM
ejde-390	200	4	λ]‖u‖pp	λ]‖u‖pp	PROPN
ejde-390	200	5	−	−	PROPN
ejde-390	200	6	η	η	PROPN
ejde-390	200	7	q	q	PROPN
ejde-390	200	8	tq‖u‖qq	tq‖u‖qq	PROPN
ejde-390	200	9	=	=	PUNCT
ejde-390	200	10	tq[c8	tq[c8	PROPN
ejde-390	200	11	−	−	NUM
ejde-390	200	12	ηc9	ηc9	PROPN
ejde-390	200	13	]	]	X
ejde-390	201	1	+	+	CCONJ
ejde-390	201	2	tpc10	tpc10	ADJ
ejde-390	201	3	for	for	ADP
ejde-390	201	4	some	some	DET
ejde-390	201	5	c8	c8	NOUN
ejde-390	201	6	,	,	PUNCT
ejde-390	201	7	c9	c9	PROPN
ejde-390	201	8	,	,	PUNCT
ejde-390	201	9	c10	c10	VERB
ejde-390	201	10	>	>	X
ejde-390	201	11	0	0	PROPN
ejde-390	201	12	.	.	PUNCT
ejde-390	202	1	since	since	SCONJ
ejde-390	202	2	η	η	PROPN
ejde-390	202	3	>	>	X
ejde-390	202	4	c∗0	c∗0	PROPN
ejde-390	202	5	is	be	AUX
ejde-390	202	6	arbitrary	arbitrary	ADJ
ejde-390	202	7	,	,	PUNCT
ejde-390	202	8	by	by	ADP
ejde-390	202	9	choosing	choose	VERB
ejde-390	202	10	η	η	PROPN
ejde-390	202	11	>	>	X
ejde-390	202	12	c8	c8	PROPN
ejde-390	202	13	c9	c9	PROPN
ejde-390	202	14	we	we	PRON
ejde-390	202	15	obtain	obtain	VERB
ejde-390	202	16	ϕ̂(tu	ϕ̂(tu	NOUN
ejde-390	202	17	)	)	PUNCT
ejde-390	202	18	≤	≤	NOUN
ejde-390	202	19	c10	c10	VERB
ejde-390	202	20	t	t	PROPN
ejde-390	202	21	p	p	PROPN
ejde-390	202	22	−	−	PROPN
ejde-390	202	23	c11	c11	NOUN
ejde-390	202	24	t	t	PROPN
ejde-390	202	25	q	q	NOUN
ejde-390	202	26	for	for	ADP
ejde-390	202	27	all	all	DET
ejde-390	202	28	t	t	PROPN
ejde-390	202	29	>	>	X
ejde-390	202	30	0	0	NUM
ejde-390	202	31	,	,	PUNCT
ejde-390	202	32	and	and	CCONJ
ejde-390	202	33	some	some	DET
ejde-390	202	34	c11	c11	NOUN
ejde-390	202	35	>	>	X
ejde-390	202	36	0	0	NUM
ejde-390	202	37	.	.	NOUN
ejde-390	202	38	8	8	NUM
ejde-390	202	39	n.	n.	PROPN
ejde-390	202	40	s.	s.	PROPN
ejde-390	202	41	papageorgiou	papageorgiou	PROPN
ejde-390	202	42	,	,	PUNCT
ejde-390	202	43	c.	c.	PROPN
ejde-390	202	44	vetro	vetro	PROPN
ejde-390	202	45	,	,	PUNCT
ejde-390	202	46	f.	f.	PROPN
ejde-390	202	47	vetro	vetro	PROPN
ejde-390	202	48	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	202	49	recall	recall	VERB
ejde-390	202	50	that	that	PRON
ejde-390	202	51	q	q	X
ejde-390	203	1	<	<	X
ejde-390	204	1	p.	p.	NOUN
ejde-390	205	1	so	so	ADV
ejde-390	205	2	,	,	PUNCT
ejde-390	205	3	by	by	ADP
ejde-390	205	4	choosing	choose	VERB
ejde-390	205	5	t	t	PROPN
ejde-390	205	6	∈	∈	PROPN
ejde-390	205	7	(	(	PUNCT
ejde-390	205	8	0	0	NUM
ejde-390	205	9	,	,	PUNCT
ejde-390	205	10	1	1	NUM
ejde-390	205	11	)	)	PUNCT
ejde-390	205	12	even	even	ADV
ejde-390	205	13	smaller	small	ADJ
ejde-390	205	14	if	if	SCONJ
ejde-390	205	15	necessary	necessary	ADJ
ejde-390	205	16	,	,	PUNCT
ejde-390	205	17	we	we	PRON
ejde-390	205	18	have	have	VERB
ejde-390	205	19	ϕ̂(tu	ϕ̂(tu	PUNCT
ejde-390	205	20	)	)	PUNCT
ejde-390	205	21	<	<	X
ejde-390	205	22	0	0	NUM
ejde-390	205	23	implies	imply	VERB
ejde-390	205	24	ϕ̂(u0	ϕ̂(u0	NOUN
ejde-390	205	25	)	)	PUNCT
ejde-390	205	26	<	<	X
ejde-390	205	27	0	0	PUNCT
ejde-390	205	28	=	=	SYM
ejde-390	205	29	ϕ̂(0	ϕ̂(0	PROPN
ejde-390	205	30	)	)	PUNCT
ejde-390	205	31	(	(	PUNCT
ejde-390	205	32	see	see	VERB
ejde-390	205	33	(	(	PUNCT
ejde-390	205	34	3.4	3.4	NUM
ejde-390	205	35	)	)	PUNCT
ejde-390	205	36	)	)	PUNCT
ejde-390	205	37	which	which	PRON
ejde-390	205	38	in	in	ADP
ejde-390	205	39	turn	turn	NOUN
ejde-390	205	40	implies	imply	VERB
ejde-390	205	41	u0	u0	ADJ
ejde-390	205	42	6=	6=	PRON
ejde-390	205	43	0	0	NUM
ejde-390	205	44	.	.	PUNCT
ejde-390	206	1	from	from	ADP
ejde-390	206	2	(	(	PUNCT
ejde-390	206	3	3.4	3.4	NUM
ejde-390	206	4	)	)	PUNCT
ejde-390	206	5	we	we	PRON
ejde-390	206	6	have	have	VERB
ejde-390	206	7	that	that	PRON
ejde-390	206	8	ϕ̂′(u0	ϕ̂′(u0	NOUN
ejde-390	206	9	)	)	PUNCT
ejde-390	206	10	=	=	SYM
ejde-390	206	11	0	0	NUM
ejde-390	206	12	implies	imply	VERB
ejde-390	206	13	〈	〈	PROPN
ejde-390	206	14	a(u0	a(u0	NOUN
ejde-390	206	15	)	)	PUNCT
ejde-390	206	16	,	,	PUNCT
ejde-390	207	1	h〉+	h〉+	PROPN
ejde-390	207	2	∫	∫	PROPN
ejde-390	207	3	ω	ω	PROPN
ejde-390	207	4	[	[	X
ejde-390	207	5	ξ(z	ξ(z	X
ejde-390	207	6	)	)	PUNCT
ejde-390	207	7	+	+	NUM
ejde-390	208	1	λ]|u0|p−2u0hdz	λ]|u0|p−2u0hdz	X
ejde-390	208	2	=	=	SYM
ejde-390	208	3	∫	∫	PROPN
ejde-390	208	4	ω	ω	PROPN
ejde-390	208	5	f̂(z	f̂(z	PROPN
ejde-390	208	6	,	,	PUNCT
ejde-390	208	7	u0)hdz	u0)hdz	ADJ
ejde-390	208	8	∀h	∀h	NOUN
ejde-390	208	9	∈w	∈w	PROPN
ejde-390	208	10	1,p(ω	1,p(ω	NUM
ejde-390	208	11	)	)	PUNCT
ejde-390	208	12	.	.	PUNCT
ejde-390	209	1	(	(	PUNCT
ejde-390	209	2	3.7	3.7	NUM
ejde-390	209	3	)	)	PUNCT
ejde-390	209	4	in	in	ADP
ejde-390	209	5	(	(	PUNCT
ejde-390	209	6	3.7	3.7	NUM
ejde-390	209	7	)	)	PUNCT
ejde-390	209	8	first	first	ADV
ejde-390	209	9	we	we	PRON
ejde-390	209	10	choose	choose	VERB
ejde-390	209	11	h	h	NOUN
ejde-390	209	12	=	=	PUNCT
ejde-390	209	13	−u−0	−u−0	SYM
ejde-390	209	14	∈w	∈w	NOUN
ejde-390	209	15	1,p(ω	1,p(ω	NUM
ejde-390	209	16	)	)	PUNCT
ejde-390	209	17	.	.	PUNCT
ejde-390	210	1	then	then	ADV
ejde-390	210	2	c1	c1	PROPN
ejde-390	210	3	p−	p−	VERB
ejde-390	210	4	1	1	NUM
ejde-390	211	1	‖∇u−0	‖∇u−0	PROPN
ejde-390	211	2	‖pp	‖pp	NUM
ejde-390	211	3	+	+	NUM
ejde-390	211	4	∫	∫	PROPN
ejde-390	211	5	ω	ω	PROPN
ejde-390	212	1	[	[	X
ejde-390	212	2	ξ(z	ξ(z	NOUN
ejde-390	212	3	)	)	PUNCT
ejde-390	212	4	+	+	SYM
ejde-390	212	5	λ](u−0	λ](u−0	X
ejde-390	212	6	)	)	PUNCT
ejde-390	212	7	pdz	pdz	NOUN
ejde-390	212	8	≤	≤	NOUN
ejde-390	212	9	0	0	NUM
ejde-390	213	1	(	(	PUNCT
ejde-390	213	2	see	see	VERB
ejde-390	213	3	lemma	lemma	PROPN
ejde-390	213	4	2.2	2.2	NUM
ejde-390	213	5	and	and	CCONJ
ejde-390	213	6	(	(	PUNCT
ejde-390	213	7	3.3	3.3	NUM
ejde-390	213	8	)	)	PUNCT
ejde-390	213	9	)	)	PUNCT
ejde-390	213	10	,	,	PUNCT
ejde-390	213	11	⇒	⇒	NOUN
ejde-390	213	12	c12‖u−0	c12‖u−0	PROPN
ejde-390	213	13	‖p	‖p	PROPN
ejde-390	213	14	≤	≤	ADV
ejde-390	213	15	0	0	NUM
ejde-390	213	16	for	for	ADP
ejde-390	213	17	some	some	DET
ejde-390	213	18	c12	c12	PROPN
ejde-390	213	19	>	>	X
ejde-390	213	20	0	0	PUNCT
ejde-390	214	1	(	(	PUNCT
ejde-390	214	2	recall	recall	NOUN
ejde-390	214	3	λ	λ	X
ejde-390	214	4	>	>	X
ejde-390	214	5	µ	µ	X
ejde-390	214	6	>	>	X
ejde-390	214	7	‖ξ‖∞	‖ξ‖∞	NUM
ejde-390	214	8	)	)	PUNCT
ejde-390	214	9	,	,	PUNCT
ejde-390	214	10	⇒	⇒	PROPN
ejde-390	214	11	u0	u0	PROPN
ejde-390	214	12	≥	≥	PROPN
ejde-390	214	13	0	0	NUM
ejde-390	214	14	,	,	PUNCT
ejde-390	214	15	u0	u0	ADJ
ejde-390	214	16	6=	6=	ADP
ejde-390	214	17	0	0	NUM
ejde-390	214	18	.	.	PUNCT
ejde-390	215	1	next	next	ADJ
ejde-390	215	2	in	in	ADP
ejde-390	215	3	(	(	PUNCT
ejde-390	215	4	3.7	3.7	NUM
ejde-390	215	5	)	)	PUNCT
ejde-390	215	6	we	we	PRON
ejde-390	215	7	choose	choose	VERB
ejde-390	215	8	h	h	NOUN
ejde-390	215	9	=	=	PUNCT
ejde-390	215	10	(	(	PUNCT
ejde-390	215	11	u0	u0	ADJ
ejde-390	215	12	−	−	PROPN
ejde-390	215	13	u)+	u)+	PROPN
ejde-390	215	14	∈w	∈w	NOUN
ejde-390	215	15	1,p(ω	1,p(ω	NUM
ejde-390	215	16	)	)	PUNCT
ejde-390	215	17	.	.	PUNCT
ejde-390	216	1	then	then	ADV
ejde-390	216	2	we	we	PRON
ejde-390	216	3	have	have	VERB
ejde-390	216	4	〈	〈	PROPN
ejde-390	216	5	a(u0	a(u0	NOUN
ejde-390	216	6	)	)	PUNCT
ejde-390	216	7	,	,	PUNCT
ejde-390	216	8	(	(	PUNCT
ejde-390	216	9	u0	u0	ADJ
ejde-390	216	10	−	−	PROPN
ejde-390	216	11	u)+〉+	u)+〉+	NOUN
ejde-390	216	12	∫	∫	PROPN
ejde-390	216	13	ω	ω	PROPN
ejde-390	217	1	[	[	X
ejde-390	217	2	ξ(z	ξ(z	NOUN
ejde-390	217	3	)	)	PUNCT
ejde-390	218	1	+	+	NOUN
ejde-390	218	2	λ]up−1	λ]up−1	X
ejde-390	218	3	0	0	PUNCT
ejde-390	219	1	(	(	PUNCT
ejde-390	219	2	u0	u0	ADJ
ejde-390	219	3	−	−	NOUN
ejde-390	219	4	u)+dz	u)+dz	PROPN
ejde-390	219	5	=	=	SYM
ejde-390	219	6	∫	∫	PROPN
ejde-390	220	1	ω	ω	NUM
ejde-390	220	2	f(z	f(z	PROPN
ejde-390	220	3	,	,	PUNCT
ejde-390	220	4	u)(u0	u)(u0	PROPN
ejde-390	220	5	−	−	NOUN
ejde-390	220	6	u)+dz	u)+dz	PROPN
ejde-390	220	7	(	(	PUNCT
ejde-390	220	8	see	see	VERB
ejde-390	220	9	(	(	PUNCT
ejde-390	220	10	3.3	3.3	NUM
ejde-390	220	11	)	)	PUNCT
ejde-390	220	12	)	)	PUNCT
ejde-390	220	13	,	,	PUNCT
ejde-390	220	14	≤	≤	PROPN
ejde-390	220	15	〈	〈	PROPN
ejde-390	220	16	a(u	a(u	PROPN
ejde-390	220	17	)	)	PUNCT
ejde-390	220	18	,	,	PUNCT
ejde-390	220	19	(	(	PUNCT
ejde-390	220	20	u0	u0	ADJ
ejde-390	220	21	−	−	PROPN
ejde-390	220	22	u)+〉+	u)+〉+	NOUN
ejde-390	220	23	∫	∫	PROPN
ejde-390	220	24	ω	ω	PROPN
ejde-390	221	1	[	[	X
ejde-390	221	2	ξ(z	ξ(z	X
ejde-390	221	3	)	)	PUNCT
ejde-390	221	4	+	+	NUM
ejde-390	221	5	λ]up−1(u0	λ]up−1(u0	PROPN
ejde-390	221	6	−	−	PROPN
ejde-390	221	7	u)+dz	u)+dz	PROPN
ejde-390	221	8	(	(	PUNCT
ejde-390	221	9	see	see	VERB
ejde-390	221	10	(	(	PUNCT
ejde-390	221	11	3.2	3.2	NUM
ejde-390	221	12	)	)	PUNCT
ejde-390	221	13	)	)	PUNCT
ejde-390	221	14	,	,	PUNCT
ejde-390	221	15	which	which	PRON
ejde-390	221	16	implies	imply	VERB
ejde-390	221	17	u0	u0	ADJ
ejde-390	221	18	≤	≤	ADJ
ejde-390	221	19	u	u	NOUN
ejde-390	221	20	(	(	PUNCT
ejde-390	221	21	see	see	VERB
ejde-390	221	22	proposition	proposition	NOUN
ejde-390	221	23	2.5	2.5	NUM
ejde-390	221	24	and	and	CCONJ
ejde-390	221	25	recall	recall	VERB
ejde-390	221	26	that	that	PRON
ejde-390	221	27	λ	λ	PROPN
ejde-390	221	28	>	>	X
ejde-390	221	29	µ	µ	X
ejde-390	221	30	>	>	X
ejde-390	221	31	‖ξ‖∞	‖ξ‖∞	NUM
ejde-390	221	32	)	)	PUNCT
ejde-390	221	33	.	.	PUNCT
ejde-390	222	1	so	so	ADV
ejde-390	222	2	,	,	PUNCT
ejde-390	222	3	we	we	PRON
ejde-390	222	4	have	have	AUX
ejde-390	222	5	proved	prove	VERB
ejde-390	222	6	that	that	DET
ejde-390	222	7	u0	u0	PROPN
ejde-390	222	8	∈	∈	PROPN
ejde-390	223	1	[	[	X
ejde-390	223	2	0	0	NUM
ejde-390	223	3	,	,	PUNCT
ejde-390	223	4	u	u	NOUN
ejde-390	223	5	]	]	X
ejde-390	223	6	,	,	PUNCT
ejde-390	223	7	u0	u0	ADJ
ejde-390	223	8	6=	6=	PRON
ejde-390	223	9	0	0	NUM
ejde-390	223	10	.	.	PUNCT
ejde-390	224	1	(	(	PUNCT
ejde-390	224	2	3.8	3.8	NUM
ejde-390	224	3	)	)	PUNCT
ejde-390	224	4	from	from	ADP
ejde-390	224	5	(	(	PUNCT
ejde-390	224	6	3.3	3.3	NUM
ejde-390	224	7	)	)	PUNCT
ejde-390	224	8	,	,	PUNCT
ejde-390	224	9	(	(	PUNCT
ejde-390	224	10	3.7	3.7	NUM
ejde-390	224	11	)	)	PUNCT
ejde-390	224	12	and	and	CCONJ
ejde-390	224	13	(	(	PUNCT
ejde-390	224	14	3.8	3.8	NUM
ejde-390	224	15	)	)	PUNCT
ejde-390	224	16	it	it	PRON
ejde-390	224	17	follows	follow	VERB
ejde-390	224	18	that	that	SCONJ
ejde-390	224	19	−	−	PROPN
ejde-390	224	20	div	div	PROPN
ejde-390	224	21	a(∇u0(z	a(∇u0(z	PROPN
ejde-390	224	22	)	)	PUNCT
ejde-390	224	23	)	)	PUNCT
ejde-390	225	1	+	+	CCONJ
ejde-390	225	2	[	[	X
ejde-390	225	3	ξ(z	ξ(z	NOUN
ejde-390	225	4	)	)	PUNCT
ejde-390	225	5	+	+	CCONJ
ejde-390	225	6	λ]u0(z)p−1	λ]u0(z)p−1	NOUN
ejde-390	225	7	=	=	PUNCT
ejde-390	225	8	f(z	f(z	PROPN
ejde-390	225	9	,	,	PUNCT
ejde-390	225	10	u0(z	u0(z	NOUN
ejde-390	225	11	)	)	PUNCT
ejde-390	225	12	)	)	PUNCT
ejde-390	225	13	for	for	ADP
ejde-390	225	14	a.a	a.a	PROPN
ejde-390	225	15	.	.	PROPN
ejde-390	225	16	z	z	PROPN
ejde-390	225	17	∈	∈	PROPN
ejde-390	225	18	ω	ω	PROPN
ejde-390	225	19	,	,	PUNCT
ejde-390	225	20	∂u0	∂u0	NOUN
ejde-390	225	21	∂n	∂n	PROPN
ejde-390	225	22	=	=	NOUN
ejde-390	225	23	0	0	NUM
ejde-390	225	24	on	on	ADP
ejde-390	225	25	∂ω	∂ω	PROPN
ejde-390	225	26	.	.	PUNCT
ejde-390	226	1	(	(	PUNCT
ejde-390	226	2	3.9	3.9	NUM
ejde-390	226	3	)	)	PUNCT
ejde-390	226	4	from	from	ADP
ejde-390	226	5	(	(	PUNCT
ejde-390	226	6	3.9	3.9	NUM
ejde-390	226	7	)	)	PUNCT
ejde-390	226	8	and	and	CCONJ
ejde-390	226	9	[	[	X
ejde-390	226	10	10	10	NUM
ejde-390	226	11	,	,	PUNCT
ejde-390	226	12	proposition	proposition	NOUN
ejde-390	226	13	2.10	2.10	NUM
ejde-390	226	14	]	]	PUNCT
ejde-390	226	15	,	,	PUNCT
ejde-390	226	16	we	we	PRON
ejde-390	226	17	have	have	VERB
ejde-390	226	18	u0	u0	ADJ
ejde-390	226	19	∈	∈	PROPN
ejde-390	226	20	l∞(ω	l∞(ω	NOUN
ejde-390	226	21	)	)	PUNCT
ejde-390	226	22	.	.	PUNCT
ejde-390	227	1	then	then	ADV
ejde-390	227	2	the	the	DET
ejde-390	227	3	nonlinear	nonlinear	ADJ
ejde-390	227	4	regularity	regularity	NOUN
ejde-390	227	5	theory	theory	NOUN
ejde-390	227	6	of	of	ADP
ejde-390	227	7	lieberman	lieberman	PROPN
ejde-390	227	8	[	[	X
ejde-390	227	9	7	7	NUM
ejde-390	227	10	]	]	PUNCT
ejde-390	227	11	implies	imply	VERB
ejde-390	227	12	that	that	SCONJ
ejde-390	227	13	u0	u0	PROPN
ejde-390	227	14	∈	∈	PROPN
ejde-390	227	15	c+	c+	X
ejde-390	227	16	\	\	X
ejde-390	227	17	{	{	PUNCT
ejde-390	227	18	0	0	NUM
ejde-390	227	19	}	}	PUNCT
ejde-390	227	20	.	.	PUNCT
ejde-390	228	1	from	from	ADP
ejde-390	228	2	(	(	PUNCT
ejde-390	228	3	3.9	3.9	NUM
ejde-390	228	4	)	)	PUNCT
ejde-390	228	5	and	and	CCONJ
ejde-390	228	6	hypothesis	hypothesis	NOUN
ejde-390	228	7	(	(	PUNCT
ejde-390	228	8	h3)(i	h3)(i	NOUN
ejde-390	228	9	)	)	PUNCT
ejde-390	228	10	,	,	PUNCT
ejde-390	228	11	we	we	PRON
ejde-390	228	12	have	have	VERB
ejde-390	228	13	that	that	DET
ejde-390	228	14	div	div	PROPN
ejde-390	228	15	a(∇u0(z	a(∇u0(z	PROPN
ejde-390	228	16	)	)	PUNCT
ejde-390	228	17	)	)	PUNCT
ejde-390	229	1	≤	≤	NOUN
ejde-390	230	1	[	[	X
ejde-390	230	2	‖η‖∞	‖η‖∞	X
ejde-390	230	3	+	+	CCONJ
ejde-390	230	4	‖ξ‖∞	‖ξ‖∞	PROPN
ejde-390	230	5	+	+	CCONJ
ejde-390	230	6	λ]u0(z)p−1	λ]u0(z)p−1	PROPN
ejde-390	230	7	for	for	ADP
ejde-390	230	8	a.a	a.a	PROPN
ejde-390	230	9	.	.	PROPN
ejde-390	230	10	z	z	PROPN
ejde-390	230	11	∈	∈	PROPN
ejde-390	230	12	ω	ω	PROPN
ejde-390	230	13	.	.	PUNCT
ejde-390	231	1	(	(	PUNCT
ejde-390	231	2	3.10	3.10	NUM
ejde-390	231	3	)	)	PUNCT
ejde-390	231	4	the	the	DET
ejde-390	231	5	nonlinear	nonlinear	ADJ
ejde-390	231	6	maximum	maximum	ADJ
ejde-390	231	7	principle	principle	NOUN
ejde-390	231	8	of	of	ADP
ejde-390	231	9	pucci	pucci	NOUN
ejde-390	231	10	-	-	PUNCT
ejde-390	231	11	serrin	serrin	NOUN
ejde-390	232	1	[	[	X
ejde-390	232	2	15	15	NUM
ejde-390	232	3	,	,	PUNCT
ejde-390	232	4	pp	pp	ADJ
ejde-390	232	5	.	.	NOUN
ejde-390	232	6	111	111	NUM
ejde-390	232	7	,	,	PUNCT
ejde-390	232	8	120	120	NUM
ejde-390	232	9	]	]	PUNCT
ejde-390	232	10	and	and	CCONJ
ejde-390	232	11	(	(	PUNCT
ejde-390	232	12	3.10	3.10	NUM
ejde-390	232	13	)	)	PUNCT
ejde-390	232	14	imply	imply	VERB
ejde-390	232	15	that	that	SCONJ
ejde-390	232	16	u0	u0	PROPN
ejde-390	232	17	∈	∈	PROPN
ejde-390	232	18	d+	d+	PUNCT
ejde-390	232	19	.	.	PUNCT
ejde-390	233	1	therefore	therefore	ADV
ejde-390	233	2	we	we	PRON
ejde-390	233	3	conclude	conclude	VERB
ejde-390	233	4	that	that	SCONJ
ejde-390	233	5	λ	λ	PROPN
ejde-390	233	6	∈	∈	PROPN
ejde-390	233	7	l	l	X
ejde-390	233	8	6=	6=	NOUN
ejde-390	233	9	∅	∅	NOUN
ejde-390	233	10	and	and	CCONJ
ejde-390	233	11	for	for	ADP
ejde-390	233	12	all	all	DET
ejde-390	233	13	λ	λ	PROPN
ejde-390	233	14	∈	∈	PROPN
ejde-390	233	15	l	l	NOUN
ejde-390	233	16	,	,	PUNCT
ejde-390	233	17	∅	∅	NOUN
ejde-390	233	18	6=	6=	X
ejde-390	233	19	sλ	sλ	ADP
ejde-390	233	20	⊆	⊆	NUM
ejde-390	233	21	d+	d+	NOUN
ejde-390	233	22	.	.	PUNCT
ejde-390	234	1	�	�	PROPN
ejde-390	234	2	in	in	ADP
ejde-390	234	3	the	the	DET
ejde-390	234	4	next	next	ADJ
ejde-390	234	5	proposition	proposition	NOUN
ejde-390	234	6	,	,	PUNCT
ejde-390	234	7	we	we	PRON
ejde-390	234	8	prove	prove	VERB
ejde-390	234	9	a	a	DET
ejde-390	234	10	structural	structural	ADJ
ejde-390	234	11	property	property	NOUN
ejde-390	234	12	of	of	ADP
ejde-390	234	13	the	the	DET
ejde-390	234	14	set	set	PROPN
ejde-390	234	15	l	l	NOUN
ejde-390	234	16	,	,	PUNCT
ejde-390	234	17	namely	namely	ADV
ejde-390	234	18	we	we	PRON
ejde-390	234	19	show	show	VERB
ejde-390	234	20	that	that	SCONJ
ejde-390	234	21	l	l	NOUN
ejde-390	234	22	is	be	AUX
ejde-390	234	23	an	an	DET
ejde-390	234	24	upper	upper	ADJ
ejde-390	234	25	half	half	ADJ
ejde-390	234	26	line	line	NOUN
ejde-390	234	27	.	.	PUNCT
ejde-390	235	1	in	in	ADP
ejde-390	235	2	addition	addition	NOUN
ejde-390	235	3	we	we	PRON
ejde-390	235	4	establish	establish	VERB
ejde-390	235	5	a	a	DET
ejde-390	235	6	kind	kind	NOUN
ejde-390	235	7	of	of	ADP
ejde-390	235	8	monotonicity	monotonicity	NOUN
ejde-390	235	9	property	property	NOUN
ejde-390	235	10	for	for	ADP
ejde-390	235	11	the	the	DET
ejde-390	235	12	solution	solution	NOUN
ejde-390	235	13	multifunction	multifunction	NOUN
ejde-390	235	14	λ→	λ→	PUNCT
ejde-390	235	15	sλ	sλ	NOUN
ejde-390	235	16	.	.	PUNCT
ejde-390	236	1	proposition	proposition	NOUN
ejde-390	236	2	3.2	3.2	NUM
ejde-390	236	3	.	.	PUNCT
ejde-390	237	1	if	if	SCONJ
ejde-390	237	2	hypotheses	hypothesis	NOUN
ejde-390	237	3	(	(	PUNCT
ejde-390	237	4	h1)–(h3	h1)–(h3	NOUN
ejde-390	237	5	)	)	PUNCT
ejde-390	237	6	hold	hold	VERB
ejde-390	237	7	,	,	PUNCT
ejde-390	237	8	λ	λ	PROPN
ejde-390	237	9	∈	∈	PROPN
ejde-390	237	10	l	l	NOUN
ejde-390	237	11	,	,	PUNCT
ejde-390	237	12	uλ	uλ	DET
ejde-390	237	13	∈	∈	PROPN
ejde-390	237	14	sλ	sλ	VERB
ejde-390	237	15	⊆	⊆	NUM
ejde-390	237	16	d+	d+	NOUN
ejde-390	237	17	and	and	CCONJ
ejde-390	237	18	η	η	PROPN
ejde-390	237	19	>	>	X
ejde-390	237	20	λ	λ	PROPN
ejde-390	237	21	,	,	PUNCT
ejde-390	237	22	then	then	ADV
ejde-390	237	23	η	η	PROPN
ejde-390	237	24	∈	∈	PROPN
ejde-390	237	25	l	l	NOUN
ejde-390	237	26	and	and	CCONJ
ejde-390	237	27	there	there	PRON
ejde-390	237	28	exists	exist	VERB
ejde-390	237	29	uη	uη	ADP
ejde-390	237	30	∈	∈	PROPN
ejde-390	237	31	sη	sη	VERB
ejde-390	237	32	⊆	⊆	NUM
ejde-390	237	33	d+	d+	NOUN
ejde-390	237	34	such	such	ADJ
ejde-390	237	35	that	that	SCONJ
ejde-390	237	36	uλ	uλ	ADP
ejde-390	237	37	−	−	PROPN
ejde-390	237	38	uη	uη	ADP
ejde-390	237	39	∈	∈	PROPN
ejde-390	237	40	int	int	NOUN
ejde-390	237	41	ĉ+	ĉ+	PROPN
ejde-390	237	42	.	.	PUNCT
ejde-390	238	1	proof	proof	NOUN
ejde-390	238	2	.	.	PUNCT
ejde-390	239	1	we	we	PRON
ejde-390	239	2	have	have	VERB
ejde-390	239	3	−	−	NUM
ejde-390	239	4	div	div	NOUN
ejde-390	239	5	a(∇uλ(z	a(∇uλ(z	NOUN
ejde-390	239	6	)	)	PUNCT
ejde-390	239	7	)	)	PUNCT
ejde-390	240	1	+	+	CCONJ
ejde-390	240	2	[	[	X
ejde-390	240	3	ξ(z	ξ(z	NOUN
ejde-390	240	4	)	)	PUNCT
ejde-390	240	5	+	+	NUM
ejde-390	240	6	λ]uλ(z)p−1	λ]uλ(z)p−1	X
ejde-390	240	7	=	=	SYM
ejde-390	240	8	f(z	f(z	PROPN
ejde-390	240	9	,	,	PUNCT
ejde-390	240	10	uλ(z	uλ(z	NOUN
ejde-390	240	11	)	)	PUNCT
ejde-390	240	12	)	)	PUNCT
ejde-390	240	13	<	<	X
ejde-390	240	14	−div	−div	NOUN
ejde-390	240	15	a(∇uλ(z	a(∇uλ(z	NOUN
ejde-390	240	16	)	)	PUNCT
ejde-390	240	17	)	)	PUNCT
ejde-390	241	1	+	+	CCONJ
ejde-390	241	2	[	[	X
ejde-390	241	3	ξ(z	ξ(z	NOUN
ejde-390	241	4	)	)	PUNCT
ejde-390	241	5	+	+	CCONJ
ejde-390	241	6	η]uλ(z)p−1	η]uλ(z)p−1	NOUN
ejde-390	241	7	for	for	ADP
ejde-390	241	8	a.a	a.a	PROPN
ejde-390	241	9	.	.	PROPN
ejde-390	241	10	z	z	PROPN
ejde-390	241	11	∈	∈	PROPN
ejde-390	241	12	ω	ω	PROPN
ejde-390	241	13	(	(	PUNCT
ejde-390	241	14	since	since	SCONJ
ejde-390	241	15	η	η	PROPN
ejde-390	241	16	>	>	X
ejde-390	241	17	λ	λ	PROPN
ejde-390	241	18	)	)	PUNCT
ejde-390	241	19	.	.	PUNCT
ejde-390	242	1	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	242	2	positive	positive	ADJ
ejde-390	242	3	and	and	CCONJ
ejde-390	242	4	nodal	nodal	ADJ
ejde-390	242	5	solutions	solution	NOUN
ejde-390	242	6	9	9	NUM
ejde-390	242	7	we	we	PRON
ejde-390	242	8	introduce	introduce	VERB
ejde-390	242	9	the	the	DET
ejde-390	242	10	carathéodory	carathéodory	NOUN
ejde-390	242	11	function	function	NOUN
ejde-390	242	12	k(z	k(z	PROPN
ejde-390	242	13	,	,	PUNCT
ejde-390	242	14	x	x	X
ejde-390	242	15	)	)	PUNCT
ejde-390	242	16	=	=	SYM
ejde-390	242	17	{	{	PUNCT
ejde-390	242	18	f(z	f(z	PROPN
ejde-390	242	19	,	,	PUNCT
ejde-390	242	20	x+	x+	PUNCT
ejde-390	242	21	)	)	PUNCT
ejde-390	243	1	+	+	CCONJ
ejde-390	243	2	µ̂(x+)p−1	µ̂(x+)p−1	VERB
ejde-390	243	3	if	if	SCONJ
ejde-390	243	4	x	x	SYM
ejde-390	243	5	≤	≤	X
ejde-390	243	6	uλ(z	uλ(z	NOUN
ejde-390	243	7	)	)	PUNCT
ejde-390	243	8	,	,	PUNCT
ejde-390	243	9	f(z	f(z	PROPN
ejde-390	243	10	,	,	PUNCT
ejde-390	243	11	uλ(z	uλ(z	NOUN
ejde-390	243	12	)	)	PUNCT
ejde-390	243	13	)	)	PUNCT
ejde-390	244	1	+	+	CCONJ
ejde-390	244	2	µ̂uλ(z)p−1	µ̂uλ(z)p−1	VERB
ejde-390	244	3	if	if	SCONJ
ejde-390	244	4	uλ(z	uλ(z	NOUN
ejde-390	244	5	)	)	PUNCT
ejde-390	244	6	<	<	X
ejde-390	244	7	x	x	X
ejde-390	244	8	,	,	PUNCT
ejde-390	244	9	(	(	PUNCT
ejde-390	244	10	3.11	3.11	NUM
ejde-390	244	11	)	)	PUNCT
ejde-390	244	12	where	where	SCONJ
ejde-390	244	13	µ̂	µ̂	DET
ejde-390	244	14	≥	≥	NOUN
ejde-390	244	15	‖ξ‖∞.	‖ξ‖∞.	NUM
ejde-390	244	16	we	we	PRON
ejde-390	244	17	set	set	VERB
ejde-390	244	18	k(z	k(z	PROPN
ejde-390	244	19	,	,	PUNCT
ejde-390	244	20	x	x	X
ejde-390	244	21	)	)	PUNCT
ejde-390	244	22	=	=	SYM
ejde-390	244	23	∫	∫	PROPN
ejde-390	244	24	x	x	SYM
ejde-390	244	25	0	0	PUNCT
ejde-390	244	26	k(z	k(z	PROPN
ejde-390	244	27	,	,	PUNCT
ejde-390	244	28	s)ds	s)ds	PROPN
ejde-390	244	29	and	and	CCONJ
ejde-390	244	30	consider	consider	VERB
ejde-390	244	31	the	the	DET
ejde-390	244	32	c1	c1	NOUN
ejde-390	244	33	-	-	PUNCT
ejde-390	244	34	functional	functional	ADJ
ejde-390	244	35	ψ̂η	ψ̂η	NOUN
ejde-390	244	36	:	:	PUNCT
ejde-390	244	37	w	w	PROPN
ejde-390	244	38	1,p(ω)→	1,p(ω)→	NUM
ejde-390	244	39	r	r	NOUN
ejde-390	244	40	defined	define	VERB
ejde-390	244	41	by	by	ADP
ejde-390	244	42	ψ̂η(u	ψ̂η(u	NOUN
ejde-390	244	43	)	)	PUNCT
ejde-390	244	44	=	=	SYM
ejde-390	244	45	1	1	NUM
ejde-390	244	46	p	p	NOUN
ejde-390	244	47	γ(u	γ(u	PROPN
ejde-390	244	48	)	)	PUNCT
ejde-390	244	49	+	+	NUM
ejde-390	244	50	η	η	X
ejde-390	244	51	+	+	PROPN
ejde-390	244	52	µ̂	µ̂	ADP
ejde-390	244	53	p	p	NOUN
ejde-390	244	54	‖u‖pp	‖u‖pp	NOUN
ejde-390	244	55	−	−	PROPN
ejde-390	244	56	∫	∫	PROPN
ejde-390	244	57	ω	ω	PROPN
ejde-390	244	58	k(z	k(z	PROPN
ejde-390	244	59	,	,	PUNCT
ejde-390	244	60	u)dz	u)dz	PROPN
ejde-390	244	61	for	for	ADP
ejde-390	244	62	all	all	DET
ejde-390	244	63	u	u	NOUN
ejde-390	244	64	∈w	∈w	NOUN
ejde-390	244	65	1,p(ω	1,p(ω	NUM
ejde-390	244	66	)	)	PUNCT
ejde-390	244	67	.	.	PUNCT
ejde-390	245	1	from	from	ADP
ejde-390	245	2	(	(	PUNCT
ejde-390	245	3	3.11	3.11	NUM
ejde-390	245	4	)	)	PUNCT
ejde-390	245	5	and	and	CCONJ
ejde-390	245	6	since	since	SCONJ
ejde-390	245	7	µ̂	µ̂	DET
ejde-390	245	8	≥	≥	NOUN
ejde-390	245	9	‖ξ‖∞	‖ξ‖∞	NUM
ejde-390	245	10	and	and	CCONJ
ejde-390	245	11	η	η	PROPN
ejde-390	245	12	>	>	X
ejde-390	245	13	λ	λ	PROPN
ejde-390	245	14	>	>	X
ejde-390	245	15	0	0	PROPN
ejde-390	245	16	,	,	PUNCT
ejde-390	245	17	we	we	PRON
ejde-390	245	18	see	see	VERB
ejde-390	245	19	that	that	SCONJ
ejde-390	245	20	ψ̂η	ψ̂η	ADP
ejde-390	245	21	(	(	PUNCT
ejde-390	245	22	·	·	PUNCT
ejde-390	245	23	)	)	PUNCT
ejde-390	245	24	is	be	AUX
ejde-390	245	25	coercive	coercive	ADJ
ejde-390	245	26	.	.	PUNCT
ejde-390	246	1	also	also	ADV
ejde-390	246	2	it	it	PRON
ejde-390	246	3	is	be	AUX
ejde-390	246	4	sequentially	sequentially	ADV
ejde-390	246	5	weakly	weakly	ADV
ejde-390	246	6	lower	low	ADJ
ejde-390	246	7	semicontinuous	semicontinuous	ADJ
ejde-390	246	8	.	.	PUNCT
ejde-390	247	1	so	so	ADV
ejde-390	247	2	,	,	PUNCT
ejde-390	247	3	we	we	PRON
ejde-390	247	4	can	can	AUX
ejde-390	247	5	find	find	VERB
ejde-390	247	6	uη	uη	ADP
ejde-390	247	7	∈	∈	PROPN
ejde-390	247	8	w	w	PROPN
ejde-390	247	9	1,p(ω	1,p(ω	NUM
ejde-390	247	10	)	)	PUNCT
ejde-390	247	11	such	such	ADJ
ejde-390	247	12	that	that	DET
ejde-390	247	13	ψ̂η(uη	ψ̂η(uη	NOUN
ejde-390	247	14	)	)	PUNCT
ejde-390	247	15	=	=	SYM
ejde-390	247	16	inf[ψ̂η(u	inf[ψ̂η(u	NOUN
ejde-390	247	17	)	)	PUNCT
ejde-390	247	18	:	:	PUNCT
ejde-390	248	1	u	u	NOUN
ejde-390	248	2	∈w	∈w	VERB
ejde-390	248	3	1,p(ω	1,p(ω	NUM
ejde-390	248	4	)	)	PUNCT
ejde-390	248	5	]	]	PUNCT
ejde-390	248	6	.	.	PUNCT
ejde-390	249	1	(	(	PUNCT
ejde-390	249	2	3.12	3.12	NUM
ejde-390	249	3	)	)	PUNCT
ejde-390	249	4	as	as	SCONJ
ejde-390	249	5	before	before	ADV
ejde-390	249	6	(	(	PUNCT
ejde-390	249	7	see	see	VERB
ejde-390	249	8	the	the	DET
ejde-390	249	9	proof	proof	NOUN
ejde-390	249	10	of	of	ADP
ejde-390	249	11	proposition	proposition	NOUN
ejde-390	249	12	3.1	3.1	NUM
ejde-390	249	13	)	)	PUNCT
ejde-390	249	14	on	on	ADP
ejde-390	249	15	account	account	NOUN
ejde-390	249	16	of	of	ADP
ejde-390	249	17	hypotheses	hypothesis	NOUN
ejde-390	249	18	(	(	PUNCT
ejde-390	249	19	h1)(iv	h1)(iv	NOUN
ejde-390	249	20	)	)	PUNCT
ejde-390	249	21	and	and	CCONJ
ejde-390	249	22	(	(	PUNCT
ejde-390	249	23	h3)(iv	h3)(iv	NOUN
ejde-390	249	24	)	)	PUNCT
ejde-390	249	25	we	we	PRON
ejde-390	249	26	have	have	AUX
ejde-390	249	27	ψ̂η(uη	ψ̂η(uη	VERB
ejde-390	249	28	)	)	PUNCT
ejde-390	249	29	<	<	X
ejde-390	249	30	0	0	PUNCT
ejde-390	249	31	=	=	SYM
ejde-390	249	32	ψ̂η(0	ψ̂η(0	NOUN
ejde-390	249	33	)	)	PUNCT
ejde-390	249	34	⇒	⇒	NOUN
ejde-390	249	35	uη	uη	ADV
ejde-390	249	36	6=	6=	ADP
ejde-390	249	37	0	0	NUM
ejde-390	249	38	.	.	PUNCT
ejde-390	250	1	from	from	ADP
ejde-390	250	2	(	(	PUNCT
ejde-390	250	3	3.12	3.12	NUM
ejde-390	250	4	)	)	PUNCT
ejde-390	250	5	we	we	PRON
ejde-390	250	6	have	have	VERB
ejde-390	250	7	that	that	DET
ejde-390	250	8	ψ̂′η(uη	ψ̂′η(uη	NOUN
ejde-390	250	9	)	)	PUNCT
ejde-390	250	10	=	=	SYM
ejde-390	250	11	0	0	NUM
ejde-390	250	12	implies	imply	VERB
ejde-390	250	13	〈	〈	PROPN
ejde-390	250	14	a(uη	a(uη	NOUN
ejde-390	250	15	)	)	PUNCT
ejde-390	250	16	,	,	PUNCT
ejde-390	250	17	h〉+	h〉+	PROPN
ejde-390	250	18	∫	∫	PROPN
ejde-390	250	19	ω	ω	PROPN
ejde-390	250	20	[	[	X
ejde-390	250	21	ξ(z)+η+µ]|uη|p−2uηhdz	ξ(z)+η+µ]|uη|p−2uηhdz	PROPN
ejde-390	250	22	=	=	PUNCT
ejde-390	250	23	∫	∫	PROPN
ejde-390	250	24	ω	ω	PROPN
ejde-390	250	25	k(z	k(z	PROPN
ejde-390	250	26	,	,	PUNCT
ejde-390	250	27	uη)hdz	uη)hdz	VERB
ejde-390	250	28	∀h	∀h	NOUN
ejde-390	250	29	∈w	∈w	NOUN
ejde-390	250	30	1,p(ω	1,p(ω	NUM
ejde-390	250	31	)	)	PUNCT
ejde-390	250	32	.	.	PUNCT
ejde-390	251	1	(	(	PUNCT
ejde-390	251	2	3.13	3.13	NUM
ejde-390	251	3	)	)	PUNCT
ejde-390	251	4	in	in	ADP
ejde-390	251	5	(	(	PUNCT
ejde-390	251	6	3.13	3.13	NUM
ejde-390	251	7	)	)	PUNCT
ejde-390	251	8	we	we	PRON
ejde-390	251	9	choose	choose	VERB
ejde-390	251	10	h	h	NOUN
ejde-390	251	11	=	=	PUNCT
ejde-390	252	1	−u−η	−u−η	PROPN
ejde-390	252	2	∈	∈	PROPN
ejde-390	252	3	w	w	PROPN
ejde-390	252	4	1,p(ω	1,p(ω	NUM
ejde-390	252	5	)	)	PUNCT
ejde-390	252	6	and	and	CCONJ
ejde-390	252	7	h	h	NOUN
ejde-390	252	8	=	=	SYM
ejde-390	252	9	(	(	PUNCT
ejde-390	252	10	uη	uη	ADP
ejde-390	252	11	−	−	PROPN
ejde-390	252	12	uλ)+	uλ)+	NOUN
ejde-390	252	13	∈	∈	PROPN
ejde-390	252	14	w	w	PROPN
ejde-390	252	15	1,p(ω	1,p(ω	NUM
ejde-390	252	16	)	)	PUNCT
ejde-390	252	17	and	and	CCONJ
ejde-390	252	18	as	as	ADP
ejde-390	252	19	in	in	ADP
ejde-390	252	20	the	the	DET
ejde-390	252	21	proof	proof	NOUN
ejde-390	252	22	of	of	ADP
ejde-390	252	23	proposition	proposition	NOUN
ejde-390	252	24	3.1	3.1	NUM
ejde-390	252	25	,	,	PUNCT
ejde-390	252	26	we	we	PRON
ejde-390	252	27	show	show	VERB
ejde-390	252	28	that	that	SCONJ
ejde-390	252	29	uη	uη	ADP
ejde-390	252	30	∈	∈	PROPN
ejde-390	253	1	[	[	X
ejde-390	253	2	0	0	NUM
ejde-390	253	3	,	,	PUNCT
ejde-390	253	4	uλ	uλ	ADP
ejde-390	253	5	]	]	X
ejde-390	253	6	,	,	PUNCT
ejde-390	253	7	uη	uη	ADP
ejde-390	253	8	6=	6=	PRON
ejde-390	253	9	0	0	NUM
ejde-390	253	10	.	.	PUNCT
ejde-390	254	1	(	(	PUNCT
ejde-390	254	2	3.14	3.14	NUM
ejde-390	254	3	)	)	PUNCT
ejde-390	254	4	from	from	ADP
ejde-390	254	5	(	(	PUNCT
ejde-390	254	6	3.11	3.11	NUM
ejde-390	254	7	)	)	PUNCT
ejde-390	254	8	,	,	PUNCT
ejde-390	254	9	(	(	PUNCT
ejde-390	254	10	3.13	3.13	NUM
ejde-390	254	11	)	)	PUNCT
ejde-390	254	12	and	and	CCONJ
ejde-390	254	13	(	(	PUNCT
ejde-390	254	14	3.14	3.14	NUM
ejde-390	254	15	)	)	PUNCT
ejde-390	254	16	we	we	PRON
ejde-390	254	17	infer	infer	VERB
ejde-390	254	18	that	that	SCONJ
ejde-390	254	19	η	η	PROPN
ejde-390	254	20	∈	∈	PROPN
ejde-390	254	21	l	l	NOUN
ejde-390	254	22	and	and	CCONJ
ejde-390	254	23	uη	uη	ADP
ejde-390	254	24	∈	∈	PROPN
ejde-390	254	25	sη	sη	VERB
ejde-390	254	26	⊆	⊆	NUM
ejde-390	254	27	d+	d+	PUNCT
ejde-390	254	28	(	(	PUNCT
ejde-390	254	29	see	see	VERB
ejde-390	254	30	proposition	proposition	NOUN
ejde-390	254	31	3.1	3.1	NUM
ejde-390	254	32	)	)	PUNCT
ejde-390	254	33	,	,	PUNCT
ejde-390	254	34	uη	uη	ADP
ejde-390	254	35	≤	≤	PROPN
ejde-390	254	36	uλ	uλ	NOUN
ejde-390	254	37	.	.	PUNCT
ejde-390	255	1	let	let	VERB
ejde-390	255	2	ρ	ρ	PROPN
ejde-390	255	3	=	=	NOUN
ejde-390	255	4	‖uλ‖∞	‖uλ‖∞	VERB
ejde-390	255	5	and	and	CCONJ
ejde-390	255	6	let	let	VERB
ejde-390	255	7	ξ̂ρ	ξ̂ρ	PROPN
ejde-390	255	8	>	>	X
ejde-390	255	9	0	0	PUNCT
ejde-390	256	1	be	be	AUX
ejde-390	256	2	as	as	SCONJ
ejde-390	256	3	postulated	postulate	VERB
ejde-390	256	4	by	by	ADP
ejde-390	256	5	hypothesis	hypothesis	NOUN
ejde-390	256	6	(	(	PUNCT
ejde-390	256	7	h3)(v	h3)(v	PROPN
ejde-390	256	8	)	)	PUNCT
ejde-390	256	9	.	.	PUNCT
ejde-390	257	1	we	we	PRON
ejde-390	257	2	have	have	VERB
ejde-390	257	3	−	−	PROPN
ejde-390	257	4	div	div	X
ejde-390	257	5	a(∇uλ	a(∇uλ	NOUN
ejde-390	257	6	)	)	PUNCT
ejde-390	258	1	+	+	CCONJ
ejde-390	259	1	[	[	X
ejde-390	259	2	ξ(z	ξ(z	NOUN
ejde-390	259	3	)	)	PUNCT
ejde-390	259	4	+	+	NUM
ejde-390	259	5	η	η	PROPN
ejde-390	259	6	+	+	PROPN
ejde-390	259	7	ξ̂ρ]u	ξ̂ρ]u	PROPN
ejde-390	259	8	p−1	p−1	PROPN
ejde-390	259	9	λ	λ	PROPN
ejde-390	259	10	=	=	SYM
ejde-390	259	11	f(z	f(z	PROPN
ejde-390	259	12	,	,	PUNCT
ejde-390	259	13	uλ	uλ	NOUN
ejde-390	259	14	)	)	PUNCT
ejde-390	259	15	+	+	NUM
ejde-390	259	16	ξ̂ρu	ξ̂ρu	NOUN
ejde-390	259	17	p−1	p−1	PROPN
ejde-390	259	18	λ	λ	PROPN
ejde-390	259	19	+	+	CCONJ
ejde-390	259	20	(	(	PUNCT
ejde-390	259	21	η	η	PROPN
ejde-390	259	22	−	−	PROPN
ejde-390	259	23	λ)up−1	λ)up−1	PROPN
ejde-390	259	24	λ	λ	PROPN
ejde-390	259	25	(	(	PUNCT
ejde-390	259	26	since	since	SCONJ
ejde-390	259	27	uλ	uλ	DET
ejde-390	259	28	∈	∈	PROPN
ejde-390	259	29	sλ	sλ	NOUN
ejde-390	259	30	)	)	PUNCT
ejde-390	259	31	≥	≥	NOUN
ejde-390	259	32	f(z	f(z	PROPN
ejde-390	259	33	,	,	PUNCT
ejde-390	259	34	uη	uη	ADJ
ejde-390	259	35	)	)	PUNCT
ejde-390	259	36	+	+	NUM
ejde-390	259	37	ξ̂ρu	ξ̂ρu	NOUN
ejde-390	259	38	p−1	p−1	PROPN
ejde-390	259	39	η	η	PROPN
ejde-390	259	40	+	+	PROPN
ejde-390	259	41	(	(	PUNCT
ejde-390	259	42	η	η	PROPN
ejde-390	259	43	−	−	PROPN
ejde-390	259	44	λ)up−1	λ)up−1	PROPN
ejde-390	259	45	η	η	PROPN
ejde-390	259	46	(	(	PUNCT
ejde-390	259	47	see	see	VERB
ejde-390	259	48	(	(	PUNCT
ejde-390	259	49	h3)(v	h3)(v	X
ejde-390	259	50	)	)	PUNCT
ejde-390	259	51	and	and	CCONJ
ejde-390	259	52	recall	recall	VERB
ejde-390	259	53	uη	uη	ADP
ejde-390	259	54	≤	≤	PROPN
ejde-390	259	55	uλ	uλ	NOUN
ejde-390	259	56	)	)	PUNCT
ejde-390	259	57	>	>	X
ejde-390	259	58	−div	−div	NOUN
ejde-390	259	59	a(∇uη	a(∇uη	NUM
ejde-390	259	60	)	)	PUNCT
ejde-390	260	1	+	+	CCONJ
ejde-390	260	2	[	[	X
ejde-390	260	3	ξ(z	ξ(z	NOUN
ejde-390	260	4	)	)	PUNCT
ejde-390	260	5	+	+	NUM
ejde-390	260	6	η	η	PROPN
ejde-390	260	7	+	+	PROPN
ejde-390	260	8	ξ̂ρ]u	ξ̂ρ]u	PROPN
ejde-390	260	9	p−1	p−1	PROPN
ejde-390	260	10	η	η	PROPN
ejde-390	260	11	for	for	ADP
ejde-390	260	12	a.a	a.a	PROPN
ejde-390	260	13	.	.	PROPN
ejde-390	260	14	z	z	PROPN
ejde-390	260	15	∈	∈	PROPN
ejde-390	260	16	ω	ω	NOUN
ejde-390	260	17	(	(	PUNCT
ejde-390	260	18	since	since	SCONJ
ejde-390	260	19	uη	uη	PROPN
ejde-390	260	20	∈	∈	PROPN
ejde-390	260	21	sη	sη	PROPN
ejde-390	260	22	)	)	PUNCT
ejde-390	260	23	.	.	PUNCT
ejde-390	261	1	(	(	PUNCT
ejde-390	261	2	3.15	3.15	NUM
ejde-390	261	3	)	)	PUNCT
ejde-390	261	4	let	let	VERB
ejde-390	261	5	mη	mη	NOUN
ejde-390	261	6	=	=	X
ejde-390	261	7	minω	minω	PROPN
ejde-390	261	8	uη	uη	ADV
ejde-390	261	9	>	>	X
ejde-390	261	10	0	0	PUNCT
ejde-390	262	1	(	(	PUNCT
ejde-390	262	2	recall	recall	VERB
ejde-390	262	3	that	that	PRON
ejde-390	262	4	uη	uη	ADP
ejde-390	262	5	∈	∈	PROPN
ejde-390	262	6	d+	d+	PUNCT
ejde-390	262	7	)	)	PUNCT
ejde-390	262	8	.	.	PUNCT
ejde-390	263	1	we	we	PRON
ejde-390	263	2	have	have	VERB
ejde-390	263	3	(	(	PUNCT
ejde-390	263	4	η	η	PROPN
ejde-390	263	5	−	−	PROPN
ejde-390	263	6	λ)up−1	λ)up−1	PROPN
ejde-390	263	7	η	η	PROPN
ejde-390	263	8	≥	≥	X
ejde-390	263	9	(	(	PUNCT
ejde-390	263	10	η	η	PROPN
ejde-390	263	11	−	−	PROPN
ejde-390	263	12	λ)mp−1	λ)mp−1	PROPN
ejde-390	263	13	η	η	PROPN
ejde-390	263	14	>	>	X
ejde-390	263	15	0	0	PUNCT
ejde-390	264	1	(	(	PUNCT
ejde-390	264	2	since	since	SCONJ
ejde-390	264	3	η	η	PROPN
ejde-390	264	4	>	>	X
ejde-390	264	5	λ	λ	PROPN
ejde-390	264	6	)	)	PUNCT
ejde-390	264	7	.	.	PUNCT
ejde-390	265	1	then	then	ADV
ejde-390	265	2	from	from	ADP
ejde-390	265	3	(	(	PUNCT
ejde-390	265	4	3.15	3.15	NUM
ejde-390	265	5	)	)	PUNCT
ejde-390	265	6	and	and	CCONJ
ejde-390	265	7	proposition	proposition	NOUN
ejde-390	265	8	2.6	2.6	NUM
ejde-390	265	9	,	,	PUNCT
ejde-390	265	10	it	it	PRON
ejde-390	265	11	follows	follow	VERB
ejde-390	265	12	that	that	SCONJ
ejde-390	265	13	uλ	uλ	SCONJ
ejde-390	265	14	−	−	PROPN
ejde-390	265	15	uη	uη	ADP
ejde-390	265	16	∈	∈	PROPN
ejde-390	265	17	int	int	NOUN
ejde-390	265	18	ĉ+	ĉ+	PROPN
ejde-390	265	19	.	.	PUNCT
ejde-390	265	20	�	�	PROPN
ejde-390	265	21	let	let	VERB
ejde-390	265	22	λ∗	λ∗	PROPN
ejde-390	265	23	=	=	SYM
ejde-390	265	24	inf	inf	PROPN
ejde-390	265	25	l.	l.	PROPN
ejde-390	265	26	proposition	proposition	NOUN
ejde-390	265	27	3.3	3.3	NUM
ejde-390	265	28	.	.	PUNCT
ejde-390	266	1	if	if	SCONJ
ejde-390	266	2	hypotheses	hypothesis	NOUN
ejde-390	266	3	(	(	PUNCT
ejde-390	266	4	h1)–(h3	h1)–(h3	NOUN
ejde-390	266	5	)	)	PUNCT
ejde-390	266	6	hold	hold	VERB
ejde-390	266	7	,	,	PUNCT
ejde-390	266	8	then	then	ADV
ejde-390	266	9	λ∗	λ∗	PROPN
ejde-390	266	10	>	>	X
ejde-390	266	11	0	0	X
ejde-390	266	12	.	.	PUNCT
ejde-390	267	1	proof	proof	NOUN
ejde-390	267	2	.	.	PUNCT
ejde-390	268	1	let	let	VERB
ejde-390	268	2	ϕλ	ϕλ	NOUN
ejde-390	268	3	:	:	PUNCT
ejde-390	268	4	w	w	PROPN
ejde-390	268	5	1,p(ω	1,p(ω	NUM
ejde-390	268	6	)	)	PUNCT
ejde-390	269	1	→	→	PUNCT
ejde-390	269	2	r	r	NOUN
ejde-390	269	3	be	be	VERB
ejde-390	269	4	the	the	DET
ejde-390	269	5	energy	energy	NOUN
ejde-390	269	6	(	(	PUNCT
ejde-390	269	7	euler	euler	NOUN
ejde-390	269	8	)	)	PUNCT
ejde-390	269	9	functional	functional	ADJ
ejde-390	269	10	for	for	ADP
ejde-390	269	11	problem	problem	NOUN
ejde-390	269	12	(	(	PUNCT
ejde-390	269	13	1.1	1.1	NUM
ejde-390	269	14	)	)	PUNCT
ejde-390	269	15	defined	define	VERB
ejde-390	269	16	by	by	ADP
ejde-390	269	17	ϕλ(u	ϕλ(u	NUM
ejde-390	269	18	)	)	PUNCT
ejde-390	269	19	=	=	SYM
ejde-390	270	1	1	1	NUM
ejde-390	270	2	p	p	NOUN
ejde-390	270	3	γ(u	γ(u	PROPN
ejde-390	270	4	)	)	PUNCT
ejde-390	271	1	+	+	NUM
ejde-390	271	2	λ	λ	AUX
ejde-390	271	3	p	p	NOUN
ejde-390	271	4	‖u‖pp	‖u‖pp	NOUN
ejde-390	271	5	−	−	PROPN
ejde-390	271	6	∫	∫	PROPN
ejde-390	272	1	ω	ω	NUM
ejde-390	272	2	f	f	PROPN
ejde-390	272	3	(	(	PUNCT
ejde-390	272	4	z	z	PROPN
ejde-390	272	5	,	,	PUNCT
ejde-390	272	6	u)dz	u)dz	PROPN
ejde-390	272	7	for	for	ADP
ejde-390	272	8	all	all	DET
ejde-390	272	9	u	u	NOUN
ejde-390	272	10	∈w	∈w	NOUN
ejde-390	272	11	1,p(ω	1,p(ω	NUM
ejde-390	272	12	)	)	PUNCT
ejde-390	272	13	.	.	PUNCT
ejde-390	273	1	10	10	NUM
ejde-390	273	2	n.	n.	PROPN
ejde-390	273	3	s.	s.	PROPN
ejde-390	273	4	papageorgiou	papageorgiou	PROPN
ejde-390	273	5	,	,	PUNCT
ejde-390	273	6	c.	c.	PROPN
ejde-390	273	7	vetro	vetro	PROPN
ejde-390	273	8	,	,	PUNCT
ejde-390	273	9	f.	f.	PROPN
ejde-390	273	10	vetro	vetro	PROPN
ejde-390	273	11	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	273	12	arguing	argue	VERB
ejde-390	273	13	by	by	ADP
ejde-390	273	14	contradiction	contradiction	NOUN
ejde-390	273	15	,	,	PUNCT
ejde-390	273	16	suppose	suppose	VERB
ejde-390	273	17	that	that	SCONJ
ejde-390	273	18	λ∗	λ∗	NOUN
ejde-390	273	19	=	=	X
ejde-390	273	20	0	0	X
ejde-390	273	21	.	.	PUNCT
ejde-390	274	1	let	let	VERB
ejde-390	274	2	{	{	PUNCT
ejde-390	274	3	λn}n≥1	λn}n≥1	NOUN
ejde-390	274	4	⊆	⊆	NUM
ejde-390	274	5	l	l	NOUN
ejde-390	274	6	such	such	ADJ
ejde-390	274	7	that	that	DET
ejde-390	274	8	λn	λn	PROPN
ejde-390	274	9	↓	↓	PROPN
ejde-390	274	10	0	0	NUM
ejde-390	274	11	.	.	PUNCT
ejde-390	275	1	we	we	PRON
ejde-390	275	2	fix	fix	VERB
ejde-390	275	3	λ	λ	PROPN
ejde-390	275	4	>	>	X
ejde-390	275	5	λ1	λ1	PROPN
ejde-390	275	6	.	.	PUNCT
ejde-390	276	1	for	for	ADP
ejde-390	276	2	every	every	DET
ejde-390	276	3	n	n	PRON
ejde-390	276	4	∈	∈	NOUN
ejde-390	276	5	n	n	NOUN
ejde-390	276	6	and	and	CCONJ
ejde-390	276	7	ûn	ûn	NUM
ejde-390	276	8	∈	∈	NOUN
ejde-390	276	9	sλn	sλn	NOUN
ejde-390	276	10	⊆	⊆	NUM
ejde-390	276	11	d+	d+	NOUN
ejde-390	276	12	,	,	PUNCT
ejde-390	276	13	on	on	ADP
ejde-390	276	14	account	account	NOUN
ejde-390	276	15	of	of	ADP
ejde-390	276	16	proposition	proposition	NOUN
ejde-390	276	17	3.2	3.2	NUM
ejde-390	276	18	and	and	CCONJ
ejde-390	276	19	its	its	PRON
ejde-390	276	20	proof	proof	NOUN
ejde-390	276	21	we	we	PRON
ejde-390	276	22	can	can	AUX
ejde-390	276	23	find	find	VERB
ejde-390	276	24	unλ	unλ	NOUN
ejde-390	276	25	∈	∈	NOUN
ejde-390	276	26	sλ	sλ	NOUN
ejde-390	276	27	⊆	⊆	NUM
ejde-390	276	28	d+	d+	NOUN
ejde-390	276	29	such	such	ADJ
ejde-390	276	30	that	that	SCONJ
ejde-390	276	31	ϕλ(unλ	ϕλ(unλ	PROPN
ejde-390	276	32	)	)	PUNCT
ejde-390	277	1	<	<	X
ejde-390	277	2	0	0	NUM
ejde-390	277	3	,	,	PUNCT
ejde-390	277	4	unλ	unλ	NOUN
ejde-390	277	5	≤	≤	NOUN
ejde-390	277	6	ûn	ûn	NOUN
ejde-390	277	7	.	.	PUNCT
ejde-390	278	1	we	we	PRON
ejde-390	278	2	have	have	VERB
ejde-390	278	3	−	−	NUM
ejde-390	278	4	div	div	X
ejde-390	278	5	a(∇un+1	a(∇un+1	NOUN
ejde-390	278	6	λ	λ	PROPN
ejde-390	278	7	)	)	PUNCT
ejde-390	279	1	+	+	CCONJ
ejde-390	279	2	[	[	X
ejde-390	279	3	ξ(z	ξ(z	NOUN
ejde-390	279	4	)	)	PUNCT
ejde-390	279	5	+	+	NUM
ejde-390	279	6	λn]un+1	λn]un+1	NOUN
ejde-390	279	7	λ	λ	NOUN
ejde-390	279	8	≤	≤	NOUN
ejde-390	279	9	f(z	f(z	PROPN
ejde-390	279	10	,	,	PUNCT
ejde-390	279	11	un+1	un+1	PROPN
ejde-390	279	12	λ	λ	PROPN
ejde-390	279	13	)	)	PUNCT
ejde-390	279	14	for	for	ADP
ejde-390	279	15	a.a	a.a	PROPN
ejde-390	279	16	.	.	PROPN
ejde-390	279	17	z	z	PROPN
ejde-390	279	18	∈	∈	PROPN
ejde-390	279	19	ω	ω	PROPN
ejde-390	279	20	,	,	PUNCT
ejde-390	279	21	(	(	PUNCT
ejde-390	279	22	3.16	3.16	NUM
ejde-390	279	23	)	)	PUNCT
ejde-390	279	24	−div	−div	NOUN
ejde-390	279	25	a(∇ûn+1	a(∇ûn+1	PROPN
ejde-390	279	26	)	)	PUNCT
ejde-390	280	1	+	+	CCONJ
ejde-390	281	1	[	[	X
ejde-390	281	2	ξ(z	ξ(z	NOUN
ejde-390	281	3	)	)	PUNCT
ejde-390	281	4	+	+	CCONJ
ejde-390	281	5	λn]ûp−1	λn]ûp−1	VERB
ejde-390	281	6	n+1	n+1	NUM
ejde-390	281	7	≥	≥	NOUN
ejde-390	281	8	f(z	f(z	PROPN
ejde-390	281	9	,	,	PUNCT
ejde-390	281	10	ûn+1	ûn+1	PROPN
ejde-390	281	11	)	)	PUNCT
ejde-390	281	12	for	for	ADP
ejde-390	281	13	a.a	a.a	PROPN
ejde-390	281	14	.	.	PROPN
ejde-390	281	15	z	z	PROPN
ejde-390	281	16	∈	∈	PROPN
ejde-390	281	17	ω	ω	PROPN
ejde-390	281	18	.	.	PUNCT
ejde-390	282	1	(	(	PUNCT
ejde-390	282	2	3.17	3.17	NUM
ejde-390	282	3	)	)	PUNCT
ejde-390	282	4	with	with	ADP
ejde-390	282	5	µ̂	µ̂	DET
ejde-390	282	6	≥	≥	NOUN
ejde-390	282	7	‖ξ‖∞	‖ξ‖∞	NUM
ejde-390	282	8	we	we	PRON
ejde-390	282	9	introduce	introduce	VERB
ejde-390	282	10	the	the	DET
ejde-390	282	11	carathéodory	carathéodory	NOUN
ejde-390	282	12	function	function	NOUN
ejde-390	282	13	kn(z	kn(z	NOUN
ejde-390	282	14	,	,	PUNCT
ejde-390	282	15	x	x	PRON
ejde-390	282	16	)	)	PUNCT
ejde-390	282	17	=	=	SYM
ejde-390	283	1			PROPN
ejde-390	283	2	f(z	f(z	PROPN
ejde-390	283	3	,	,	PUNCT
ejde-390	283	4	un+1	un+1	PROPN
ejde-390	283	5	λ	λ	X
ejde-390	283	6	(	(	PUNCT
ejde-390	283	7	z	z	NOUN
ejde-390	283	8	)	)	PUNCT
ejde-390	283	9	)	)	PUNCT
ejde-390	284	1	+	+	PUNCT
ejde-390	284	2	µ̂un+1	µ̂un+1	NUM
ejde-390	284	3	λ	λ	PROPN
ejde-390	284	4	(	(	PUNCT
ejde-390	284	5	z)p−1	z)p−1	NOUN
ejde-390	284	6	if	if	SCONJ
ejde-390	284	7	x	x	X
ejde-390	284	8	<	<	X
ejde-390	284	9	un+1	un+1	PROPN
ejde-390	284	10	λ	λ	X
ejde-390	284	11	(	(	PUNCT
ejde-390	284	12	z	z	NOUN
ejde-390	284	13	)	)	PUNCT
ejde-390	284	14	,	,	PUNCT
ejde-390	284	15	f(z	f(z	PROPN
ejde-390	284	16	,	,	PUNCT
ejde-390	284	17	x	x	NOUN
ejde-390	284	18	)	)	PUNCT
ejde-390	284	19	+	+	CCONJ
ejde-390	284	20	µ̂xp−1	µ̂xp−1	PROPN
ejde-390	284	21	if	if	SCONJ
ejde-390	284	22	un+1	un+1	PROPN
ejde-390	284	23	λ	λ	X
ejde-390	284	24	(	(	PUNCT
ejde-390	284	25	z	z	NOUN
ejde-390	284	26	)	)	PUNCT
ejde-390	284	27	≤	≤	NUM
ejde-390	284	28	x	x	SYM
ejde-390	284	29	≤	≤	NUM
ejde-390	284	30	ûn+1(z	ûn+1(z	NOUN
ejde-390	284	31	)	)	PUNCT
ejde-390	284	32	,	,	PUNCT
ejde-390	284	33	f(z	f(z	PROPN
ejde-390	284	34	,	,	PUNCT
ejde-390	284	35	ûn+1(z	ûn+1(z	NOUN
ejde-390	284	36	)	)	PUNCT
ejde-390	284	37	)	)	PUNCT
ejde-390	285	1	+	+	CCONJ
ejde-390	285	2	µ̂ûn+1(z)p−1	µ̂ûn+1(z)p−1	AUX
ejde-390	285	3	if	if	SCONJ
ejde-390	285	4	ûn+1	ûn+1	PROPN
ejde-390	285	5	<	<	X
ejde-390	285	6	x.	x.	X
ejde-390	285	7	(	(	PUNCT
ejde-390	285	8	3.18	3.18	NUM
ejde-390	285	9	)	)	PUNCT
ejde-390	285	10	we	we	PRON
ejde-390	285	11	set	set	VERB
ejde-390	285	12	kn(z	kn(z	NOUN
ejde-390	285	13	,	,	PUNCT
ejde-390	285	14	x	x	X
ejde-390	285	15	)	)	PUNCT
ejde-390	285	16	=	=	SYM
ejde-390	286	1	∫	∫	PROPN
ejde-390	286	2	x	x	SYM
ejde-390	286	3	0	0	NUM
ejde-390	286	4	kn(z	kn(z	NOUN
ejde-390	286	5	,	,	PUNCT
ejde-390	286	6	s)ds	s)ds	PROPN
ejde-390	287	1	and	and	CCONJ
ejde-390	287	2	consider	consider	VERB
ejde-390	287	3	the	the	DET
ejde-390	287	4	c1	c1	NOUN
ejde-390	287	5	-	-	PUNCT
ejde-390	287	6	functional	functional	ADJ
ejde-390	287	7	ϕ̃λn	ϕ̃λn	ADV
ejde-390	288	1	:	:	PUNCT
ejde-390	288	2	w	w	PROPN
ejde-390	288	3	1,p(ω)→	1,p(ω)→	NUM
ejde-390	288	4	r	r	NOUN
ejde-390	288	5	defined	define	VERB
ejde-390	288	6	by	by	ADP
ejde-390	288	7	ϕ̃λn(u	ϕ̃λn(u	NOUN
ejde-390	288	8	)	)	PUNCT
ejde-390	288	9	=	=	SYM
ejde-390	288	10	1	1	NUM
ejde-390	288	11	p	p	NOUN
ejde-390	288	12	γ(u	γ(u	PROPN
ejde-390	288	13	)	)	PUNCT
ejde-390	289	1	+	+	CCONJ
ejde-390	289	2	λn	λn	X
ejde-390	290	1	+	+	CCONJ
ejde-390	290	2	µ̂	µ̂	ADP
ejde-390	290	3	p	p	NOUN
ejde-390	290	4	‖u‖pp	‖u‖pp	NOUN
ejde-390	290	5	−	−	PROPN
ejde-390	290	6	∫	∫	PROPN
ejde-390	290	7	ω	ω	NUM
ejde-390	290	8	kn(z	kn(z	NOUN
ejde-390	290	9	,	,	PUNCT
ejde-390	290	10	u)dz	u)dz	PROPN
ejde-390	290	11	for	for	ADP
ejde-390	290	12	all	all	DET
ejde-390	290	13	u	u	NOUN
ejde-390	290	14	∈w	∈w	NOUN
ejde-390	290	15	1,p(ω	1,p(ω	NUM
ejde-390	290	16	)	)	PUNCT
ejde-390	290	17	,	,	PUNCT
ejde-390	290	18	with	with	ADP
ejde-390	290	19	µ̂	µ̂	DET
ejde-390	290	20	≥	≥	NOUN
ejde-390	290	21	‖ξ‖∞.	‖ξ‖∞.	NUM
ejde-390	290	22	evidently	evidently	ADV
ejde-390	290	23	ϕ̃λn	ϕ̃λn	VERB
ejde-390	290	24	(	(	PUNCT
ejde-390	290	25	·	·	PUNCT
ejde-390	290	26	)	)	PUNCT
ejde-390	290	27	is	be	AUX
ejde-390	290	28	coercive	coercive	ADJ
ejde-390	290	29	(	(	PUNCT
ejde-390	290	30	see	see	VERB
ejde-390	290	31	(	(	PUNCT
ejde-390	290	32	3.18	3.18	NUM
ejde-390	290	33	)	)	PUNCT
ejde-390	290	34	)	)	PUNCT
ejde-390	290	35	and	and	CCONJ
ejde-390	290	36	sequentially	sequentially	ADV
ejde-390	290	37	weakly	weakly	ADV
ejde-390	290	38	lower	low	ADJ
ejde-390	290	39	semicontinuous	semicontinuous	ADJ
ejde-390	290	40	and	and	CCONJ
ejde-390	290	41	so	so	ADV
ejde-390	290	42	we	we	PRON
ejde-390	290	43	can	can	AUX
ejde-390	290	44	find	find	VERB
ejde-390	290	45	un	un	PROPN
ejde-390	290	46	∈w	∈w	PROPN
ejde-390	290	47	1,p(ω	1,p(ω	NUM
ejde-390	290	48	)	)	PUNCT
ejde-390	290	49	such	such	ADJ
ejde-390	290	50	that	that	DET
ejde-390	290	51	ϕ̃λn(un	ϕ̃λn(un	PROPN
ejde-390	290	52	)	)	PUNCT
ejde-390	290	53	=	=	SYM
ejde-390	290	54	inf[ϕ̃λn(u	inf[ϕ̃λn(u	PROPN
ejde-390	290	55	)	)	PUNCT
ejde-390	290	56	:	:	PUNCT
ejde-390	291	1	u	u	NOUN
ejde-390	291	2	∈w	∈w	VERB
ejde-390	291	3	1,p(ω	1,p(ω	NUM
ejde-390	291	4	)	)	PUNCT
ejde-390	291	5	]	]	PUNCT
ejde-390	291	6	,	,	PUNCT
ejde-390	291	7	⇒	⇒	PROPN
ejde-390	291	8	ϕ̃′λn(un	ϕ̃′λn(un	PROPN
ejde-390	291	9	)	)	PUNCT
ejde-390	292	1	=	=	SYM
ejde-390	292	2	0	0	NUM
ejde-390	292	3	,	,	PUNCT
ejde-390	292	4	⇒	⇒	VERB
ejde-390	292	5	〈	〈	PROPN
ejde-390	292	6	a(un	a(un	PROPN
ejde-390	292	7	)	)	PUNCT
ejde-390	292	8	,	,	PUNCT
ejde-390	292	9	h〉+	h〉+	PROPN
ejde-390	292	10	∫	∫	PROPN
ejde-390	292	11	ω	ω	PROPN
ejde-390	293	1	[	[	X
ejde-390	293	2	ξ(z	ξ(z	NOUN
ejde-390	293	3	)	)	PUNCT
ejde-390	294	1	+	+	CCONJ
ejde-390	294	2	λn	λn	X
ejde-390	294	3	+	+	NOUN
ejde-390	294	4	µ̂]|un|p−2unhdz	µ̂]|un|p−2unhdz	NOUN
ejde-390	294	5	=	=	SYM
ejde-390	294	6	∫	∫	PROPN
ejde-390	294	7	ω	ω	NUM
ejde-390	294	8	kn(z	kn(z	NOUN
ejde-390	294	9	,	,	PUNCT
ejde-390	294	10	un)hdz	un)hdz	VERB
ejde-390	294	11	(	(	PUNCT
ejde-390	294	12	3.19	3.19	NUM
ejde-390	294	13	)	)	PUNCT
ejde-390	294	14	for	for	ADP
ejde-390	294	15	all	all	DET
ejde-390	294	16	h	h	NOUN
ejde-390	294	17	∈w	∈w	PROPN
ejde-390	294	18	1,p(ω	1,p(ω	NUM
ejde-390	294	19	)	)	PUNCT
ejde-390	294	20	.	.	PUNCT
ejde-390	295	1	choosing	choose	VERB
ejde-390	295	2	h	h	NOUN
ejde-390	296	1	=	=	PUNCT
ejde-390	296	2	(	(	PUNCT
ejde-390	296	3	unλ	unλ	NOUN
ejde-390	296	4	−	−	NOUN
ejde-390	296	5	un)+	un)+	NOUN
ejde-390	296	6	∈w	∈w	NOUN
ejde-390	296	7	1,p(ω	1,p(ω	NUM
ejde-390	296	8	)	)	PUNCT
ejde-390	296	9	and	and	CCONJ
ejde-390	296	10	h	h	NOUN
ejde-390	296	11	=	=	SYM
ejde-390	296	12	(	(	PUNCT
ejde-390	296	13	un	un	PROPN
ejde-390	296	14	−	−	PROPN
ejde-390	296	15	ûn+1)+	ûn+1)+	PROPN
ejde-390	296	16	∈	∈	PROPN
ejde-390	296	17	w	w	PROPN
ejde-390	296	18	1,p(ω	1,p(ω	NUM
ejde-390	296	19	)	)	PUNCT
ejde-390	296	20	and	and	CCONJ
ejde-390	296	21	using	use	VERB
ejde-390	296	22	(	(	PUNCT
ejde-390	296	23	3.16	3.16	NUM
ejde-390	296	24	)	)	PUNCT
ejde-390	296	25	,	,	PUNCT
ejde-390	296	26	(	(	PUNCT
ejde-390	296	27	3.17	3.17	NUM
ejde-390	296	28	)	)	PUNCT
ejde-390	296	29	and	and	CCONJ
ejde-390	296	30	(	(	PUNCT
ejde-390	296	31	3.18	3.18	NUM
ejde-390	296	32	)	)	PUNCT
ejde-390	296	33	,	,	PUNCT
ejde-390	296	34	we	we	PRON
ejde-390	296	35	show	show	VERB
ejde-390	296	36	(	(	PUNCT
ejde-390	296	37	see	see	VERB
ejde-390	296	38	also	also	ADV
ejde-390	296	39	the	the	DET
ejde-390	296	40	proof	proof	NOUN
ejde-390	296	41	of	of	ADP
ejde-390	296	42	proposition	proposition	NOUN
ejde-390	296	43	3.1	3.1	NUM
ejde-390	296	44	)	)	PUNCT
ejde-390	297	1	that	that	PRON
ejde-390	297	2	un	un	PROPN
ejde-390	297	3	∈	∈	PROPN
ejde-390	297	4	[	[	X
ejde-390	297	5	unλ	unλ	NOUN
ejde-390	297	6	,	,	PUNCT
ejde-390	297	7	ûn+1	ûn+1	PROPN
ejde-390	297	8	]	]	X
ejde-390	297	9	∩d+	∩d+	X
ejde-390	297	10	(	(	PUNCT
ejde-390	297	11	by	by	ADP
ejde-390	297	12	the	the	DET
ejde-390	297	13	nonlinear	nonlinear	ADJ
ejde-390	297	14	regularity	regularity	NOUN
ejde-390	297	15	theory	theory	NOUN
ejde-390	297	16	)	)	PUNCT
ejde-390	297	17	.	.	PUNCT
ejde-390	298	1	we	we	PRON
ejde-390	298	2	have	have	VERB
ejde-390	298	3	ϕ̃λn(unλ	ϕ̃λn(unλ	NUM
ejde-390	298	4	)	)	PUNCT
ejde-390	298	5	≤	≤	NOUN
ejde-390	298	6	1	1	NUM
ejde-390	298	7	p	p	PROPN
ejde-390	298	8	γ(unλ	γ(unλ	PROPN
ejde-390	298	9	)	)	PUNCT
ejde-390	299	1	+	+	CCONJ
ejde-390	299	2	λn	λn	X
ejde-390	299	3	p	p	NOUN
ejde-390	299	4	‖unλ‖pp	‖unλ‖pp	NOUN
ejde-390	299	5	−	−	PROPN
ejde-390	299	6	∫	∫	PROPN
ejde-390	300	1	ω	ω	NUM
ejde-390	300	2	f(z	f(z	PROPN
ejde-390	300	3	,	,	PUNCT
ejde-390	300	4	unλ)unλdz	unλ)unλdz	NOUN
ejde-390	300	5	(	(	PUNCT
ejde-390	300	6	see	see	VERB
ejde-390	300	7	(	(	PUNCT
ejde-390	300	8	3.18	3.18	NUM
ejde-390	300	9	)	)	PUNCT
ejde-390	300	10	)	)	PUNCT
ejde-390	300	11	≤	≤	ADV
ejde-390	300	12	1	1	NUM
ejde-390	300	13	p	p	PROPN
ejde-390	300	14	γ(unλ	γ(unλ	PROPN
ejde-390	300	15	)	)	PUNCT
ejde-390	301	1	+	+	NUM
ejde-390	301	2	λ	λ	X
ejde-390	301	3	p	p	NOUN
ejde-390	301	4	‖unλ‖pp	‖unλ‖pp	NOUN
ejde-390	301	5	−	−	PROPN
ejde-390	302	1	∫	∫	PROPN
ejde-390	303	1	ω	ω	NUM
ejde-390	303	2	pf	pf	X
ejde-390	303	3	(	(	PUNCT
ejde-390	303	4	z	z	NOUN
ejde-390	303	5	,	,	PUNCT
ejde-390	303	6	unλ)dz	unλ)dz	PROPN
ejde-390	304	1	+	+	CCONJ
ejde-390	304	2	‖e‖1	‖e‖1	PROPN
ejde-390	304	3	(	(	PUNCT
ejde-390	304	4	see	see	VERB
ejde-390	304	5	(	(	PUNCT
ejde-390	304	6	h3)(iii	h3)(iii	NOUN
ejde-390	304	7	)	)	PUNCT
ejde-390	304	8	)	)	PUNCT
ejde-390	304	9	≤	≤	ADV
ejde-390	304	10	1	1	NUM
ejde-390	304	11	p	p	PROPN
ejde-390	304	12	γ(unλ	γ(unλ	PROPN
ejde-390	304	13	)	)	PUNCT
ejde-390	305	1	+	+	NUM
ejde-390	305	2	λ	λ	X
ejde-390	305	3	p	p	NOUN
ejde-390	305	4	‖unλ‖pp	‖unλ‖pp	NOUN
ejde-390	305	5	−	−	PROPN
ejde-390	306	1	∫	∫	PROPN
ejde-390	307	1	ω	ω	NUM
ejde-390	307	2	f	f	PROPN
ejde-390	307	3	(	(	PUNCT
ejde-390	307	4	z	z	NOUN
ejde-390	307	5	,	,	PUNCT
ejde-390	307	6	unλ)dz	unλ)dz	PROPN
ejde-390	308	1	+	+	CCONJ
ejde-390	308	2	‖e‖1	‖e‖1	ADJ
ejde-390	308	3	(	(	PUNCT
ejde-390	308	4	since	since	SCONJ
ejde-390	308	5	f	f	PROPN
ejde-390	308	6	≥	≥	NUM
ejde-390	308	7	0	0	NUM
ejde-390	308	8	)	)	PUNCT
ejde-390	308	9	=	=	SYM
ejde-390	308	10	ϕλ(unλ	ϕλ(unλ	PROPN
ejde-390	308	11	)	)	PUNCT
ejde-390	309	1	+	+	CCONJ
ejde-390	309	2	‖e‖1	‖e‖1	ADJ
ejde-390	309	3	<	<	X
ejde-390	309	4	‖e‖1	‖e‖1	PROPN
ejde-390	309	5	,	,	PUNCT
ejde-390	309	6	which	which	PRON
ejde-390	309	7	implies	imply	VERB
ejde-390	309	8	ϕ̃λn(un	ϕ̃λn(un	NOUN
ejde-390	309	9	)	)	PUNCT
ejde-390	309	10	<	<	X
ejde-390	309	11	‖e‖1	‖e‖1	PROPN
ejde-390	309	12	for	for	ADP
ejde-390	309	13	all	all	PRON
ejde-390	309	14	n	n	PRON
ejde-390	309	15	∈	∈	NOUN
ejde-390	309	16	n	n	CCONJ
ejde-390	309	17	(	(	PUNCT
ejde-390	309	18	see	see	VERB
ejde-390	309	19	(	(	PUNCT
ejde-390	309	20	3.19	3.19	NUM
ejde-390	309	21	)	)	PUNCT
ejde-390	309	22	)	)	PUNCT
ejde-390	309	23	.	.	PUNCT
ejde-390	310	1	this	this	PRON
ejde-390	310	2	in	in	ADP
ejde-390	310	3	turn	turn	NOUN
ejde-390	310	4	implies	imply	VERB
ejde-390	310	5	ϕλn(un	ϕλn(un	NOUN
ejde-390	310	6	)	)	PUNCT
ejde-390	310	7	≤	≤	NOUN
ejde-390	310	8	c13	c13	NOUN
ejde-390	310	9	for	for	ADP
ejde-390	310	10	some	some	DET
ejde-390	310	11	c13	c13	NOUN
ejde-390	310	12	>	>	X
ejde-390	310	13	0	0	PUNCT
ejde-390	310	14	and	and	CCONJ
ejde-390	310	15	all	all	PRON
ejde-390	310	16	n	n	ADP
ejde-390	310	17	∈	∈	PROPN
ejde-390	310	18	n	n	CCONJ
ejde-390	310	19	(	(	PUNCT
ejde-390	310	20	see	see	VERB
ejde-390	310	21	(	(	PUNCT
ejde-390	310	22	3.18	3.18	NUM
ejde-390	310	23	)	)	PUNCT
ejde-390	310	24	)	)	PUNCT
ejde-390	310	25	.	.	PUNCT
ejde-390	311	1	therefore	therefore	ADV
ejde-390	311	2	we	we	PRON
ejde-390	311	3	have	have	AUX
ejde-390	311	4	produced	produce	VERB
ejde-390	311	5	a	a	DET
ejde-390	311	6	sequence	sequence	NOUN
ejde-390	311	7	{	{	PUNCT
ejde-390	311	8	un}n≥1	un}n≥1	NOUN
ejde-390	311	9	⊆w	⊆w	NOUN
ejde-390	311	10	1,p(ω	1,p(ω	PROPN
ejde-390	311	11	)	)	PUNCT
ejde-390	311	12	such	such	ADJ
ejde-390	311	13	that	that	SCONJ
ejde-390	311	14	un	un	PROPN
ejde-390	311	15	∈	∈	PROPN
ejde-390	311	16	sλn	sλn	NOUN
ejde-390	312	1	⊆	⊆	NUM
ejde-390	312	2	d+	d+	NOUN
ejde-390	312	3	and	and	CCONJ
ejde-390	312	4	ϕλn(un	ϕλn(un	NOUN
ejde-390	312	5	)	)	PUNCT
ejde-390	312	6	≤	≤	NOUN
ejde-390	312	7	c13	c13	NOUN
ejde-390	312	8	for	for	ADP
ejde-390	312	9	all	all	DET
ejde-390	312	10	n	n	PRON
ejde-390	312	11	∈	∈	PROPN
ejde-390	312	12	n.	n.	NOUN
ejde-390	312	13	(	(	PUNCT
ejde-390	312	14	3.20	3.20	NUM
ejde-390	312	15	)	)	PUNCT
ejde-390	312	16	ejde-2020/12	ejde-2020/12	NOUN
ejde-390	312	17	positive	positive	ADJ
ejde-390	312	18	and	and	CCONJ
ejde-390	312	19	nodal	nodal	ADJ
ejde-390	312	20	solutions	solution	NOUN
ejde-390	312	21	11	11	NUM
ejde-390	312	22	from	from	ADP
ejde-390	312	23	(	(	PUNCT
ejde-390	312	24	3.20	3.20	NUM
ejde-390	312	25	)	)	PUNCT
ejde-390	312	26	we	we	PRON
ejde-390	312	27	have	have	VERB
ejde-390	312	28	〈	〈	PROPN
ejde-390	312	29	a(un	a(un	PROPN
ejde-390	312	30	)	)	PUNCT
ejde-390	312	31	,	,	PUNCT
ejde-390	312	32	h〉+	h〉+	PROPN
ejde-390	312	33	∫	∫	PROPN
ejde-390	312	34	ω	ω	PROPN
ejde-390	313	1	[	[	X
ejde-390	313	2	ξ(z	ξ(z	NOUN
ejde-390	313	3	)	)	PUNCT
ejde-390	313	4	+	+	CCONJ
ejde-390	313	5	λn]up−1	λn]up−1	NOUN
ejde-390	313	6	n	n	NOUN
ejde-390	313	7	hdz	hdz	NOUN
ejde-390	313	8	=	=	SYM
ejde-390	313	9	∫	∫	PROPN
ejde-390	313	10	ω	ω	NUM
ejde-390	313	11	f(z	f(z	PROPN
ejde-390	313	12	,	,	PUNCT
ejde-390	313	13	un)hdz	un)hdz	VERB
ejde-390	313	14	for	for	ADP
ejde-390	313	15	all	all	DET
ejde-390	313	16	h	h	NOUN
ejde-390	313	17	∈w	∈w	PROPN
ejde-390	313	18	1,p(ω	1,p(ω	NUM
ejde-390	313	19	)	)	PUNCT
ejde-390	313	20	,	,	PUNCT
ejde-390	313	21	and	and	CCONJ
ejde-390	313	22	all	all	DET
ejde-390	313	23	n	n	PRON
ejde-390	313	24	∈	∈	PROPN
ejde-390	313	25	n	n	CCONJ
ejde-390	313	26	,	,	PUNCT
ejde-390	313	27	(	(	PUNCT
ejde-390	313	28	3.21	3.21	NUM
ejde-390	313	29	)	)	PUNCT
ejde-390	313	30	γ(un	γ(un	PROPN
ejde-390	313	31	)	)	PUNCT
ejde-390	314	1	+	+	CCONJ
ejde-390	314	2	λn‖un‖pp	λn‖un‖pp	ADJ
ejde-390	314	3	−	−	PROPN
ejde-390	314	4	∫	∫	PROPN
ejde-390	315	1	ω	ω	NUM
ejde-390	315	2	pf	pf	X
ejde-390	315	3	(	(	PUNCT
ejde-390	315	4	z	z	NOUN
ejde-390	315	5	,	,	PUNCT
ejde-390	315	6	un)dz	un)dz	SYM
ejde-390	315	7	≤	≤	ADJ
ejde-390	315	8	pc13	pc13	PROPN
ejde-390	315	9	for	for	ADP
ejde-390	315	10	all	all	DET
ejde-390	315	11	n	n	PRON
ejde-390	315	12	∈	∈	PROPN
ejde-390	315	13	n.	n.	NOUN
ejde-390	315	14	(	(	PUNCT
ejde-390	315	15	3.22	3.22	NUM
ejde-390	315	16	)	)	PUNCT
ejde-390	315	17	in	in	ADP
ejde-390	315	18	(	(	PUNCT
ejde-390	315	19	3.21	3.21	NUM
ejde-390	315	20	)	)	PUNCT
ejde-390	315	21	we	we	PRON
ejde-390	315	22	choose	choose	VERB
ejde-390	315	23	h	h	PROPN
ejde-390	315	24	=	=	SYM
ejde-390	315	25	un	un	PROPN
ejde-390	315	26	∈w	∈w	PROPN
ejde-390	315	27	1,p(ω	1,p(ω	NUM
ejde-390	315	28	)	)	PUNCT
ejde-390	315	29	.	.	PUNCT
ejde-390	316	1	then	then	ADV
ejde-390	316	2	−	−	PROPN
ejde-390	316	3	γ(un)−	γ(un)−	AUX
ejde-390	316	4	λn‖un‖pp	λn‖un‖pp	ADJ
ejde-390	316	5	+	+	CCONJ
ejde-390	316	6	∫	∫	PROPN
ejde-390	316	7	ω	ω	NUM
ejde-390	316	8	f(z	f(z	PROPN
ejde-390	316	9	,	,	PUNCT
ejde-390	316	10	un)undz	un)undz	NOUN
ejde-390	316	11	=	=	SYM
ejde-390	316	12	0	0	NUM
ejde-390	316	13	for	for	ADP
ejde-390	316	14	all	all	DET
ejde-390	316	15	n	n	PRON
ejde-390	316	16	∈	∈	PROPN
ejde-390	316	17	n.	n.	NOUN
ejde-390	316	18	(	(	PUNCT
ejde-390	316	19	3.23	3.23	NUM
ejde-390	316	20	)	)	PUNCT
ejde-390	316	21	we	we	PRON
ejde-390	316	22	add	add	VERB
ejde-390	316	23	(	(	PUNCT
ejde-390	316	24	3.22	3.22	NUM
ejde-390	316	25	)	)	PUNCT
ejde-390	316	26	and	and	CCONJ
ejde-390	316	27	(	(	PUNCT
ejde-390	316	28	3.23	3.23	NUM
ejde-390	316	29	)	)	PUNCT
ejde-390	316	30	to	to	PART
ejde-390	316	31	obtain∫	obtain∫	VERB
ejde-390	316	32	ω	ω	PROPN
ejde-390	317	1	[	[	X
ejde-390	317	2	f(z	f(z	PROPN
ejde-390	317	3	,	,	PUNCT
ejde-390	317	4	un)un	un)un	X
ejde-390	317	5	−	−	PROPN
ejde-390	317	6	pf	pf	PROPN
ejde-390	317	7	(	(	PUNCT
ejde-390	317	8	z	z	NOUN
ejde-390	317	9	,	,	PUNCT
ejde-390	317	10	un)]dz	un)]dz	PROPN
ejde-390	317	11	=	=	SYM
ejde-390	317	12	∫	∫	PROPN
ejde-390	317	13	ω	ω	PROPN
ejde-390	317	14	d(z	d(z	PROPN
ejde-390	317	15	,	,	PUNCT
ejde-390	317	16	un)dz	un)dz	SYM
ejde-390	318	1	≤	≤	PUNCT
ejde-390	318	2	pc13	pc13	PROPN
ejde-390	318	3	for	for	ADP
ejde-390	318	4	all	all	DET
ejde-390	318	5	n	n	PRON
ejde-390	318	6	∈	∈	PROPN
ejde-390	318	7	n.	n.	NOUN
ejde-390	318	8	(	(	PUNCT
ejde-390	318	9	3.24	3.24	NUM
ejde-390	318	10	)	)	PUNCT
ejde-390	318	11	we	we	PRON
ejde-390	318	12	will	will	AUX
ejde-390	318	13	show	show	VERB
ejde-390	318	14	that	that	SCONJ
ejde-390	318	15	{	{	PUNCT
ejde-390	318	16	un}n≥1	un}n≥1	NOUN
ejde-390	318	17	⊆	⊆	NUM
ejde-390	318	18	w	w	PROPN
ejde-390	318	19	1,p(ω	1,p(ω	NUM
ejde-390	318	20	)	)	PUNCT
ejde-390	318	21	is	be	AUX
ejde-390	318	22	bounded	bound	VERB
ejde-390	318	23	.	.	PUNCT
ejde-390	318	24	arguing	argue	VERB
ejde-390	318	25	indirectly	indirectly	ADV
ejde-390	318	26	,	,	PUNCT
ejde-390	318	27	suppose	suppose	VERB
ejde-390	318	28	that	that	SCONJ
ejde-390	318	29	at	at	ADP
ejde-390	318	30	least	least	ADJ
ejde-390	318	31	for	for	ADP
ejde-390	318	32	a	a	DET
ejde-390	318	33	subsequence	subsequence	NOUN
ejde-390	318	34	we	we	PRON
ejde-390	318	35	have	have	VERB
ejde-390	318	36	‖un‖	‖un‖	NOUN
ejde-390	318	37	→	→	SYM
ejde-390	318	38	+	+	PROPN
ejde-390	318	39	∞.	∞.	PROPN
ejde-390	318	40	(	(	PUNCT
ejde-390	318	41	3.25	3.25	NUM
ejde-390	318	42	)	)	PUNCT
ejde-390	318	43	we	we	PRON
ejde-390	318	44	set	set	VERB
ejde-390	318	45	yn	yn	PRON
ejde-390	318	46	=	=	NOUN
ejde-390	318	47	un/‖un‖	un/‖un‖	NOUN
ejde-390	318	48	for	for	ADP
ejde-390	318	49	n	n	DET
ejde-390	318	50	∈	∈	PROPN
ejde-390	318	51	n.	n.	NOUN
ejde-390	318	52	then	then	ADV
ejde-390	318	53	‖yn‖	‖yn‖	PROPN
ejde-390	318	54	=	=	PUNCT
ejde-390	318	55	1	1	NUM
ejde-390	318	56	,	,	PUNCT
ejde-390	318	57	yn	yn	PRON
ejde-390	318	58	≥	≥	NOUN
ejde-390	318	59	0	0	NUM
ejde-390	318	60	for	for	ADP
ejde-390	318	61	all	all	DET
ejde-390	318	62	n	n	PRON
ejde-390	318	63	∈	∈	PROPN
ejde-390	318	64	n.	n.	NOUN
ejde-390	318	65	so	so	ADV
ejde-390	318	66	,	,	PUNCT
ejde-390	318	67	we	we	PRON
ejde-390	318	68	may	may	AUX
ejde-390	318	69	assume	assume	VERB
ejde-390	318	70	that	that	SCONJ
ejde-390	318	71	yn	yn	PROPN
ejde-390	318	72	w−→	w−→	PROPN
ejde-390	318	73	y	y	PROPN
ejde-390	318	74	in	in	ADP
ejde-390	318	75	w	w	PROPN
ejde-390	318	76	1,p(ω	1,p(ω	NUM
ejde-390	318	77	)	)	PUNCT
ejde-390	318	78	and	and	CCONJ
ejde-390	318	79	yn	yn	X
ejde-390	318	80	→	→	SYM
ejde-390	318	81	y	y	PROPN
ejde-390	318	82	in	in	ADP
ejde-390	318	83	lr(ω	lr(ω	PROPN
ejde-390	318	84	)	)	PUNCT
ejde-390	318	85	,	,	PUNCT
ejde-390	318	86	y	y	PROPN
ejde-390	318	87	≥	≥	NUM
ejde-390	318	88	0	0	NUM
ejde-390	318	89	.	.	PUNCT
ejde-390	319	1	first	first	ADV
ejde-390	319	2	,	,	PUNCT
ejde-390	319	3	we	we	PRON
ejde-390	319	4	assume	assume	VERB
ejde-390	319	5	that	that	SCONJ
ejde-390	319	6	y	y	PROPN
ejde-390	319	7	6=	6=	PROPN
ejde-390	319	8	0	0	X
ejde-390	319	9	.	.	PUNCT
ejde-390	320	1	let	let	VERB
ejde-390	320	2	ω+	ω+	NOUN
ejde-390	320	3	=	=	SYM
ejde-390	320	4	{	{	PUNCT
ejde-390	320	5	z	z	PROPN
ejde-390	320	6	∈	∈	PROPN
ejde-390	320	7	ω	ω	NOUN
ejde-390	320	8	:	:	PUNCT
ejde-390	320	9	y(z	y(z	NOUN
ejde-390	320	10	)	)	PUNCT
ejde-390	320	11	>	>	X
ejde-390	320	12	0	0	NUM
ejde-390	320	13	}	}	PUNCT
ejde-390	320	14	.	.	PUNCT
ejde-390	321	1	then	then	ADV
ejde-390	321	2	|ω+|n	|ω+|n	X
ejde-390	321	3	>	>	X
ejde-390	321	4	0	0	PUNCT
ejde-390	322	1	(	(	PUNCT
ejde-390	322	2	recall	recall	VERB
ejde-390	322	3	that	that	SCONJ
ejde-390	322	4	y	y	PROPN
ejde-390	322	5	≥	≥	NUM
ejde-390	322	6	0	0	NUM
ejde-390	322	7	)	)	PUNCT
ejde-390	322	8	.	.	PUNCT
ejde-390	323	1	from	from	ADP
ejde-390	323	2	(	(	PUNCT
ejde-390	323	3	3.25	3.25	NUM
ejde-390	323	4	)	)	PUNCT
ejde-390	323	5	it	it	PRON
ejde-390	323	6	follows	follow	VERB
ejde-390	323	7	that	that	SCONJ
ejde-390	323	8	un(z	un(z	NOUN
ejde-390	323	9	)	)	PUNCT
ejde-390	323	10	→	→	PUNCT
ejde-390	324	1	+	+	NUM
ejde-390	324	2	∞	∞	NUM
ejde-390	324	3	for	for	ADP
ejde-390	324	4	all	all	DET
ejde-390	324	5	z	z	NOUN
ejde-390	324	6	∈	∈	PROPN
ejde-390	324	7	ω+	ω+	NOUN
ejde-390	324	8	.	.	PUNCT
ejde-390	325	1	so	so	ADV
ejde-390	325	2	,	,	PUNCT
ejde-390	325	3	we	we	PRON
ejde-390	325	4	have	have	VERB
ejde-390	325	5	d(z	d(z	NOUN
ejde-390	325	6	,	,	PUNCT
ejde-390	325	7	un(z))→	un(z))→	VERB
ejde-390	326	1	+	+	NOUN
ejde-390	326	2	∞	∞	PROPN
ejde-390	326	3	for	for	ADP
ejde-390	326	4	a.a	a.a	PROPN
ejde-390	326	5	.	.	PROPN
ejde-390	326	6	z	z	PROPN
ejde-390	326	7	∈	∈	PROPN
ejde-390	326	8	ω	ω	PROPN
ejde-390	326	9	(	(	PUNCT
ejde-390	326	10	see	see	VERB
ejde-390	326	11	hypothesis	hypothesis	NOUN
ejde-390	326	12	(	(	PUNCT
ejde-390	326	13	h3)(iii	h3)(iii	NOUN
ejde-390	326	14	)	)	PUNCT
ejde-390	326	15	)	)	PUNCT
ejde-390	326	16	.	.	PUNCT
ejde-390	327	1	this	this	PRON
ejde-390	327	2	implies∫	implies∫	VERB
ejde-390	327	3	ω+	ω+	X
ejde-390	327	4	d(z	d(z	NOUN
ejde-390	327	5	,	,	PUNCT
ejde-390	327	6	un)dz	un)dz	PUNCT
ejde-390	327	7	→	→	SYM
ejde-390	327	8	+	+	NUM
ejde-390	327	9	∞	∞	PROPN
ejde-390	327	10	(	(	PUNCT
ejde-390	327	11	by	by	ADP
ejde-390	327	12	fatou	fatou	NOUN
ejde-390	327	13	’s	’s	PART
ejde-390	327	14	lemma	lemma	PROPN
ejde-390	327	15	)	)	PUNCT
ejde-390	327	16	.	.	PUNCT
ejde-390	328	1	(	(	PUNCT
ejde-390	328	2	3.26	3.26	NUM
ejde-390	328	3	)	)	PUNCT
ejde-390	328	4	from	from	ADP
ejde-390	328	5	hypothesis	hypothesis	NOUN
ejde-390	328	6	(	(	PUNCT
ejde-390	328	7	h3)(iii	h3)(iii	NOUN
ejde-390	328	8	)	)	PUNCT
ejde-390	328	9	we	we	PRON
ejde-390	328	10	have	have	VERB
ejde-390	328	11	d(z	d(z	NOUN
ejde-390	328	12	,	,	PUNCT
ejde-390	328	13	x	x	NOUN
ejde-390	328	14	)	)	PUNCT
ejde-390	328	15	≥	≥	NOUN
ejde-390	328	16	−e(z	−e(z	ADV
ejde-390	328	17	)	)	PUNCT
ejde-390	328	18	for	for	ADP
ejde-390	328	19	a.a	a.a	PROPN
ejde-390	328	20	.	.	PROPN
ejde-390	328	21	z	z	PROPN
ejde-390	328	22	∈	∈	PROPN
ejde-390	328	23	ω	ω	PROPN
ejde-390	328	24	,	,	PUNCT
ejde-390	328	25	all	all	PRON
ejde-390	328	26	x	x	PRON
ejde-390	328	27	≥	≥	NOUN
ejde-390	328	28	0	0	NUM
ejde-390	328	29	.	.	PUNCT
ejde-390	329	1	(	(	PUNCT
ejde-390	329	2	3.27	3.27	NUM
ejde-390	329	3	)	)	PUNCT
ejde-390	329	4	then	then	ADV
ejde-390	329	5	we	we	PRON
ejde-390	329	6	have∫	have∫	VERB
ejde-390	329	7	ω	ω	PROPN
ejde-390	329	8	d(z	d(z	PROPN
ejde-390	329	9	,	,	PUNCT
ejde-390	329	10	un)dz	un)dz	PUNCT
ejde-390	329	11	=	=	SYM
ejde-390	329	12	∫	∫	PROPN
ejde-390	329	13	ω+	ω+	NUM
ejde-390	329	14	d(z	d(z	PROPN
ejde-390	329	15	,	,	PUNCT
ejde-390	329	16	un)dz	un)dz	PUNCT
ejde-390	329	17	+	+	NUM
ejde-390	329	18	∫	∫	PROPN
ejde-390	329	19	ω\ω+	ω\ω+	PROPN
ejde-390	329	20	d(z	d(z	PROPN
ejde-390	329	21	,	,	PUNCT
ejde-390	329	22	un)dz	un)dz	PRON
ejde-390	329	23	≥	≥	PROPN
ejde-390	329	24	∫	∫	PROPN
ejde-390	329	25	ω+	ω+	NUM
ejde-390	329	26	d(z	d(z	PROPN
ejde-390	329	27	,	,	PUNCT
ejde-390	329	28	un)dz	un)dz	PUNCT
ejde-390	329	29	−	−	NOUN
ejde-390	329	30	‖e‖1	‖e‖1	NOUN
ejde-390	329	31	for	for	ADP
ejde-390	329	32	all	all	PRON
ejde-390	329	33	n	n	PRON
ejde-390	329	34	∈	∈	NOUN
ejde-390	329	35	n	n	CCONJ
ejde-390	329	36	(	(	PUNCT
ejde-390	329	37	see	see	VERB
ejde-390	329	38	(	(	PUNCT
ejde-390	329	39	3.27	3.27	NUM
ejde-390	329	40	)	)	PUNCT
ejde-390	329	41	)	)	PUNCT
ejde-390	329	42	,	,	PUNCT
ejde-390	329	43	which	which	PRON
ejde-390	329	44	implies	imply	VERB
ejde-390	329	45	∫	∫	PROPN
ejde-390	329	46	ω	ω	PROPN
ejde-390	329	47	d(z	d(z	PROPN
ejde-390	329	48	,	,	PUNCT
ejde-390	329	49	un)dz	un)dz	PUNCT
ejde-390	329	50	→	→	SYM
ejde-390	329	51	+	+	NUM
ejde-390	329	52	∞	∞	PROPN
ejde-390	329	53	as	as	ADP
ejde-390	329	54	n	n	PROPN
ejde-390	329	55	→	→	SYM
ejde-390	329	56	+	+	NUM
ejde-390	329	57	∞	∞	PROPN
ejde-390	329	58	(	(	PUNCT
ejde-390	329	59	see	see	VERB
ejde-390	329	60	(	(	PUNCT
ejde-390	329	61	3.26	3.26	NUM
ejde-390	329	62	)	)	PUNCT
ejde-390	329	63	)	)	PUNCT
ejde-390	329	64	.	.	PUNCT
ejde-390	330	1	this	this	PRON
ejde-390	330	2	contradicts	contradict	VERB
ejde-390	330	3	(	(	PUNCT
ejde-390	330	4	3.24	3.24	NUM
ejde-390	330	5	)	)	PUNCT
ejde-390	330	6	.	.	PUNCT
ejde-390	331	1	now	now	ADV
ejde-390	331	2	we	we	PRON
ejde-390	331	3	assume	assume	VERB
ejde-390	331	4	that	that	SCONJ
ejde-390	331	5	y	y	PROPN
ejde-390	331	6	=	=	NOUN
ejde-390	331	7	0	0	X
ejde-390	331	8	.	.	PUNCT
ejde-390	332	1	let	let	VERB
ejde-390	332	2	τ	τ	PROPN
ejde-390	332	3	>	>	X
ejde-390	332	4	0	0	PUNCT
ejde-390	333	1	and	and	CCONJ
ejde-390	333	2	set	set	VERB
ejde-390	333	3	vn	vn	PROPN
ejde-390	333	4	=	=	SYM
ejde-390	333	5	(	(	PUNCT
ejde-390	333	6	pτ)1	pτ)1	PROPN
ejde-390	333	7	/	/	SYM
ejde-390	333	8	pyn	pyn	PROPN
ejde-390	333	9	∈w	∈w	NOUN
ejde-390	333	10	1,p(ω	1,p(ω	NUM
ejde-390	333	11	)	)	PUNCT
ejde-390	333	12	for	for	ADP
ejde-390	333	13	all	all	DET
ejde-390	333	14	n	n	PRON
ejde-390	333	15	∈	∈	PROPN
ejde-390	333	16	n.	n.	NOUN
ejde-390	333	17	let	let	VERB
ejde-390	333	18	γ	γ	X
ejde-390	333	19	:	:	PUNCT
ejde-390	333	20	w	w	PROPN
ejde-390	333	21	1,p(ω)→	1,p(ω)→	NUM
ejde-390	333	22	r	r	NOUN
ejde-390	333	23	be	be	VERB
ejde-390	333	24	the	the	DET
ejde-390	333	25	c1	c1	NOUN
ejde-390	333	26	-	-	PUNCT
ejde-390	333	27	functional	functional	ADJ
ejde-390	333	28	defined	define	VERB
ejde-390	333	29	by	by	ADP
ejde-390	333	30	γ(u	γ(u	PROPN
ejde-390	333	31	)	)	PUNCT
ejde-390	333	32	=	=	SYM
ejde-390	333	33	c1	c1	NOUN
ejde-390	333	34	p−	p−	VERB
ejde-390	333	35	1	1	NUM
ejde-390	333	36	‖∇u‖pp	‖∇u‖pp	NOUN
ejde-390	333	37	+	+	NUM
ejde-390	333	38	∫	∫	PROPN
ejde-390	333	39	ω	ω	NUM
ejde-390	333	40	ξ(z)|u|pdz	ξ(z)|u|pdz	NOUN
ejde-390	333	41	for	for	ADP
ejde-390	333	42	all	all	DET
ejde-390	333	43	u	u	NOUN
ejde-390	333	44	∈w	∈w	NOUN
ejde-390	333	45	1,p(ω	1,p(ω	NUM
ejde-390	333	46	)	)	PUNCT
ejde-390	333	47	.	.	PUNCT
ejde-390	334	1	we	we	PRON
ejde-390	334	2	introduce	introduce	VERB
ejde-390	334	3	the	the	DET
ejde-390	334	4	c1	c1	NOUN
ejde-390	334	5	-	-	PUNCT
ejde-390	334	6	functionals	functional	NOUN
ejde-390	334	7	ϕλn	ϕλn	VERB
ejde-390	334	8	:	:	PUNCT
ejde-390	334	9	w	w	PROPN
ejde-390	334	10	1,p(ω)→	1,p(ω)→	NUM
ejde-390	334	11	r	r	PROPN
ejde-390	334	12	,	,	PUNCT
ejde-390	334	13	n	n	PROPN
ejde-390	334	14	∈	∈	PROPN
ejde-390	334	15	n	n	CCONJ
ejde-390	334	16	,	,	PUNCT
ejde-390	334	17	defined	define	VERB
ejde-390	334	18	by	by	ADP
ejde-390	334	19	ϕλn(u	ϕλn(u	PROPN
ejde-390	334	20	)	)	PUNCT
ejde-390	334	21	=	=	SYM
ejde-390	335	1	1	1	NUM
ejde-390	335	2	p	p	NOUN
ejde-390	335	3	γ(u	γ(u	PROPN
ejde-390	335	4	)	)	PUNCT
ejde-390	336	1	+	+	CCONJ
ejde-390	336	2	λn	λn	X
ejde-390	336	3	p	p	NOUN
ejde-390	336	4	‖u‖pp	‖u‖pp	NOUN
ejde-390	336	5	−	−	PROPN
ejde-390	336	6	∫	∫	PROPN
ejde-390	337	1	ω	ω	NUM
ejde-390	337	2	f	f	PROPN
ejde-390	337	3	(	(	PUNCT
ejde-390	337	4	z	z	PROPN
ejde-390	337	5	,	,	PUNCT
ejde-390	337	6	u)dz	u)dz	PROPN
ejde-390	337	7	for	for	ADP
ejde-390	337	8	all	all	DET
ejde-390	337	9	u	u	NOUN
ejde-390	337	10	∈w	∈w	NOUN
ejde-390	337	11	1,p(ω	1,p(ω	NUM
ejde-390	337	12	)	)	PUNCT
ejde-390	337	13	.	.	PUNCT
ejde-390	338	1	12	12	NUM
ejde-390	338	2	n.	n.	PROPN
ejde-390	338	3	s.	s.	PROPN
ejde-390	338	4	papageorgiou	papageorgiou	PROPN
ejde-390	338	5	,	,	PUNCT
ejde-390	338	6	c.	c.	PROPN
ejde-390	338	7	vetro	vetro	PROPN
ejde-390	338	8	,	,	PUNCT
ejde-390	338	9	f.	f.	PROPN
ejde-390	338	10	vetro	vetro	PROPN
ejde-390	338	11	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	338	12	let	let	VERB
ejde-390	338	13	tn	tn	PRON
ejde-390	338	14	∈	∈	PROPN
ejde-390	339	1	[	[	X
ejde-390	339	2	0	0	NUM
ejde-390	339	3	,	,	PUNCT
ejde-390	339	4	1	1	NUM
ejde-390	339	5	]	]	PUNCT
ejde-390	339	6	be	be	AUX
ejde-390	339	7	such	such	ADJ
ejde-390	339	8	that	that	PRON
ejde-390	339	9	ϕλn(tnun	ϕλn(tnun	NOUN
ejde-390	339	10	)	)	PUNCT
ejde-390	339	11	=	=	PUNCT
ejde-390	339	12	max[ϕλn(tun	max[ϕλn(tun	X
ejde-390	339	13	)	)	PUNCT
ejde-390	339	14	:	:	PUNCT
ejde-390	339	15	0	0	NUM
ejde-390	339	16	≤	≤	NUM
ejde-390	339	17	t	t	X
ejde-390	339	18	≤	≤	NOUN
ejde-390	339	19	1	1	NUM
ejde-390	339	20	]	]	PUNCT
ejde-390	339	21	for	for	ADP
ejde-390	339	22	all	all	DET
ejde-390	339	23	n	n	PRON
ejde-390	339	24	∈	∈	PROPN
ejde-390	339	25	n.	n.	NOUN
ejde-390	339	26	(	(	PUNCT
ejde-390	339	27	3.28	3.28	NUM
ejde-390	339	28	)	)	PUNCT
ejde-390	339	29	on	on	ADP
ejde-390	339	30	account	account	NOUN
ejde-390	339	31	of	of	ADP
ejde-390	339	32	(	(	PUNCT
ejde-390	339	33	3.25	3.25	NUM
ejde-390	339	34	)	)	PUNCT
ejde-390	339	35	,	,	PUNCT
ejde-390	339	36	we	we	PRON
ejde-390	339	37	see	see	VERB
ejde-390	339	38	that	that	SCONJ
ejde-390	339	39	we	we	PRON
ejde-390	339	40	can	can	AUX
ejde-390	339	41	find	find	VERB
ejde-390	339	42	n0	n0	ADJ
ejde-390	339	43	∈	∈	PROPN
ejde-390	339	44	n	n	PRON
ejde-390	339	45	such	such	ADJ
ejde-390	339	46	that	that	SCONJ
ejde-390	339	47	(	(	PUNCT
ejde-390	339	48	pτ)1	pτ)1	PROPN
ejde-390	339	49	/	/	SYM
ejde-390	339	50	p	p	NOUN
ejde-390	339	51	1	1	NUM
ejde-390	339	52	‖un‖	‖un‖	NOUN
ejde-390	339	53	≤	≤	NOUN
ejde-390	339	54	1	1	NUM
ejde-390	339	55	for	for	ADP
ejde-390	339	56	all	all	DET
ejde-390	339	57	n	n	PRON
ejde-390	339	58	≥	≥	NOUN
ejde-390	339	59	n0	n0	NUM
ejde-390	339	60	.	.	PUNCT
ejde-390	340	1	(	(	PUNCT
ejde-390	340	2	3.29	3.29	NUM
ejde-390	340	3	)	)	PUNCT
ejde-390	340	4	from	from	ADP
ejde-390	340	5	(	(	PUNCT
ejde-390	340	6	3.28	3.28	NUM
ejde-390	340	7	)	)	PUNCT
ejde-390	340	8	and	and	CCONJ
ejde-390	340	9	(	(	PUNCT
ejde-390	340	10	3.29	3.29	NUM
ejde-390	340	11	)	)	PUNCT
ejde-390	340	12	it	it	PRON
ejde-390	340	13	follows	follow	VERB
ejde-390	340	14	that	that	SCONJ
ejde-390	340	15	ϕλn(tnun	ϕλn(tnun	PROPN
ejde-390	340	16	)	)	PUNCT
ejde-390	340	17	≥	≥	NOUN
ejde-390	340	18	ϕλn(vn	ϕλn(vn	NUM
ejde-390	340	19	)	)	PUNCT
ejde-390	341	1	=	=	PUNCT
ejde-390	341	2	τ	τ	PROPN
ejde-390	342	1	[	[	X
ejde-390	342	2	γ(yn	γ(yn	X
ejde-390	342	3	)	)	PUNCT
ejde-390	342	4	+	+	CCONJ
ejde-390	343	1	[	[	X
ejde-390	343	2	λn	λn	X
ejde-390	343	3	+	+	CCONJ
ejde-390	343	4	µ̂]‖yn‖pp]−	µ̂]‖yn‖pp]−	PROPN
ejde-390	343	5	∫	∫	PROPN
ejde-390	343	6	ω	ω	PROPN
ejde-390	344	1	[	[	X
ejde-390	344	2	f	f	X
ejde-390	344	3	(	(	PUNCT
ejde-390	344	4	z	z	NOUN
ejde-390	344	5	,	,	PUNCT
ejde-390	344	6	vn	vn	PROPN
ejde-390	344	7	)	)	PUNCT
ejde-390	345	1	+	+	CCONJ
ejde-390	345	2	µ̂	µ̂	ADP
ejde-390	345	3	p	p	PRON
ejde-390	345	4	vpn]dz	vpn]dz	NOUN
ejde-390	345	5	for	for	ADP
ejde-390	345	6	all	all	DET
ejde-390	345	7	n	n	PRON
ejde-390	345	8	≥	≥	NOUN
ejde-390	345	9	n0	n0	NUM
ejde-390	345	10	,	,	PUNCT
ejde-390	345	11	with	with	ADP
ejde-390	345	12	µ̂	µ̂	DET
ejde-390	345	13	≥	≥	NOUN
ejde-390	345	14	‖ξ‖∞	‖ξ‖∞	NUM
ejde-390	345	15	≥	≥	PRON
ejde-390	346	1	τc14	τc14	PROPN
ejde-390	346	2	−	−	PROPN
ejde-390	346	3	∫	∫	PROPN
ejde-390	346	4	ω	ω	PROPN
ejde-390	347	1	[	[	X
ejde-390	347	2	f	f	X
ejde-390	347	3	(	(	PUNCT
ejde-390	347	4	z	z	NOUN
ejde-390	347	5	,	,	PUNCT
ejde-390	347	6	vn	vn	PROPN
ejde-390	347	7	)	)	PUNCT
ejde-390	348	1	+	+	CCONJ
ejde-390	348	2	µ̂	µ̂	ADP
ejde-390	348	3	p	p	PRON
ejde-390	348	4	vpn]dz	vpn]dz	NOUN
ejde-390	348	5	for	for	ADP
ejde-390	348	6	some	some	DET
ejde-390	348	7	c14	c14	NOUN
ejde-390	348	8	>	>	X
ejde-390	348	9	0	0	PROPN
ejde-390	348	10	,	,	PUNCT
ejde-390	348	11	all	all	DET
ejde-390	348	12	n	n	PRON
ejde-390	348	13	≥	≥	NOUN
ejde-390	348	14	n0	n0	NUM
ejde-390	348	15	(	(	PUNCT
ejde-390	348	16	since	since	SCONJ
ejde-390	348	17	µ̂	µ̂	PRON
ejde-390	348	18	≥	≥	NOUN
ejde-390	348	19	‖ξ‖∞	‖ξ‖∞	NUM
ejde-390	348	20	)	)	PUNCT
ejde-390	348	21	.	.	PUNCT
ejde-390	349	1	(	(	PUNCT
ejde-390	349	2	3.30	3.30	NUM
ejde-390	349	3	)	)	PUNCT
ejde-390	349	4	evidently	evidently	ADV
ejde-390	349	5	∫	∫	PROPN
ejde-390	350	1	ω	ω	PROPN
ejde-390	351	1	[	[	X
ejde-390	351	2	f	f	X
ejde-390	351	3	(	(	PUNCT
ejde-390	351	4	z	z	NOUN
ejde-390	351	5	,	,	PUNCT
ejde-390	351	6	vn	vn	PROPN
ejde-390	351	7	)	)	PUNCT
ejde-390	352	1	+	+	CCONJ
ejde-390	352	2	µ̂	µ̂	ADP
ejde-390	352	3	p	p	NOUN
ejde-390	352	4	v	v	ADP
ejde-390	352	5	p	p	X
ejde-390	352	6	n]dz	n]dz	PROPN
ejde-390	352	7	→	→	SYM
ejde-390	352	8	0	0	NUM
ejde-390	352	9	as	as	ADP
ejde-390	352	10	n→	n→	ADV
ejde-390	352	11	+	+	PROPN
ejde-390	352	12	∞	∞	PROPN
ejde-390	352	13	(	(	PUNCT
ejde-390	352	14	recall	recall	VERB
ejde-390	352	15	y	y	PROPN
ejde-390	352	16	=	=	PROPN
ejde-390	352	17	0	0	NUM
ejde-390	352	18	)	)	PUNCT
ejde-390	352	19	.	.	PUNCT
ejde-390	353	1	hence	hence	ADV
ejde-390	353	2	from	from	ADP
ejde-390	353	3	(	(	PUNCT
ejde-390	353	4	3.30	3.30	NUM
ejde-390	353	5	)	)	PUNCT
ejde-390	353	6	it	it	PRON
ejde-390	353	7	follows	follow	VERB
ejde-390	353	8	that	that	SCONJ
ejde-390	353	9	ϕλn(tnun	ϕλn(tnun	PROPN
ejde-390	353	10	)	)	PUNCT
ejde-390	353	11	≥	≥	NOUN
ejde-390	353	12	τ	τ	PROPN
ejde-390	353	13	2	2	NUM
ejde-390	353	14	c14	c14	NOUN
ejde-390	353	15	for	for	ADP
ejde-390	353	16	all	all	DET
ejde-390	353	17	n	n	PRON
ejde-390	353	18	≥	≥	NOUN
ejde-390	353	19	n1	n1	PROPN
ejde-390	353	20	≥	≥	PROPN
ejde-390	353	21	n0	n0	NUM
ejde-390	353	22	.	.	PUNCT
ejde-390	354	1	since	since	SCONJ
ejde-390	354	2	τ	τ	PROPN
ejde-390	354	3	>	>	X
ejde-390	354	4	0	0	NUM
ejde-390	354	5	is	be	AUX
ejde-390	354	6	arbitrary	arbitrary	ADJ
ejde-390	354	7	,	,	PUNCT
ejde-390	354	8	we	we	PRON
ejde-390	354	9	infer	infer	VERB
ejde-390	354	10	that	that	SCONJ
ejde-390	354	11	ϕλn(tnun)→	ϕλn(tnun)→	PRON
ejde-390	355	1	+	+	NOUN
ejde-390	355	2	∞	∞	NUM
ejde-390	355	3	as	as	ADP
ejde-390	355	4	n→	n→	ADV
ejde-390	355	5	+	+	PROPN
ejde-390	355	6	∞.	∞.	PROPN
ejde-390	355	7	(	(	PUNCT
ejde-390	355	8	3.31	3.31	NUM
ejde-390	355	9	)	)	PUNCT
ejde-390	355	10	we	we	PRON
ejde-390	355	11	have	have	VERB
ejde-390	355	12	ϕλn(0	ϕλn(0	ADJ
ejde-390	355	13	)	)	PUNCT
ejde-390	356	1	=	=	SYM
ejde-390	356	2	0	0	NUM
ejde-390	356	3	and	and	CCONJ
ejde-390	356	4	ϕλn(un	ϕλn(un	NOUN
ejde-390	356	5	)	)	PUNCT
ejde-390	356	6	≤	≤	NUM
ejde-390	356	7	ϕλn(un	ϕλn(un	NOUN
ejde-390	356	8	)	)	PUNCT
ejde-390	356	9	≤	≤	NOUN
ejde-390	356	10	c13	c13	NOUN
ejde-390	356	11	for	for	ADP
ejde-390	356	12	all	all	PRON
ejde-390	356	13	n	n	PRON
ejde-390	356	14	∈	∈	PROPN
ejde-390	356	15	n	n	CCONJ
ejde-390	356	16	(	(	PUNCT
ejde-390	356	17	see	see	VERB
ejde-390	356	18	(	(	PUNCT
ejde-390	356	19	3.20	3.20	NUM
ejde-390	356	20	)	)	PUNCT
ejde-390	356	21	)	)	PUNCT
ejde-390	356	22	.	.	PUNCT
ejde-390	357	1	then	then	ADV
ejde-390	357	2	on	on	ADP
ejde-390	357	3	account	account	NOUN
ejde-390	357	4	of	of	ADP
ejde-390	357	5	(	(	PUNCT
ejde-390	357	6	3.31	3.31	NUM
ejde-390	357	7	)	)	PUNCT
ejde-390	357	8	,	,	PUNCT
ejde-390	357	9	we	we	PRON
ejde-390	357	10	have	have	VERB
ejde-390	357	11	tn	tn	NOUN
ejde-390	357	12	∈	∈	PROPN
ejde-390	357	13	(	(	PUNCT
ejde-390	357	14	0	0	NUM
ejde-390	357	15	,	,	PUNCT
ejde-390	357	16	1	1	NUM
ejde-390	357	17	)	)	PUNCT
ejde-390	357	18	for	for	ADP
ejde-390	357	19	all	all	DET
ejde-390	357	20	n	n	PRON
ejde-390	357	21	≥	≥	NOUN
ejde-390	357	22	n2	n2	NOUN
ejde-390	357	23	.	.	PUNCT
ejde-390	358	1	(	(	PUNCT
ejde-390	358	2	3.32	3.32	NUM
ejde-390	358	3	)	)	PUNCT
ejde-390	358	4	from	from	ADP
ejde-390	358	5	(	(	PUNCT
ejde-390	358	6	3.28	3.28	NUM
ejde-390	358	7	)	)	PUNCT
ejde-390	358	8	and	and	CCONJ
ejde-390	358	9	(	(	PUNCT
ejde-390	358	10	3.32	3.32	NUM
ejde-390	358	11	)	)	PUNCT
ejde-390	358	12	it	it	PRON
ejde-390	358	13	follows	follow	VERB
ejde-390	358	14	that	that	SCONJ
ejde-390	358	15	d	d	NOUN
ejde-390	358	16	dt	dt	NOUN
ejde-390	358	17	ϕλn(tun	ϕλn(tun	NUM
ejde-390	358	18	)	)	PUNCT
ejde-390	358	19	∣∣	∣∣	PROPN
ejde-390	358	20	t	t	PROPN
ejde-390	358	21	=	=	SYM
ejde-390	358	22	tn	tn	NOUN
ejde-390	358	23	=	=	SYM
ejde-390	358	24	0	0	NUM
ejde-390	358	25	for	for	ADP
ejde-390	358	26	all	all	DET
ejde-390	358	27	n	n	PRON
ejde-390	358	28	≥	≥	NOUN
ejde-390	358	29	n2	n2	NOUN
ejde-390	358	30	,	,	PUNCT
ejde-390	358	31	⇒	⇒	NOUN
ejde-390	358	32	〈	〈	PROPN
ejde-390	358	33	ϕ′λn(tnun	ϕ′λn(tnun	PROPN
ejde-390	358	34	)	)	PUNCT
ejde-390	358	35	,	,	PUNCT
ejde-390	358	36	tnun	tnun	VERB
ejde-390	358	37	〉	〉	NOUN
ejde-390	358	38	=	=	SYM
ejde-390	358	39	0	0	NUM
ejde-390	358	40	for	for	ADP
ejde-390	358	41	all	all	DET
ejde-390	358	42	n	n	PRON
ejde-390	358	43	≥	≥	NOUN
ejde-390	358	44	n2	n2	NOUN
ejde-390	358	45	(	(	PUNCT
ejde-390	358	46	by	by	ADP
ejde-390	358	47	the	the	DET
ejde-390	358	48	chain	chain	NOUN
ejde-390	358	49	rule	rule	NOUN
ejde-390	358	50	)	)	PUNCT
ejde-390	358	51	,	,	PUNCT
ejde-390	358	52	⇒	⇒	PROPN
ejde-390	358	53	c1	c1	PROPN
ejde-390	358	54	p−	p−	VERB
ejde-390	358	55	1	1	NUM
ejde-390	358	56	‖∇(tnun)‖pp	‖∇(tnun)‖pp	NOUN
ejde-390	358	57	+	+	CCONJ
ejde-390	358	58	∫	∫	PROPN
ejde-390	358	59	ω	ω	PROPN
ejde-390	359	1	[	[	X
ejde-390	359	2	ξ(z	ξ(z	NOUN
ejde-390	359	3	)	)	PUNCT
ejde-390	360	1	+	+	NUM
ejde-390	360	2	λn](tnun)pdz	λn](tnun)pdz	NOUN
ejde-390	360	3	=	=	SYM
ejde-390	360	4	∫	∫	PROPN
ejde-390	360	5	ω	ω	NUM
ejde-390	360	6	f(z	f(z	PROPN
ejde-390	360	7	,	,	PUNCT
ejde-390	360	8	tnun)(tnun)dz	tnun)(tnun)dz	NOUN
ejde-390	360	9	for	for	ADP
ejde-390	360	10	all	all	DET
ejde-390	360	11	n	n	PRON
ejde-390	360	12	≥	≥	NOUN
ejde-390	360	13	n2	n2	NOUN
ejde-390	360	14	,	,	PUNCT
ejde-390	360	15	⇒	⇒	NOUN
ejde-390	360	16	pϕλn(tnun	pϕλn(tnun	PROPN
ejde-390	360	17	)	)	PUNCT
ejde-390	360	18	≤	≤	NUM
ejde-390	360	19	∫	∫	PROPN
ejde-390	360	20	ω	ω	PROPN
ejde-390	360	21	d(z	d(z	PROPN
ejde-390	360	22	,	,	PUNCT
ejde-390	360	23	tnun)dz	tnun)dz	NUM
ejde-390	360	24	≤	≤	NUM
ejde-390	360	25	∫	∫	PROPN
ejde-390	360	26	ω	ω	PROPN
ejde-390	360	27	d(z	d(z	PROPN
ejde-390	360	28	,	,	PUNCT
ejde-390	360	29	un)dz	un)dz	X
ejde-390	360	30	+	+	CCONJ
ejde-390	360	31	‖e‖1	‖e‖1	NOUN
ejde-390	360	32	for	for	ADP
ejde-390	360	33	all	all	PRON
ejde-390	360	34	n	n	DET
ejde-390	360	35	≥	≥	NOUN
ejde-390	360	36	n2	n2	NOUN
ejde-390	360	37	(	(	PUNCT
ejde-390	360	38	see	see	VERB
ejde-390	360	39	hypothesis	hypothesis	NOUN
ejde-390	360	40	(	(	PUNCT
ejde-390	360	41	h3	h3	NOUN
ejde-390	360	42	)	)	PUNCT
ejde-390	360	43	(	(	PUNCT
ejde-390	360	44	iii	iii	NOUN
ejde-390	360	45	)	)	PUNCT
ejde-390	360	46	and	and	CCONJ
ejde-390	360	47	(	(	PUNCT
ejde-390	360	48	3.32	3.32	NUM
ejde-390	360	49	)	)	PUNCT
ejde-390	360	50	)	)	PUNCT
ejde-390	360	51	,	,	PUNCT
ejde-390	360	52	⇒	⇒	PROPN
ejde-390	360	53	pϕλn(tnun	pϕλn(tnun	PROPN
ejde-390	360	54	)	)	PUNCT
ejde-390	360	55	≤	≤	PUNCT
ejde-390	361	1	pc13	pc13	PROPN
ejde-390	361	2	+	+	CCONJ
ejde-390	361	3	‖e‖1	‖e‖1	NOUN
ejde-390	361	4	for	for	ADP
ejde-390	361	5	all	all	PRON
ejde-390	361	6	n	n	DET
ejde-390	361	7	≥	≥	NOUN
ejde-390	361	8	n2	n2	NOUN
ejde-390	361	9	(	(	PUNCT
ejde-390	361	10	see	see	VERB
ejde-390	361	11	(	(	PUNCT
ejde-390	361	12	3.24	3.24	NUM
ejde-390	361	13	)	)	PUNCT
ejde-390	361	14	)	)	PUNCT
ejde-390	361	15	,	,	PUNCT
ejde-390	361	16	which	which	PRON
ejde-390	361	17	contradicts	contradict	VERB
ejde-390	361	18	(	(	PUNCT
ejde-390	361	19	3.31	3.31	NUM
ejde-390	361	20	)	)	PUNCT
ejde-390	361	21	.	.	PUNCT
ejde-390	362	1	so	so	ADV
ejde-390	362	2	,	,	PUNCT
ejde-390	362	3	we	we	PRON
ejde-390	362	4	have	have	VERB
ejde-390	362	5	that	that	PRON
ejde-390	362	6	{	{	PUNCT
ejde-390	362	7	un}n≥1	un}n≥1	NOUN
ejde-390	362	8	⊆w	⊆w	PROPN
ejde-390	362	9	1,p(ω	1,p(ω	PROPN
ejde-390	362	10	)	)	PUNCT
ejde-390	362	11	is	be	AUX
ejde-390	362	12	bounded	bound	VERB
ejde-390	362	13	.	.	PUNCT
ejde-390	363	1	we	we	PRON
ejde-390	363	2	may	may	AUX
ejde-390	363	3	assume	assume	VERB
ejde-390	363	4	that	that	SCONJ
ejde-390	363	5	un	un	PROPN
ejde-390	363	6	w−→	w−→	PROPN
ejde-390	363	7	u∗	u∗	ADJ
ejde-390	363	8	in	in	ADP
ejde-390	363	9	w	w	PROPN
ejde-390	363	10	1,p(ω	1,p(ω	NUM
ejde-390	363	11	)	)	PUNCT
ejde-390	363	12	and	and	CCONJ
ejde-390	363	13	un	un	PROPN
ejde-390	363	14	→	→	X
ejde-390	363	15	u∗	u∗	PROPN
ejde-390	363	16	in	in	ADP
ejde-390	363	17	lr(ω	lr(ω	NOUN
ejde-390	363	18	)	)	PUNCT
ejde-390	363	19	.	.	PUNCT
ejde-390	364	1	(	(	PUNCT
ejde-390	364	2	3.33	3.33	NUM
ejde-390	364	3	)	)	PUNCT
ejde-390	364	4	in	in	ADP
ejde-390	364	5	(	(	PUNCT
ejde-390	364	6	3.21	3.21	NUM
ejde-390	364	7	)	)	PUNCT
ejde-390	364	8	we	we	PRON
ejde-390	364	9	choose	choose	VERB
ejde-390	364	10	h	h	PROPN
ejde-390	364	11	=	=	SYM
ejde-390	364	12	un	un	PROPN
ejde-390	364	13	−	−	PROPN
ejde-390	364	14	u∗	u∗	PROPN
ejde-390	364	15	∈w	∈w	PROPN
ejde-390	364	16	1,p(ω	1,p(ω	NUM
ejde-390	364	17	)	)	PUNCT
ejde-390	364	18	,	,	PUNCT
ejde-390	364	19	pass	pass	VERB
ejde-390	364	20	to	to	ADP
ejde-390	364	21	the	the	DET
ejde-390	364	22	limit	limit	NOUN
ejde-390	364	23	as	as	ADP
ejde-390	364	24	n→	n→	ADV
ejde-390	364	25	+	+	PROPN
ejde-390	364	26	∞	∞	NOUN
ejde-390	364	27	and	and	CCONJ
ejde-390	364	28	use	use	NOUN
ejde-390	364	29	(	(	PUNCT
ejde-390	364	30	3.33	3.33	NUM
ejde-390	364	31	)	)	PUNCT
ejde-390	364	32	.	.	PUNCT
ejde-390	365	1	then	then	ADV
ejde-390	365	2	we	we	PRON
ejde-390	365	3	obtain	obtain	VERB
ejde-390	365	4	lim	lim	PROPN
ejde-390	365	5	n→+∞	n→+∞	PROPN
ejde-390	365	6	〈	〈	PROPN
ejde-390	365	7	a(un	a(un	PROPN
ejde-390	365	8	)	)	PUNCT
ejde-390	365	9	,	,	PUNCT
ejde-390	365	10	un	un	PROPN
ejde-390	366	1	−	−	PROPN
ejde-390	366	2	u∗	u∗	PROPN
ejde-390	366	3	〉	〉	PROPN
ejde-390	366	4	=	=	SYM
ejde-390	366	5	0	0	PROPN
ejde-390	366	6	,	,	PUNCT
ejde-390	366	7	ejde-2020/12	ejde-2020/12	NOUN
ejde-390	366	8	positive	positive	ADJ
ejde-390	366	9	and	and	CCONJ
ejde-390	366	10	nodal	nodal	ADJ
ejde-390	366	11	solutions	solution	NOUN
ejde-390	366	12	13	13	NUM
ejde-390	366	13	which	which	PRON
ejde-390	366	14	implies	imply	VERB
ejde-390	366	15	un	un	PROPN
ejde-390	366	16	→	→	SYM
ejde-390	366	17	u∗	u∗	PROPN
ejde-390	366	18	in	in	ADP
ejde-390	366	19	w	w	PROPN
ejde-390	366	20	1,p(ω	1,p(ω	NUM
ejde-390	366	21	)	)	PUNCT
ejde-390	366	22	(	(	PUNCT
ejde-390	366	23	see	see	VERB
ejde-390	366	24	proposition	proposition	NOUN
ejde-390	366	25	2.5	2.5	NUM
ejde-390	366	26	)	)	PUNCT
ejde-390	366	27	.	.	PUNCT
ejde-390	367	1	(	(	PUNCT
ejde-390	367	2	3.34	3.34	NUM
ejde-390	367	3	)	)	PUNCT
ejde-390	368	1	so	so	ADV
ejde-390	368	2	,	,	PUNCT
ejde-390	368	3	if	if	SCONJ
ejde-390	368	4	in	in	ADP
ejde-390	368	5	(	(	PUNCT
ejde-390	368	6	3.21	3.21	NUM
ejde-390	368	7	)	)	PUNCT
ejde-390	368	8	we	we	PRON
ejde-390	368	9	pass	pass	VERB
ejde-390	368	10	to	to	ADP
ejde-390	368	11	the	the	DET
ejde-390	368	12	limit	limit	NOUN
ejde-390	368	13	as	as	ADP
ejde-390	368	14	n	n	PROPN
ejde-390	368	15	→	→	SYM
ejde-390	368	16	+	+	NOUN
ejde-390	368	17	∞	∞	NUM
ejde-390	368	18	and	and	CCONJ
ejde-390	368	19	use	use	NOUN
ejde-390	368	20	(	(	PUNCT
ejde-390	368	21	3.34	3.34	NUM
ejde-390	368	22	)	)	PUNCT
ejde-390	368	23	and	and	CCONJ
ejde-390	368	24	the	the	DET
ejde-390	368	25	fact	fact	NOUN
ejde-390	368	26	that	that	SCONJ
ejde-390	368	27	λn	λn	PROPN
ejde-390	368	28	↓	↓	PROPN
ejde-390	368	29	0	0	PUNCT
ejde-390	368	30	(	(	PUNCT
ejde-390	368	31	recall	recall	VERB
ejde-390	368	32	we	we	PRON
ejde-390	368	33	have	have	AUX
ejde-390	368	34	assumed	assume	VERB
ejde-390	368	35	that	that	DET
ejde-390	368	36	λ∗	λ∗	NOUN
ejde-390	368	37	=	=	PUNCT
ejde-390	368	38	0	0	NUM
ejde-390	368	39	)	)	PUNCT
ejde-390	368	40	,	,	PUNCT
ejde-390	368	41	we	we	PRON
ejde-390	368	42	obtain	obtain	VERB
ejde-390	368	43	〈	〈	NOUN
ejde-390	368	44	a(u∗	a(u∗	NOUN
ejde-390	368	45	)	)	PUNCT
ejde-390	368	46	,	,	PUNCT
ejde-390	368	47	h〉+	h〉+	PROPN
ejde-390	368	48	∫	∫	PROPN
ejde-390	368	49	ω	ω	PROPN
ejde-390	368	50	ξ(z)up−1	ξ(z)up−1	NOUN
ejde-390	368	51	∗	∗	NOUN
ejde-390	368	52	hdz	hdz	NOUN
ejde-390	369	1	=	=	SYM
ejde-390	369	2	∫	∫	PROPN
ejde-390	369	3	ω	ω	NUM
ejde-390	369	4	f(z	f(z	PROPN
ejde-390	369	5	,	,	PUNCT
ejde-390	369	6	u∗)hdz	u∗)hdz	ADP
ejde-390	369	7	for	for	ADP
ejde-390	369	8	all	all	DET
ejde-390	369	9	h	h	NOUN
ejde-390	369	10	∈w	∈w	PROPN
ejde-390	369	11	1,p(ω	1,p(ω	NUM
ejde-390	369	12	)	)	PUNCT
ejde-390	369	13	.	.	PUNCT
ejde-390	370	1	(	(	PUNCT
ejde-390	370	2	3.35	3.35	NUM
ejde-390	370	3	)	)	PUNCT
ejde-390	370	4	in	in	ADP
ejde-390	370	5	(	(	PUNCT
ejde-390	370	6	3.35	3.35	NUM
ejde-390	370	7	)	)	PUNCT
ejde-390	370	8	we	we	PRON
ejde-390	370	9	choose	choose	VERB
ejde-390	370	10	h	h	NOUN
ejde-390	370	11	≡	≡	PROPN
ejde-390	370	12	1	1	NUM
ejde-390	370	13	.	.	PUNCT
ejde-390	371	1	then∫	then∫	NOUN
ejde-390	371	2	ω	ω	PROPN
ejde-390	371	3	ξ(z)up−1	ξ(z)up−1	PROPN
ejde-390	371	4	∗	∗	NOUN
ejde-390	371	5	dz	dz	PROPN
ejde-390	371	6	=	=	SYM
ejde-390	371	7	∫	∫	PROPN
ejde-390	371	8	ω	ω	NUM
ejde-390	371	9	f(z	f(z	PROPN
ejde-390	371	10	,	,	PUNCT
ejde-390	371	11	u∗)dz	u∗)dz	ADP
ejde-390	371	12	≥	≥	NUM
ejde-390	371	13	∫	∫	PROPN
ejde-390	371	14	ω	ω	PROPN
ejde-390	371	15	η(z)up−1	η(z)up−1	PROPN
ejde-390	371	16	∗	∗	NOUN
ejde-390	371	17	dz	dz	PROPN
ejde-390	371	18	(	(	PUNCT
ejde-390	371	19	see	see	VERB
ejde-390	371	20	(	(	PUNCT
ejde-390	371	21	h3)(i	h3)(i	NOUN
ejde-390	371	22	)	)	PUNCT
ejde-390	371	23	)	)	PUNCT
ejde-390	371	24	,	,	PUNCT
ejde-390	371	25	which	which	PRON
ejde-390	371	26	implies	imply	VERB
ejde-390	371	27	∫	∫	PROPN
ejde-390	371	28	ω	ω	PROPN
ejde-390	372	1	[	[	X
ejde-390	372	2	η(z)−	η(z)−	PROPN
ejde-390	372	3	ξ(z)]up−1	ξ(z)]up−1	PROPN
ejde-390	372	4	∗	∗	NOUN
ejde-390	372	5	dz	dz	ADJ
ejde-390	372	6	≤	≤	NOUN
ejde-390	372	7	0	0	NUM
ejde-390	372	8	.	.	PUNCT
ejde-390	373	1	(	(	PUNCT
ejde-390	373	2	3.36	3.36	NUM
ejde-390	373	3	)	)	PUNCT
ejde-390	373	4	note	note	NOUN
ejde-390	373	5	that	that	SCONJ
ejde-390	373	6	hypotheses	hypothesis	NOUN
ejde-390	373	7	(	(	PUNCT
ejde-390	373	8	h3)(i),(iv	h3)(i),(iv	NOUN
ejde-390	373	9	)	)	PUNCT
ejde-390	373	10	imply	imply	VERB
ejde-390	373	11	that	that	SCONJ
ejde-390	373	12	we	we	PRON
ejde-390	373	13	can	can	AUX
ejde-390	373	14	find	find	VERB
ejde-390	373	15	c15	c15	NOUN
ejde-390	373	16	>	>	X
ejde-390	373	17	0	0	NUM
ejde-390	373	18	such	such	ADJ
ejde-390	373	19	that	that	DET
ejde-390	373	20	f(z	f(z	PROPN
ejde-390	373	21	,	,	PUNCT
ejde-390	373	22	x	x	X
ejde-390	373	23	)	)	PUNCT
ejde-390	373	24	≥	≥	PROPN
ejde-390	374	1	xq−1	xq−1	NOUN
ejde-390	374	2	−	−	PROPN
ejde-390	374	3	c15x	c15x	PROPN
ejde-390	374	4	r−1	r−1	PROPN
ejde-390	374	5	for	for	ADP
ejde-390	374	6	a.a	a.a	PROPN
ejde-390	374	7	.	.	PROPN
ejde-390	374	8	z	z	PROPN
ejde-390	374	9	∈	∈	PROPN
ejde-390	374	10	ω	ω	PROPN
ejde-390	374	11	,	,	PUNCT
ejde-390	374	12	all	all	PRON
ejde-390	374	13	x	x	PRON
ejde-390	374	14	≥	≥	NOUN
ejde-390	374	15	0	0	NUM
ejde-390	374	16	.	.	PUNCT
ejde-390	375	1	evidently	evidently	ADV
ejde-390	375	2	we	we	PRON
ejde-390	375	3	can	can	AUX
ejde-390	375	4	always	always	ADV
ejde-390	375	5	assume	assume	VERB
ejde-390	375	6	that	that	SCONJ
ejde-390	375	7	c15	c15	NOUN
ejde-390	375	8	>	>	X
ejde-390	375	9	‖ξ‖∞.	‖ξ‖∞.	NUM
ejde-390	375	10	we	we	PRON
ejde-390	375	11	consider	consider	VERB
ejde-390	375	12	the	the	DET
ejde-390	375	13	following	follow	VERB
ejde-390	375	14	auxiliary	auxiliary	ADJ
ejde-390	375	15	neumann	neumann	PROPN
ejde-390	375	16	problem	problem	PROPN
ejde-390	375	17	−div	−div	X
ejde-390	375	18	a(∇u(z	a(∇u(z	NOUN
ejde-390	375	19	)	)	PUNCT
ejde-390	375	20	)	)	PUNCT
ejde-390	376	1	+	+	CCONJ
ejde-390	376	2	ξ(z)u(z)p−1	ξ(z)u(z)p−1	NOUN
ejde-390	376	3	=	=	SYM
ejde-390	376	4	u(z)q−1	u(z)q−1	NOUN
ejde-390	376	5	−	−	PROPN
ejde-390	376	6	c15u(z)r−1	c15u(z)r−1	PROPN
ejde-390	376	7	in	in	ADP
ejde-390	376	8	ω	ω	NUM
ejde-390	376	9	,	,	PUNCT
ejde-390	376	10	∂u	∂u	PROPN
ejde-390	376	11	∂n	∂n	PROPN
ejde-390	376	12	=	=	SYM
ejde-390	376	13	0	0	NUM
ejde-390	376	14	,	,	PUNCT
ejde-390	376	15	u	u	NOUN
ejde-390	376	16	>	>	X
ejde-390	376	17	0	0	NUM
ejde-390	376	18	.	.	PUNCT
ejde-390	376	19	from	from	ADP
ejde-390	376	20	[	[	X
ejde-390	376	21	9	9	NUM
ejde-390	376	22	,	,	PUNCT
ejde-390	376	23	proposition	proposition	NOUN
ejde-390	376	24	3.5	3.5	NUM
ejde-390	376	25	]	]	PUNCT
ejde-390	376	26	we	we	PRON
ejde-390	376	27	know	know	VERB
ejde-390	376	28	that	that	SCONJ
ejde-390	376	29	this	this	DET
ejde-390	376	30	problem	problem	NOUN
ejde-390	376	31	has	have	VERB
ejde-390	376	32	a	a	DET
ejde-390	376	33	unique	unique	ADJ
ejde-390	376	34	positive	positive	ADJ
ejde-390	376	35	solution	solution	NOUN
ejde-390	376	36	ũ	ũ	PROPN
ejde-390	376	37	∈	∈	PROPN
ejde-390	376	38	d+	d+	PUNCT
ejde-390	376	39	.	.	PUNCT
ejde-390	377	1	let	let	VERB
ejde-390	377	2	λ	λ	X
ejde-390	377	3	∈	∈	PROPN
ejde-390	377	4	l	l	NOUN
ejde-390	377	5	and	and	CCONJ
ejde-390	377	6	u	u	PROPN
ejde-390	377	7	∈	∈	NOUN
ejde-390	377	8	sλ	sλ	ADP
ejde-390	377	9	⊆	⊆	NUM
ejde-390	377	10	d+	d+	NOUN
ejde-390	377	11	.	.	PUNCT
ejde-390	378	1	we	we	PRON
ejde-390	378	2	introduce	introduce	VERB
ejde-390	378	3	the	the	DET
ejde-390	378	4	carathéodory	carathéodory	NOUN
ejde-390	378	5	function	function	NOUN
ejde-390	378	6	β(z	β(z	PROPN
ejde-390	378	7	,	,	PUNCT
ejde-390	378	8	x	x	NOUN
ejde-390	378	9	)	)	PUNCT
ejde-390	378	10	=	=	PRON
ejde-390	378	11	{	{	PUNCT
ejde-390	378	12	(	(	PUNCT
ejde-390	378	13	x+)q−1	x+)q−1	NUM
ejde-390	378	14	−	−	NOUN
ejde-390	378	15	c15(x+)r−1	c15(x+)r−1	PROPN
ejde-390	379	1	+	+	CCONJ
ejde-390	379	2	µ̂(x+)p−1	µ̂(x+)p−1	VERB
ejde-390	379	3	if	if	SCONJ
ejde-390	379	4	x	x	SYM
ejde-390	379	5	≤	≤	NUM
ejde-390	379	6	u(z	u(z	NOUN
ejde-390	379	7	)	)	PUNCT
ejde-390	379	8	,	,	PUNCT
ejde-390	379	9	u(z)q−1	u(z)q−1	PROPN
ejde-390	379	10	−	−	PROPN
ejde-390	380	1	c15u(z)r−1	c15u(z)r−1	PROPN
ejde-390	380	2	+	+	CCONJ
ejde-390	380	3	µ̂u(z)p−1	µ̂u(z)p−1	PROPN
ejde-390	380	4	if	if	SCONJ
ejde-390	380	5	u(z	u(z	NOUN
ejde-390	380	6	)	)	PUNCT
ejde-390	380	7	<	<	X
ejde-390	380	8	x	x	X
ejde-390	380	9	,	,	PUNCT
ejde-390	380	10	(	(	PUNCT
ejde-390	380	11	3.37	3.37	NUM
ejde-390	380	12	)	)	PUNCT
ejde-390	380	13	with	with	ADP
ejde-390	380	14	µ̂	µ̂	DET
ejde-390	380	15	≥	≥	NOUN
ejde-390	380	16	‖ξ‖∞.	‖ξ‖∞.	NUM
ejde-390	381	1	we	we	PRON
ejde-390	381	2	set	set	VERB
ejde-390	381	3	b(z	b(z	NOUN
ejde-390	381	4	,	,	PUNCT
ejde-390	381	5	x	x	X
ejde-390	381	6	)	)	PUNCT
ejde-390	381	7	=	=	SYM
ejde-390	382	1	∫	∫	PROPN
ejde-390	382	2	x	x	SYM
ejde-390	382	3	0	0	PROPN
ejde-390	382	4	β(z	β(z	PROPN
ejde-390	382	5	,	,	PUNCT
ejde-390	382	6	s)ds	s)ds	PROPN
ejde-390	382	7	and	and	CCONJ
ejde-390	382	8	consider	consider	VERB
ejde-390	382	9	the	the	DET
ejde-390	382	10	c1	c1	NOUN
ejde-390	382	11	-	-	PUNCT
ejde-390	382	12	functional	functional	ADJ
ejde-390	382	13	σ̃λ	σ̃λ	NOUN
ejde-390	382	14	:	:	PUNCT
ejde-390	382	15	w	w	PROPN
ejde-390	382	16	1,p(ω)→	1,p(ω)→	NUM
ejde-390	382	17	r	r	NOUN
ejde-390	382	18	defined	define	VERB
ejde-390	382	19	by	by	ADP
ejde-390	382	20	σ̃λ(u	σ̃λ(u	NUM
ejde-390	382	21	)	)	PUNCT
ejde-390	382	22	=	=	SYM
ejde-390	382	23	1	1	NUM
ejde-390	382	24	p	p	NOUN
ejde-390	382	25	γ(u	γ(u	PROPN
ejde-390	382	26	)	)	PUNCT
ejde-390	383	1	+	+	CCONJ
ejde-390	383	2	λ+	λ+	PUNCT
ejde-390	383	3	µ̂	µ̂	PRON
ejde-390	383	4	p	p	PRON
ejde-390	383	5	‖u‖pp	‖u‖pp	NOUN
ejde-390	383	6	−	−	PROPN
ejde-390	383	7	∫	∫	PROPN
ejde-390	383	8	ω	ω	NUM
ejde-390	383	9	b(z	b(z	PROPN
ejde-390	383	10	,	,	PUNCT
ejde-390	383	11	u)dz	u)dz	PROPN
ejde-390	383	12	for	for	ADP
ejde-390	383	13	u	u	NOUN
ejde-390	383	14	∈w	∈w	NOUN
ejde-390	383	15	1,p(ω	1,p(ω	NUM
ejde-390	383	16	)	)	PUNCT
ejde-390	383	17	.	.	PUNCT
ejde-390	384	1	the	the	DET
ejde-390	384	2	direct	direct	ADJ
ejde-390	384	3	method	method	NOUN
ejde-390	384	4	of	of	ADP
ejde-390	384	5	calculus	calculus	NOUN
ejde-390	384	6	of	of	ADP
ejde-390	384	7	variations	variation	NOUN
ejde-390	384	8	gives	give	VERB
ejde-390	384	9	ũ0	ũ0	PROPN
ejde-390	384	10	∈w	∈w	NOUN
ejde-390	384	11	1,p(ω	1,p(ω	NUM
ejde-390	384	12	)	)	PUNCT
ejde-390	384	13	such	such	ADJ
ejde-390	384	14	that	that	PRON
ejde-390	384	15	σ̃λ(ũ0	σ̃λ(ũ0	NOUN
ejde-390	384	16	)	)	PUNCT
ejde-390	384	17	=	=	SYM
ejde-390	384	18	inf[σ̃λ(u	inf[σ̃λ(u	NOUN
ejde-390	384	19	)	)	PUNCT
ejde-390	384	20	:	:	PUNCT
ejde-390	384	21	u	u	NOUN
ejde-390	384	22	∈w	∈w	VERB
ejde-390	384	23	1,p(ω	1,p(ω	NUM
ejde-390	384	24	)	)	PUNCT
ejde-390	384	25	]	]	PUNCT
ejde-390	385	1	<	<	X
ejde-390	385	2	0	0	PUNCT
ejde-390	385	3	=	=	SYM
ejde-390	385	4	σ̃λ(0	σ̃λ(0	NOUN
ejde-390	385	5	)	)	PUNCT
ejde-390	385	6	(	(	PUNCT
ejde-390	385	7	since	since	SCONJ
ejde-390	385	8	q	q	X
ejde-390	385	9	<	<	X
ejde-390	385	10	p	p	X
ejde-390	385	11	)	)	PUNCT
ejde-390	385	12	.	.	PUNCT
ejde-390	386	1	so	so	ADV
ejde-390	386	2	,	,	PUNCT
ejde-390	386	3	ũ0	ũ0	PROPN
ejde-390	386	4	6=	6=	ADP
ejde-390	386	5	0	0	NUM
ejde-390	386	6	and	and	CCONJ
ejde-390	386	7	ũ0	ũ0	PROPN
ejde-390	386	8	∈	∈	PROPN
ejde-390	386	9	kσ̃λ	kσ̃λ	NOUN
ejde-390	387	1	⊆	⊆	NUM
ejde-390	388	1	[	[	X
ejde-390	388	2	0	0	NUM
ejde-390	388	3	,	,	PUNCT
ejde-390	388	4	u	u	NOUN
ejde-390	388	5	]	]	X
ejde-390	388	6	∩	∩	X
ejde-390	388	7	c+	c+	X
ejde-390	388	8	(	(	PUNCT
ejde-390	388	9	see	see	VERB
ejde-390	388	10	(	(	PUNCT
ejde-390	388	11	3.37	3.37	NUM
ejde-390	388	12	)	)	PUNCT
ejde-390	388	13	and	and	CCONJ
ejde-390	388	14	use	use	VERB
ejde-390	388	15	the	the	DET
ejde-390	388	16	nonlinear	nonlinear	ADJ
ejde-390	388	17	regularity	regularity	NOUN
ejde-390	388	18	theory	theory	NOUN
ejde-390	388	19	)	)	PUNCT
ejde-390	388	20	.	.	PUNCT
ejde-390	389	1	hence	hence	ADV
ejde-390	389	2	from	from	ADP
ejde-390	389	3	(	(	PUNCT
ejde-390	389	4	3.37	3.37	NUM
ejde-390	389	5	)	)	PUNCT
ejde-390	389	6	we	we	PRON
ejde-390	389	7	infer	infer	VERB
ejde-390	389	8	that	that	SCONJ
ejde-390	389	9	ũ0	ũ0	PROPN
ejde-390	389	10	=	=	PUNCT
ejde-390	389	11	ũ	ũ	PROPN
ejde-390	389	12	∈	∈	PROPN
ejde-390	389	13	d+	d+	PUNCT
ejde-390	389	14	and	and	CCONJ
ejde-390	389	15	so	so	ADV
ejde-390	389	16	ũ	ũ	PROPN
ejde-390	389	17	≤	≤	PROPN
ejde-390	389	18	u	u	NOUN
ejde-390	389	19	for	for	ADP
ejde-390	389	20	all	all	DET
ejde-390	389	21	u	u	PROPN
ejde-390	389	22	∈	∈	NOUN
ejde-390	389	23	sλ	sλ	NOUN
ejde-390	389	24	,	,	PUNCT
ejde-390	389	25	all	all	DET
ejde-390	389	26	λ	λ	PROPN
ejde-390	389	27	∈	∈	PROPN
ejde-390	389	28	l.	l.	NOUN
ejde-390	389	29	it	it	PRON
ejde-390	389	30	follows	follow	VERB
ejde-390	389	31	that	that	SCONJ
ejde-390	389	32	ũ	ũ	PROPN
ejde-390	389	33	≤	≤	PROPN
ejde-390	389	34	u∗	u∗	ADJ
ejde-390	389	35	⇒	⇒	NOUN
ejde-390	390	1	∫	∫	PROPN
ejde-390	390	2	ω	ω	PROPN
ejde-390	391	1	[	[	X
ejde-390	391	2	η(z)−	η(z)−	PROPN
ejde-390	391	3	ξ(z)]up−1	ξ(z)]up−1	PROPN
ejde-390	391	4	∗	∗	NOUN
ejde-390	391	5	dz	dz	PROPN
ejde-390	391	6	>	>	X
ejde-390	391	7	0	0	PUNCT
ejde-390	392	1	(	(	PUNCT
ejde-390	392	2	since	since	SCONJ
ejde-390	392	3	ξ	ξ	PROPN
ejde-390	392	4	≺	≺	NOUN
ejde-390	392	5	η	η	NOUN
ejde-390	392	6	)	)	PUNCT
ejde-390	392	7	which	which	PRON
ejde-390	392	8	contradicts	contradict	VERB
ejde-390	392	9	(	(	PUNCT
ejde-390	392	10	3.36	3.36	NUM
ejde-390	392	11	)	)	PUNCT
ejde-390	392	12	.	.	PUNCT
ejde-390	393	1	so	so	ADV
ejde-390	393	2	,	,	PUNCT
ejde-390	393	3	we	we	PRON
ejde-390	393	4	conclude	conclude	VERB
ejde-390	393	5	that	that	DET
ejde-390	393	6	λ∗	λ∗	PROPN
ejde-390	393	7	>	>	X
ejde-390	393	8	0	0	X
ejde-390	393	9	.	.	PUNCT
ejde-390	393	10	�	�	PROPN
ejde-390	393	11	proposition	proposition	NOUN
ejde-390	393	12	3.4	3.4	NUM
ejde-390	393	13	.	.	PUNCT
ejde-390	394	1	if	if	SCONJ
ejde-390	394	2	hypotheses	hypothesis	NOUN
ejde-390	394	3	(	(	PUNCT
ejde-390	394	4	h1)–(h3	h1)–(h3	NOUN
ejde-390	394	5	)	)	PUNCT
ejde-390	394	6	hold	hold	VERB
ejde-390	394	7	and	and	CCONJ
ejde-390	394	8	λ	λ	X
ejde-390	394	9	∈	∈	PROPN
ejde-390	394	10	(	(	PUNCT
ejde-390	394	11	λ∗,+∞	λ∗,+∞	PROPN
ejde-390	394	12	)	)	PUNCT
ejde-390	394	13	,	,	PUNCT
ejde-390	394	14	then	then	ADV
ejde-390	394	15	problem	problem	NOUN
ejde-390	394	16	(	(	PUNCT
ejde-390	394	17	1.1	1.1	NUM
ejde-390	394	18	)	)	PUNCT
ejde-390	394	19	admits	admit	VERB
ejde-390	394	20	at	at	ADP
ejde-390	394	21	least	least	ADV
ejde-390	394	22	two	two	NUM
ejde-390	394	23	positive	positive	ADJ
ejde-390	394	24	solutions	solution	NOUN
ejde-390	394	25	u0	u0	ADJ
ejde-390	394	26	,	,	PUNCT
ejde-390	394	27	û	û	NUM
ejde-390	394	28	∈	∈	NOUN
ejde-390	394	29	sλ	sλ	ADP
ejde-390	394	30	⊆	⊆	NUM
ejde-390	394	31	d+	d+	NOUN
ejde-390	394	32	.	.	PUNCT
ejde-390	395	1	14	14	NUM
ejde-390	395	2	n.	n.	PROPN
ejde-390	395	3	s.	s.	PROPN
ejde-390	395	4	papageorgiou	papageorgiou	PROPN
ejde-390	395	5	,	,	PUNCT
ejde-390	395	6	c.	c.	PROPN
ejde-390	395	7	vetro	vetro	PROPN
ejde-390	395	8	,	,	PUNCT
ejde-390	395	9	f.	f.	PROPN
ejde-390	395	10	vetro	vetro	PROPN
ejde-390	395	11	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	395	12	proof	proof	NOUN
ejde-390	395	13	.	.	PUNCT
ejde-390	396	1	let	let	VERB
ejde-390	396	2	λ∗	λ∗	PROPN
ejde-390	396	3	<	<	X
ejde-390	396	4	θ	θ	X
ejde-390	396	5	<	<	X
ejde-390	396	6	λ	λ	X
ejde-390	396	7	<	<	X
ejde-390	396	8	η	η	PROPN
ejde-390	396	9	.	.	PROPN
ejde-390	396	10	by	by	ADP
ejde-390	396	11	proposition	proposition	NOUN
ejde-390	396	12	3.2	3.2	NUM
ejde-390	396	13	,	,	PUNCT
ejde-390	396	14	we	we	PRON
ejde-390	396	15	can	can	AUX
ejde-390	396	16	find	find	VERB
ejde-390	396	17	uθ	uθ	ADP
ejde-390	396	18	∈	∈	NOUN
ejde-390	396	19	sθ	sθ	ADP
ejde-390	396	20	⊆	⊆	NUM
ejde-390	396	21	d+	d+	X
ejde-390	396	22	,	,	PUNCT
ejde-390	396	23	u0	u0	PROPN
ejde-390	396	24	∈	∈	PROPN
ejde-390	396	25	sλ	sλ	NOUN
ejde-390	396	26	⊆	⊆	NUM
ejde-390	396	27	d+	d+	NOUN
ejde-390	396	28	and	and	CCONJ
ejde-390	396	29	uη	uη	ADP
ejde-390	396	30	∈	∈	PROPN
ejde-390	396	31	sη	sη	VERB
ejde-390	396	32	⊆	⊆	NUM
ejde-390	396	33	d+	d+	NOUN
ejde-390	396	34	such	such	ADJ
ejde-390	396	35	that	that	SCONJ
ejde-390	396	36	uθ	uθ	ADP
ejde-390	396	37	−	−	PROPN
ejde-390	396	38	u0	u0	PROPN
ejde-390	396	39	∈	∈	PROPN
ejde-390	396	40	int	int	NOUN
ejde-390	396	41	ĉ+	ĉ+	PUNCT
ejde-390	396	42	and	and	CCONJ
ejde-390	396	43	u0	u0	ADJ
ejde-390	396	44	−	−	PROPN
ejde-390	396	45	uη	uη	ADP
ejde-390	396	46	∈	∈	PROPN
ejde-390	396	47	int	int	NOUN
ejde-390	396	48	ĉ+	ĉ+	PROPN
ejde-390	396	49	,	,	PUNCT
ejde-390	396	50	⇒	⇒	VERB
ejde-390	396	51	u0	u0	PROPN
ejde-390	396	52	∈	∈	PROPN
ejde-390	396	53	intc1(ω)[uη	intc1(ω)[uη	NOUN
ejde-390	396	54	,	,	PUNCT
ejde-390	396	55	uθ	uθ	ADP
ejde-390	396	56	]	]	PUNCT
ejde-390	396	57	.	.	PUNCT
ejde-390	397	1	(	(	PUNCT
ejde-390	397	2	3.38	3.38	NUM
ejde-390	397	3	)	)	PUNCT
ejde-390	397	4	we	we	PRON
ejde-390	397	5	introduce	introduce	VERB
ejde-390	397	6	the	the	DET
ejde-390	397	7	carathéodory	carathéodory	NOUN
ejde-390	397	8	function	function	NOUN
ejde-390	397	9	j(z	j(z	PROPN
ejde-390	397	10	,	,	PUNCT
ejde-390	397	11	x	x	NOUN
ejde-390	397	12	)	)	PUNCT
ejde-390	397	13	=	=	SYM
ejde-390	397	14	{	{	PUNCT
ejde-390	397	15	f(z	f(z	PROPN
ejde-390	397	16	,	,	PUNCT
ejde-390	397	17	uη(z	uη(z	NOUN
ejde-390	397	18	)	)	PUNCT
ejde-390	397	19	)	)	PUNCT
ejde-390	398	1	+	+	CCONJ
ejde-390	398	2	µ̂uη(z)p−1	µ̂uη(z)p−1	PART
ejde-390	398	3	if	if	SCONJ
ejde-390	398	4	x	x	SYM
ejde-390	398	5	≤	≤	NUM
ejde-390	398	6	uη(z	uη(z	NOUN
ejde-390	398	7	)	)	PUNCT
ejde-390	398	8	,	,	PUNCT
ejde-390	398	9	f(z	f(z	PROPN
ejde-390	398	10	,	,	PUNCT
ejde-390	398	11	x	x	NOUN
ejde-390	398	12	)	)	PUNCT
ejde-390	398	13	+	+	CCONJ
ejde-390	398	14	µ̂xp−1	µ̂xp−1	PROPN
ejde-390	398	15	if	if	SCONJ
ejde-390	398	16	uη(z	uη(z	NOUN
ejde-390	398	17	)	)	PUNCT
ejde-390	398	18	<	<	X
ejde-390	398	19	x	x	X
ejde-390	398	20	,	,	PUNCT
ejde-390	398	21	(	(	PUNCT
ejde-390	398	22	3.39	3.39	NUM
ejde-390	398	23	)	)	PUNCT
ejde-390	398	24	with	with	ADP
ejde-390	398	25	µ̂	µ̂	DET
ejde-390	398	26	≥	≥	NOUN
ejde-390	398	27	‖ξ‖∞.	‖ξ‖∞.	NUM
ejde-390	398	28	we	we	PRON
ejde-390	398	29	set	set	VERB
ejde-390	398	30	j(z	j(z	PROPN
ejde-390	398	31	,	,	PUNCT
ejde-390	398	32	x	x	NOUN
ejde-390	398	33	)	)	PUNCT
ejde-390	398	34	=	=	SYM
ejde-390	399	1	∫	∫	PROPN
ejde-390	399	2	x	x	SYM
ejde-390	399	3	0	0	NUM
ejde-390	399	4	j(z	j(z	PROPN
ejde-390	399	5	,	,	PUNCT
ejde-390	399	6	s)ds	s)ds	PROPN
ejde-390	399	7	and	and	CCONJ
ejde-390	399	8	consider	consider	VERB
ejde-390	399	9	the	the	DET
ejde-390	399	10	c1	c1	NOUN
ejde-390	399	11	-	-	PUNCT
ejde-390	399	12	functional	functional	ADJ
ejde-390	399	13	ψ̂λ	ψ̂λ	X
ejde-390	399	14	:	:	PUNCT
ejde-390	399	15	w	w	PROPN
ejde-390	399	16	1,p(ω)→	1,p(ω)→	NUM
ejde-390	399	17	r	r	NOUN
ejde-390	399	18	defined	define	VERB
ejde-390	399	19	by	by	ADP
ejde-390	399	20	ψ̂λ(u	ψ̂λ(u	PROPN
ejde-390	399	21	)	)	PUNCT
ejde-390	399	22	=	=	PUNCT
ejde-390	399	23	1	1	NUM
ejde-390	399	24	p	p	NOUN
ejde-390	399	25	γ(u	γ(u	PROPN
ejde-390	399	26	)	)	PUNCT
ejde-390	400	1	+	+	CCONJ
ejde-390	400	2	λ+	λ+	PUNCT
ejde-390	400	3	µ̂	µ̂	PRON
ejde-390	400	4	p	p	PRON
ejde-390	400	5	‖u‖pp	‖u‖pp	NOUN
ejde-390	400	6	−	−	PROPN
ejde-390	400	7	∫	∫	PROPN
ejde-390	400	8	ω	ω	PROPN
ejde-390	400	9	j(z	j(z	PROPN
ejde-390	400	10	,	,	PUNCT
ejde-390	400	11	u)dz	u)dz	PROPN
ejde-390	400	12	for	for	ADP
ejde-390	400	13	all	all	DET
ejde-390	400	14	u	u	NOUN
ejde-390	400	15	∈w	∈w	NOUN
ejde-390	400	16	1,p(ω	1,p(ω	NUM
ejde-390	400	17	)	)	PUNCT
ejde-390	400	18	.	.	PUNCT
ejde-390	401	1	in	in	ADP
ejde-390	401	2	addition	addition	NOUN
ejde-390	401	3	,	,	PUNCT
ejde-390	401	4	we	we	PRON
ejde-390	401	5	introduce	introduce	VERB
ejde-390	401	6	the	the	DET
ejde-390	401	7	following	following	ADJ
ejde-390	401	8	truncation	truncation	NOUN
ejde-390	401	9	of	of	ADP
ejde-390	401	10	j(z	j(z	PROPN
ejde-390	401	11	,	,	PUNCT
ejde-390	401	12	·	·	PUNCT
ejde-390	401	13	)	)	PUNCT
ejde-390	401	14	,	,	PUNCT
ejde-390	401	15	j̃(z	j̃(z	PROPN
ejde-390	401	16	,	,	PUNCT
ejde-390	401	17	x	x	NOUN
ejde-390	401	18	)	)	PUNCT
ejde-390	401	19	=	=	PRON
ejde-390	401	20	{	{	PUNCT
ejde-390	401	21	j(z	j(z	PROPN
ejde-390	401	22	,	,	PUNCT
ejde-390	401	23	x	x	NOUN
ejde-390	401	24	)	)	PUNCT
ejde-390	401	25	if	if	SCONJ
ejde-390	401	26	x	x	SYM
ejde-390	401	27	≤	≤	X
ejde-390	401	28	uθ(z	uθ(z	ADV
ejde-390	401	29	)	)	PUNCT
ejde-390	401	30	,	,	PUNCT
ejde-390	401	31	j(z	j(z	PROPN
ejde-390	401	32	,	,	PUNCT
ejde-390	401	33	uθ(z	uθ(z	NUM
ejde-390	401	34	)	)	PUNCT
ejde-390	401	35	)	)	PUNCT
ejde-390	402	1	if	if	SCONJ
ejde-390	402	2	uθ(z	uθ(z	ADV
ejde-390	402	3	)	)	PUNCT
ejde-390	402	4	<	<	X
ejde-390	402	5	x.	x.	X
ejde-390	402	6	(	(	PUNCT
ejde-390	402	7	3.40	3.40	NUM
ejde-390	402	8	)	)	PUNCT
ejde-390	402	9	this	this	PRON
ejde-390	402	10	is	be	AUX
ejde-390	402	11	a	a	DET
ejde-390	402	12	carathéodory	carathéodory	NOUN
ejde-390	402	13	function	function	NOUN
ejde-390	402	14	.	.	PUNCT
ejde-390	403	1	we	we	PRON
ejde-390	403	2	set	set	VERB
ejde-390	403	3	j̃(z	j̃(z	PROPN
ejde-390	403	4	,	,	PUNCT
ejde-390	403	5	x	x	NOUN
ejde-390	403	6	)	)	PUNCT
ejde-390	403	7	=	=	SYM
ejde-390	404	1	∫	∫	PROPN
ejde-390	404	2	x	x	SYM
ejde-390	404	3	0	0	NUM
ejde-390	404	4	j̃(z	j̃(z	PROPN
ejde-390	404	5	,	,	PUNCT
ejde-390	404	6	s)ds	s)ds	PROPN
ejde-390	404	7	and	and	CCONJ
ejde-390	404	8	consider	consider	VERB
ejde-390	404	9	the	the	DET
ejde-390	404	10	c1	c1	NOUN
ejde-390	404	11	-	-	PUNCT
ejde-390	404	12	functional	functional	ADJ
ejde-390	404	13	ψ̃λ	ψ̃λ	X
ejde-390	404	14	:	:	PUNCT
ejde-390	404	15	w	w	PROPN
ejde-390	404	16	1,p(ω)→	1,p(ω)→	NUM
ejde-390	404	17	r	r	NOUN
ejde-390	404	18	defined	define	VERB
ejde-390	404	19	by	by	ADP
ejde-390	404	20	ψ̃λ(u	ψ̃λ(u	PUNCT
ejde-390	404	21	)	)	PUNCT
ejde-390	404	22	=	=	NOUN
ejde-390	405	1	1	1	NUM
ejde-390	405	2	p	p	NOUN
ejde-390	405	3	γ(u	γ(u	PROPN
ejde-390	405	4	)	)	PUNCT
ejde-390	406	1	+	+	CCONJ
ejde-390	406	2	λ+	λ+	PUNCT
ejde-390	406	3	µ̂	µ̂	PRON
ejde-390	406	4	p	p	PRON
ejde-390	406	5	‖u‖pp	‖u‖pp	NOUN
ejde-390	406	6	−	−	PROPN
ejde-390	406	7	∫	∫	PROPN
ejde-390	406	8	ω	ω	NUM
ejde-390	406	9	j̃(z	j̃(z	PROPN
ejde-390	406	10	,	,	PUNCT
ejde-390	406	11	u)dz	u)dz	PROPN
ejde-390	406	12	for	for	ADP
ejde-390	406	13	all	all	DET
ejde-390	406	14	u	u	NOUN
ejde-390	406	15	∈w	∈w	NOUN
ejde-390	406	16	1,p(ω	1,p(ω	NUM
ejde-390	406	17	)	)	PUNCT
ejde-390	406	18	.	.	PUNCT
ejde-390	407	1	from	from	ADP
ejde-390	407	2	(	(	PUNCT
ejde-390	407	3	3.39	3.39	NUM
ejde-390	407	4	)	)	PUNCT
ejde-390	407	5	,	,	PUNCT
ejde-390	407	6	(	(	PUNCT
ejde-390	407	7	3.40	3.40	NUM
ejde-390	407	8	)	)	PUNCT
ejde-390	407	9	and	and	CCONJ
ejde-390	407	10	the	the	DET
ejde-390	407	11	nonlinear	nonlinear	ADJ
ejde-390	407	12	regularity	regularity	NOUN
ejde-390	407	13	theory	theory	NOUN
ejde-390	407	14	of	of	ADP
ejde-390	407	15	lieberman	lieberman	PROPN
ejde-390	407	16	[	[	X
ejde-390	407	17	7	7	NUM
ejde-390	407	18	]	]	PUNCT
ejde-390	407	19	,	,	PUNCT
ejde-390	407	20	we	we	PRON
ejde-390	407	21	have	have	VERB
ejde-390	407	22	kψ̂λ	kψ̂λ	PROPN
ejde-390	407	23	⊆	⊆	NUM
ejde-390	407	24	[	[	X
ejde-390	407	25	uη	uη	ADJ
ejde-390	407	26	)	)	PUNCT
ejde-390	407	27	∩d+	∩d+	NOUN
ejde-390	407	28	and	and	CCONJ
ejde-390	407	29	kψ̃λ	kψ̃λ	PROPN
ejde-390	407	30	⊆	⊆	NUM
ejde-390	407	31	[	[	X
ejde-390	407	32	uη	uη	ADP
ejde-390	407	33	,	,	PUNCT
ejde-390	407	34	uθ	uθ	PROPN
ejde-390	407	35	]	]	X
ejde-390	407	36	∩d+	∩d+	PROPN
ejde-390	407	37	.	.	PUNCT
ejde-390	408	1	(	(	PUNCT
ejde-390	408	2	3.41	3.41	NUM
ejde-390	408	3	)	)	PUNCT
ejde-390	408	4	from	from	ADP
ejde-390	408	5	(	(	PUNCT
ejde-390	408	6	3.39	3.39	NUM
ejde-390	408	7	)	)	PUNCT
ejde-390	408	8	,	,	PUNCT
ejde-390	408	9	(	(	PUNCT
ejde-390	408	10	3.40	3.40	NUM
ejde-390	408	11	)	)	PUNCT
ejde-390	408	12	,	,	PUNCT
ejde-390	408	13	(	(	PUNCT
ejde-390	408	14	3.41	3.41	NUM
ejde-390	408	15	)	)	PUNCT
ejde-390	408	16	,	,	PUNCT
ejde-390	408	17	we	we	PRON
ejde-390	408	18	see	see	VERB
ejde-390	408	19	that	that	SCONJ
ejde-390	408	20	we	we	PRON
ejde-390	408	21	may	may	AUX
ejde-390	408	22	assume	assume	VERB
ejde-390	408	23	that	that	SCONJ
ejde-390	408	24	kψ̃λ	kψ̃λ	PROPN
ejde-390	409	1	=	=	PUNCT
ejde-390	409	2	{	{	PUNCT
ejde-390	409	3	u0	u0	PROPN
ejde-390	409	4	}	}	PUNCT
ejde-390	409	5	.	.	PUNCT
ejde-390	410	1	(	(	PUNCT
ejde-390	410	2	3.42	3.42	NUM
ejde-390	410	3	)	)	PUNCT
ejde-390	410	4	otherwise	otherwise	ADV
ejde-390	410	5	we	we	PRON
ejde-390	410	6	already	already	ADV
ejde-390	410	7	have	have	VERB
ejde-390	410	8	a	a	DET
ejde-390	410	9	second	second	ADJ
ejde-390	410	10	positive	positive	ADJ
ejde-390	410	11	solution	solution	NOUN
ejde-390	410	12	of	of	ADP
ejde-390	410	13	(	(	PUNCT
ejde-390	410	14	1.1	1.1	NUM
ejde-390	410	15	)	)	PUNCT
ejde-390	410	16	,	,	PUNCT
ejde-390	410	17	distinct	distinct	ADJ
ejde-390	410	18	from	from	ADP
ejde-390	410	19	u0	u0	ADJ
ejde-390	410	20	and	and	CCONJ
ejde-390	410	21	the	the	DET
ejde-390	410	22	proof	proof	NOUN
ejde-390	410	23	is	be	AUX
ejde-390	410	24	complete	complete	ADJ
ejde-390	410	25	.	.	PUNCT
ejde-390	411	1	clearly	clearly	ADV
ejde-390	411	2	ψ̃λ	ψ̃λ	ADP
ejde-390	411	3	(	(	PUNCT
ejde-390	411	4	·	·	PUNCT
ejde-390	411	5	)	)	PUNCT
ejde-390	411	6	is	be	AUX
ejde-390	411	7	coercive	coercive	ADJ
ejde-390	411	8	(	(	PUNCT
ejde-390	411	9	see	see	VERB
ejde-390	411	10	(	(	PUNCT
ejde-390	411	11	3.40	3.40	NUM
ejde-390	411	12	)	)	PUNCT
ejde-390	411	13	)	)	PUNCT
ejde-390	411	14	and	and	CCONJ
ejde-390	411	15	sequentially	sequentially	ADV
ejde-390	411	16	weakly	weakly	ADV
ejde-390	411	17	lower	low	ADJ
ejde-390	411	18	semicontinuous	semicontinuous	ADJ
ejde-390	411	19	.	.	PUNCT
ejde-390	412	1	so	so	ADV
ejde-390	412	2	,	,	PUNCT
ejde-390	412	3	we	we	PRON
ejde-390	412	4	can	can	AUX
ejde-390	412	5	find	find	VERB
ejde-390	412	6	ũ0	ũ0	PROPN
ejde-390	412	7	∈w	∈w	NOUN
ejde-390	412	8	1,p(ω	1,p(ω	NUM
ejde-390	412	9	)	)	PUNCT
ejde-390	412	10	such	such	ADJ
ejde-390	412	11	that	that	PRON
ejde-390	412	12	ψ̃λ(ũ0	ψ̃λ(ũ0	NOUN
ejde-390	412	13	)	)	PUNCT
ejde-390	412	14	=	=	SYM
ejde-390	412	15	inf[ψ̃λ(u	inf[ψ̃λ(u	NOUN
ejde-390	412	16	)	)	PUNCT
ejde-390	412	17	:	:	PUNCT
ejde-390	412	18	u	u	NOUN
ejde-390	412	19	∈w	∈w	VERB
ejde-390	412	20	1,p(ω	1,p(ω	NUM
ejde-390	412	21	)	)	PUNCT
ejde-390	412	22	]	]	PUNCT
ejde-390	413	1	⇒	⇒	VERB
ejde-390	413	2	ũ0	ũ0	PROPN
ejde-390	413	3	∈	∈	PROPN
ejde-390	413	4	kψ̃λ	kψ̃λ	NOUN
ejde-390	413	5	⇒	⇒	VERB
ejde-390	413	6	ũ0	ũ0	PROPN
ejde-390	413	7	=	=	SYM
ejde-390	413	8	u0	u0	ADJ
ejde-390	413	9	(	(	PUNCT
ejde-390	413	10	see	see	VERB
ejde-390	413	11	(	(	PUNCT
ejde-390	413	12	3.42	3.42	NUM
ejde-390	413	13	)	)	PUNCT
ejde-390	413	14	)	)	PUNCT
ejde-390	413	15	.	.	PUNCT
ejde-390	414	1	from	from	ADP
ejde-390	414	2	(	(	PUNCT
ejde-390	414	3	3.39	3.39	NUM
ejde-390	414	4	)	)	PUNCT
ejde-390	414	5	and	and	CCONJ
ejde-390	414	6	(	(	PUNCT
ejde-390	414	7	3.40	3.40	NUM
ejde-390	414	8	)	)	PUNCT
ejde-390	414	9	we	we	PRON
ejde-390	414	10	see	see	VERB
ejde-390	414	11	that	that	PRON
ejde-390	414	12	ψ̂λ	ψ̂λ	NUM
ejde-390	414	13	∣∣	∣∣	X
ejde-390	415	1	[	[	X
ejde-390	415	2	uη	uη	ADP
ejde-390	415	3	,	,	PUNCT
ejde-390	415	4	uθ	uθ	PRON
ejde-390	415	5	]	]	X
ejde-390	415	6	=	=	PUNCT
ejde-390	415	7	ψ̃λ	ψ̃λ	NOUN
ejde-390	415	8	∣∣	∣∣	X
ejde-390	415	9	[	[	X
ejde-390	415	10	uη	uη	ADP
ejde-390	415	11	,	,	PUNCT
ejde-390	415	12	uθ	uθ	ADP
ejde-390	415	13	]	]	PUNCT
ejde-390	415	14	.	.	PUNCT
ejde-390	416	1	then	then	ADV
ejde-390	416	2	from	from	ADP
ejde-390	416	3	(	(	PUNCT
ejde-390	416	4	3.38	3.38	NUM
ejde-390	416	5	)	)	PUNCT
ejde-390	416	6	it	it	PRON
ejde-390	416	7	follows	follow	VERB
ejde-390	416	8	that	that	SCONJ
ejde-390	416	9	u0	u0	PROPN
ejde-390	416	10	∈	∈	PROPN
ejde-390	416	11	d+	d+	PUNCT
ejde-390	416	12	is	be	AUX
ejde-390	416	13	a	a	DET
ejde-390	416	14	local	local	ADJ
ejde-390	416	15	c1(ω)-minimizer	c1(ω)-minimizer	NOUN
ejde-390	416	16	of	of	ADP
ejde-390	416	17	ψ̂λ	ψ̂λ	PROPN
ejde-390	416	18	,	,	PUNCT
ejde-390	416	19	⇒	⇒	VERB
ejde-390	416	20	u0	u0	PROPN
ejde-390	416	21	∈	∈	PROPN
ejde-390	416	22	d+	d+	PUNCT
ejde-390	416	23	is	be	AUX
ejde-390	416	24	a	a	DET
ejde-390	416	25	local	local	ADJ
ejde-390	416	26	w	w	NOUN
ejde-390	416	27	1,p(ω)-minimizer	1,p(ω)-minimizer	NUM
ejde-390	416	28	of	of	ADP
ejde-390	416	29	ψ̂λ	ψ̂λ	X
ejde-390	416	30	(	(	PUNCT
ejde-390	416	31	3.43	3.43	NUM
ejde-390	416	32	)	)	PUNCT
ejde-390	416	33	(	(	PUNCT
ejde-390	416	34	see	see	VERB
ejde-390	416	35	papageorgiou	papageorgiou	NOUN
ejde-390	416	36	-	-	PUNCT
ejde-390	416	37	rǎdulescu	rǎdulescu	NOUN
ejde-390	417	1	[	[	X
ejde-390	417	2	10	10	NUM
ejde-390	417	3	]	]	NUM
ejde-390	417	4	)	)	PUNCT
ejde-390	417	5	.	.	PUNCT
ejde-390	418	1	from	from	ADP
ejde-390	418	2	(	(	PUNCT
ejde-390	418	3	3.41	3.41	NUM
ejde-390	418	4	)	)	PUNCT
ejde-390	418	5	we	we	PRON
ejde-390	418	6	can	can	AUX
ejde-390	418	7	assume	assume	VERB
ejde-390	418	8	that	that	SCONJ
ejde-390	418	9	kψ̂λ	kψ̂λ	PROPN
ejde-390	418	10	is	be	AUX
ejde-390	418	11	finite	finite	ADJ
ejde-390	418	12	.	.	PUNCT
ejde-390	419	1	(	(	PUNCT
ejde-390	419	2	3.44	3.44	NUM
ejde-390	419	3	)	)	PUNCT
ejde-390	419	4	ejde-2020/12	ejde-2020/12	NOUN
ejde-390	419	5	positive	positive	ADJ
ejde-390	419	6	and	and	CCONJ
ejde-390	419	7	nodal	nodal	ADJ
ejde-390	419	8	solutions	solution	NOUN
ejde-390	419	9	15	15	NUM
ejde-390	419	10	using	use	VERB
ejde-390	419	11	(	(	PUNCT
ejde-390	419	12	3.43	3.43	NUM
ejde-390	419	13	)	)	PUNCT
ejde-390	419	14	,	,	PUNCT
ejde-390	419	15	(	(	PUNCT
ejde-390	419	16	3.44	3.44	NUM
ejde-390	419	17	)	)	PUNCT
ejde-390	419	18	and	and	CCONJ
ejde-390	419	19	[	[	X
ejde-390	419	20	14	14	NUM
ejde-390	419	21	,	,	PUNCT
ejde-390	419	22	theorem	theorem	VERB
ejde-390	419	23	5.7.6	5.7.6	NUM
ejde-390	419	24	,	,	PUNCT
ejde-390	419	25	p.	p.	NOUN
ejde-390	419	26	367	367	NUM
ejde-390	419	27	,	,	PUNCT
ejde-390	419	28	]	]	PUNCT
ejde-390	419	29	,	,	PUNCT
ejde-390	419	30	we	we	PRON
ejde-390	419	31	see	see	VERB
ejde-390	419	32	that	that	SCONJ
ejde-390	419	33	we	we	PRON
ejde-390	419	34	can	can	AUX
ejde-390	419	35	find	find	VERB
ejde-390	419	36	ρ	ρ	X
ejde-390	419	37	∈	∈	PROPN
ejde-390	419	38	(	(	PUNCT
ejde-390	419	39	0	0	NUM
ejde-390	419	40	,	,	PUNCT
ejde-390	419	41	1	1	X
ejde-390	419	42	)	)	PUNCT
ejde-390	419	43	small	small	ADJ
ejde-390	419	44	such	such	ADJ
ejde-390	419	45	that	that	DET
ejde-390	419	46	ψ̂λ(u0	ψ̂λ(u0	NOUN
ejde-390	419	47	)	)	PUNCT
ejde-390	419	48	<	<	X
ejde-390	419	49	inf[ψ̂λ(u	inf[ψ̂λ(u	NOUN
ejde-390	419	50	)	)	PUNCT
ejde-390	419	51	:	:	PUNCT
ejde-390	420	1	‖u−	‖u−	PROPN
ejde-390	420	2	u0‖	u0‖	NOUN
ejde-390	420	3	=	=	SYM
ejde-390	420	4	ρ	ρ	NOUN
ejde-390	420	5	]	]	X
ejde-390	420	6	=	=	SYM
ejde-390	420	7	m̂λ	m̂λ	NOUN
ejde-390	420	8	.	.	PUNCT
ejde-390	420	9	(	(	PUNCT
ejde-390	420	10	3.45	3.45	NUM
ejde-390	420	11	)	)	PUNCT
ejde-390	420	12	by	by	ADP
ejde-390	420	13	(	(	PUNCT
ejde-390	420	14	h3)(ii	h3)(ii	PROPN
ejde-390	420	15	)	)	PUNCT
ejde-390	420	16	,	,	PUNCT
ejde-390	420	17	for	for	ADP
ejde-390	420	18	u	u	PROPN
ejde-390	420	19	∈	∈	PROPN
ejde-390	420	20	d+	d+	PUNCT
ejde-390	420	21	we	we	PRON
ejde-390	420	22	have	have	VERB
ejde-390	420	23	ψ̂λ(tu)→	ψ̂λ(tu)→	NOUN
ejde-390	420	24	−∞	−∞	PUNCT
ejde-390	420	25	as	as	ADP
ejde-390	420	26	t→	t→	PRON
ejde-390	420	27	+	+	PROPN
ejde-390	420	28	∞.	∞.	PROPN
ejde-390	420	29	(	(	PUNCT
ejde-390	420	30	3.46	3.46	NUM
ejde-390	420	31	)	)	PUNCT
ejde-390	420	32	moreover	moreover	ADV
ejde-390	420	33	,	,	PUNCT
ejde-390	420	34	reasoning	reason	VERB
ejde-390	420	35	as	as	ADP
ejde-390	420	36	in	in	ADP
ejde-390	420	37	the	the	DET
ejde-390	420	38	proof	proof	NOUN
ejde-390	420	39	of	of	ADP
ejde-390	420	40	proposition	proposition	NOUN
ejde-390	420	41	3.3	3.3	NUM
ejde-390	420	42	(	(	PUNCT
ejde-390	420	43	see	see	VERB
ejde-390	420	44	the	the	DET
ejde-390	420	45	part	part	NOUN
ejde-390	420	46	of	of	ADP
ejde-390	420	47	the	the	DET
ejde-390	420	48	proof	proof	NOUN
ejde-390	420	49	from	from	ADP
ejde-390	420	50	(	(	PUNCT
ejde-390	420	51	3.20	3.20	NUM
ejde-390	420	52	)	)	PUNCT
ejde-390	420	53	up	up	ADP
ejde-390	420	54	to	to	ADP
ejde-390	420	55	(	(	PUNCT
ejde-390	420	56	3.33	3.33	NUM
ejde-390	420	57	)	)	PUNCT
ejde-390	420	58	)	)	PUNCT
ejde-390	420	59	,	,	PUNCT
ejde-390	420	60	we	we	PRON
ejde-390	420	61	can	can	AUX
ejde-390	420	62	show	show	VERB
ejde-390	420	63	that	that	DET
ejde-390	420	64	ψ̂λ	ψ̂λ	PROPN
ejde-390	420	65	(	(	PUNCT
ejde-390	420	66	·	·	PUNCT
ejde-390	420	67	)	)	PUNCT
ejde-390	420	68	satisfies	satisfy	VERB
ejde-390	420	69	the	the	DET
ejde-390	420	70	c	c	NOUN
ejde-390	420	71	-	-	NOUN
ejde-390	420	72	condition	condition	NOUN
ejde-390	420	73	.	.	PUNCT
ejde-390	421	1	(	(	PUNCT
ejde-390	421	2	3.47	3.47	NUM
ejde-390	421	3	)	)	PUNCT
ejde-390	421	4	then	then	ADV
ejde-390	421	5	(	(	PUNCT
ejde-390	421	6	3.45	3.45	NUM
ejde-390	421	7	)	)	PUNCT
ejde-390	421	8	,	,	PUNCT
ejde-390	421	9	(	(	PUNCT
ejde-390	421	10	3.46	3.46	NUM
ejde-390	421	11	)	)	PUNCT
ejde-390	421	12	,	,	PUNCT
ejde-390	421	13	(	(	PUNCT
ejde-390	421	14	3.47	3.47	NUM
ejde-390	421	15	)	)	PUNCT
ejde-390	421	16	permit	permit	VERB
ejde-390	421	17	the	the	DET
ejde-390	421	18	use	use	NOUN
ejde-390	421	19	of	of	ADP
ejde-390	421	20	the	the	DET
ejde-390	421	21	mountain	mountain	NOUN
ejde-390	421	22	pass	pass	NOUN
ejde-390	421	23	theorem	theorem	NOUN
ejde-390	421	24	.	.	PUNCT
ejde-390	422	1	so	so	ADV
ejde-390	422	2	,	,	PUNCT
ejde-390	422	3	we	we	PRON
ejde-390	422	4	can	can	AUX
ejde-390	422	5	find	find	VERB
ejde-390	422	6	û	û	NUM
ejde-390	422	7	∈w	∈w	NOUN
ejde-390	422	8	1,p(ω	1,p(ω	NUM
ejde-390	422	9	)	)	PUNCT
ejde-390	422	10	such	such	ADJ
ejde-390	422	11	that	that	SCONJ
ejde-390	422	12	û	û	NUM
ejde-390	422	13	∈	∈	PROPN
ejde-390	422	14	kψ̂λ	kψ̂λ	NOUN
ejde-390	422	15	⊆	⊆	NUM
ejde-390	422	16	[	[	X
ejde-390	422	17	uη	uη	ADJ
ejde-390	422	18	)	)	PUNCT
ejde-390	422	19	∩d+	∩d+	PROPN
ejde-390	422	20	(	(	PUNCT
ejde-390	422	21	see	see	VERB
ejde-390	422	22	(	(	PUNCT
ejde-390	422	23	3.41	3.41	NUM
ejde-390	422	24	)	)	PUNCT
ejde-390	422	25	)	)	PUNCT
ejde-390	422	26	and	and	CCONJ
ejde-390	422	27	m̂λ	m̂λ	ADP
ejde-390	422	28	≤	≤	ADJ
ejde-390	422	29	ψ̂λ(û	ψ̂λ(û	ADJ
ejde-390	422	30	)	)	PUNCT
ejde-390	422	31	(	(	PUNCT
ejde-390	422	32	see	see	VERB
ejde-390	422	33	(	(	PUNCT
ejde-390	422	34	3.45	3.45	NUM
ejde-390	422	35	)	)	PUNCT
ejde-390	422	36	)	)	PUNCT
ejde-390	422	37	,	,	PUNCT
ejde-390	422	38	⇒	⇒	VERB
ejde-390	422	39	û	û	NUM
ejde-390	422	40	6=	6=	NUM
ejde-390	422	41	u0	u0	ADJ
ejde-390	422	42	(	(	PUNCT
ejde-390	422	43	see	see	VERB
ejde-390	422	44	(	(	PUNCT
ejde-390	422	45	3.45	3.45	NUM
ejde-390	422	46	)	)	PUNCT
ejde-390	422	47	)	)	PUNCT
ejde-390	422	48	and	and	CCONJ
ejde-390	422	49	û	û	NUM
ejde-390	422	50	∈	∈	NOUN
ejde-390	422	51	sλ	sλ	ADP
ejde-390	422	52	⊆	⊆	NUM
ejde-390	422	53	d+	d+	X
ejde-390	422	54	(	(	PUNCT
ejde-390	422	55	see	see	VERB
ejde-390	422	56	(	(	PUNCT
ejde-390	422	57	3.39	3.39	NUM
ejde-390	422	58	)	)	PUNCT
ejde-390	422	59	)	)	PUNCT
ejde-390	422	60	.	.	PUNCT
ejde-390	423	1	�	�	PROPN
ejde-390	423	2	proposition	proposition	NOUN
ejde-390	423	3	3.5	3.5	NUM
ejde-390	423	4	.	.	PUNCT
ejde-390	424	1	if	if	SCONJ
ejde-390	424	2	hypotheses	hypothesis	NOUN
ejde-390	424	3	(	(	PUNCT
ejde-390	424	4	h1)–(h3	h1)–(h3	NOUN
ejde-390	424	5	)	)	PUNCT
ejde-390	424	6	hold	hold	VERB
ejde-390	424	7	,	,	PUNCT
ejde-390	424	8	then	then	ADV
ejde-390	424	9	λ∗	λ∗	PROPN
ejde-390	424	10	∈	∈	PROPN
ejde-390	424	11	l.	l.	PROPN
ejde-390	424	12	proof	proof	PROPN
ejde-390	424	13	.	.	PUNCT
ejde-390	425	1	let	let	VERB
ejde-390	425	2	{	{	PUNCT
ejde-390	425	3	λn}n≥1	λn}n≥1	NOUN
ejde-390	425	4	⊆	⊆	NUM
ejde-390	425	5	l	l	NOUN
ejde-390	425	6	such	such	ADJ
ejde-390	426	1	that	that	DET
ejde-390	426	2	λn	λn	PROPN
ejde-390	426	3	↓	↓	NOUN
ejde-390	426	4	λ∗.	λ∗.	X
ejde-390	426	5	from	from	ADP
ejde-390	426	6	the	the	DET
ejde-390	426	7	proof	proof	NOUN
ejde-390	426	8	of	of	ADP
ejde-390	426	9	proposition	proposition	NOUN
ejde-390	426	10	3.3	3.3	NUM
ejde-390	426	11	,	,	PUNCT
ejde-390	426	12	we	we	PRON
ejde-390	426	13	know	know	VERB
ejde-390	426	14	that	that	SCONJ
ejde-390	426	15	we	we	PRON
ejde-390	426	16	can	can	AUX
ejde-390	426	17	find	find	VERB
ejde-390	426	18	un	un	PROPN
ejde-390	426	19	∈	∈	PROPN
ejde-390	426	20	sλn	sλn	NOUN
ejde-390	427	1	⊆	⊆	NUM
ejde-390	427	2	d+	d+	NOUN
ejde-390	427	3	,	,	PUNCT
ejde-390	427	4	n	n	PROPN
ejde-390	427	5	∈	∈	PROPN
ejde-390	427	6	n	n	CCONJ
ejde-390	427	7	,	,	PUNCT
ejde-390	427	8	such	such	ADJ
ejde-390	427	9	that	that	SCONJ
ejde-390	427	10	ũ	ũ	PROPN
ejde-390	427	11	≤	≤	PROPN
ejde-390	427	12	un	un	PROPN
ejde-390	427	13	and	and	CCONJ
ejde-390	427	14	ϕλn(un	ϕλn(un	PROPN
ejde-390	427	15	)	)	PUNCT
ejde-390	427	16	≤	≤	NUM
ejde-390	427	17	c16	c16	NOUN
ejde-390	427	18	for	for	ADP
ejde-390	427	19	some	some	DET
ejde-390	427	20	c16	c16	PROPN
ejde-390	427	21	>	>	X
ejde-390	427	22	0	0	PROPN
ejde-390	427	23	,	,	PUNCT
ejde-390	427	24	all	all	DET
ejde-390	427	25	n	n	PRON
ejde-390	427	26	∈	∈	NOUN
ejde-390	427	27	n.	n.	NOUN
ejde-390	427	28	as	as	ADP
ejde-390	427	29	in	in	ADP
ejde-390	427	30	the	the	DET
ejde-390	427	31	proof	proof	NOUN
ejde-390	427	32	of	of	ADP
ejde-390	427	33	proposition	proposition	NOUN
ejde-390	427	34	3.3	3.3	NUM
ejde-390	427	35	,	,	PUNCT
ejde-390	427	36	we	we	PRON
ejde-390	427	37	can	can	AUX
ejde-390	427	38	show	show	VERB
ejde-390	427	39	that	that	SCONJ
ejde-390	427	40	un	un	PROPN
ejde-390	427	41	→	→	X
ejde-390	427	42	u∗	u∗	PROPN
ejde-390	427	43	in	in	ADP
ejde-390	427	44	w	w	PROPN
ejde-390	427	45	1,p(ω	1,p(ω	NUM
ejde-390	427	46	)	)	PUNCT
ejde-390	427	47	.	.	PUNCT
ejde-390	428	1	then	then	ADV
ejde-390	428	2	in	in	ADP
ejde-390	428	3	the	the	DET
ejde-390	428	4	limit	limit	NOUN
ejde-390	428	5	as	as	ADP
ejde-390	428	6	n→	n→	ADV
ejde-390	428	7	+	+	SYM
ejde-390	428	8	∞	∞	NUM
ejde-390	428	9	we	we	PRON
ejde-390	428	10	have	have	VERB
ejde-390	428	11	ũ	ũ	PROPN
ejde-390	428	12	≤	≤	X
ejde-390	428	13	u∗	u∗	NOUN
ejde-390	428	14	and	and	CCONJ
ejde-390	428	15	〈	〈	PROPN
ejde-390	428	16	a(u∗	a(u∗	X
ejde-390	428	17	)	)	PUNCT
ejde-390	428	18	,	,	PUNCT
ejde-390	429	1	h〉+	h〉+	PROPN
ejde-390	429	2	∫	∫	PROPN
ejde-390	429	3	ω	ω	PROPN
ejde-390	430	1	[	[	X
ejde-390	430	2	ξ(z	ξ(z	NOUN
ejde-390	430	3	)	)	PUNCT
ejde-390	431	1	+	+	NOUN
ejde-390	431	2	λ∗]u	λ∗]u	PROPN
ejde-390	431	3	p−1	p−1	PROPN
ejde-390	431	4	∗	∗	NOUN
ejde-390	431	5	hdz	hdz	PROPN
ejde-390	431	6	=	=	SYM
ejde-390	431	7	∫	∫	PROPN
ejde-390	431	8	ω	ω	NUM
ejde-390	431	9	f(z	f(z	PROPN
ejde-390	431	10	,	,	PUNCT
ejde-390	431	11	u∗)hdz	u∗)hdz	PROPN
ejde-390	431	12	,	,	PUNCT
ejde-390	431	13	for	for	ADP
ejde-390	431	14	all	all	PRON
ejde-390	431	15	h	h	NOUN
ejde-390	431	16	∈w	∈w	PROPN
ejde-390	431	17	1,p(ω	1,p(ω	NUM
ejde-390	431	18	)	)	PUNCT
ejde-390	431	19	,	,	PUNCT
ejde-390	431	20	which	which	PRON
ejde-390	431	21	implies	imply	VERB
ejde-390	431	22	u∗	u∗	PROPN
ejde-390	431	23	∈	∈	PROPN
ejde-390	431	24	sλ∗	sλ∗	NOUN
ejde-390	431	25	⊆	⊆	NUM
ejde-390	431	26	d+	d+	NOUN
ejde-390	431	27	,	,	PUNCT
ejde-390	431	28	and	and	CCONJ
ejde-390	431	29	so	so	ADV
ejde-390	431	30	λ∗	λ∗	PROPN
ejde-390	431	31	∈	∈	PROPN
ejde-390	431	32	l.	l.	PROPN
ejde-390	431	33	�	�	PROPN
ejde-390	431	34	note	note	VERB
ejde-390	431	35	that	that	SCONJ
ejde-390	431	36	proposition	proposition	NOUN
ejde-390	431	37	3.5	3.5	NUM
ejde-390	431	38	implies	imply	VERB
ejde-390	431	39	that	that	SCONJ
ejde-390	431	40	l	l	NOUN
ejde-390	431	41	=	=	PUNCT
ejde-390	432	1	[	[	X
ejde-390	432	2	λ∗,+∞	λ∗,+∞	X
ejde-390	432	3	)	)	PUNCT
ejde-390	432	4	.	.	PUNCT
ejde-390	433	1	summarizing	summarize	VERB
ejde-390	433	2	our	our	PRON
ejde-390	433	3	results	result	NOUN
ejde-390	433	4	on	on	ADP
ejde-390	433	5	the	the	DET
ejde-390	433	6	dependence	dependence	NOUN
ejde-390	433	7	of	of	ADP
ejde-390	433	8	the	the	DET
ejde-390	433	9	set	set	NOUN
ejde-390	433	10	of	of	ADP
ejde-390	433	11	positive	positive	ADJ
ejde-390	433	12	solutions	solution	NOUN
ejde-390	433	13	of	of	ADP
ejde-390	433	14	(	(	PUNCT
ejde-390	433	15	1.1	1.1	NUM
ejde-390	433	16	)	)	PUNCT
ejde-390	433	17	on	on	ADP
ejde-390	433	18	the	the	DET
ejde-390	433	19	parameter	parameter	NOUN
ejde-390	433	20	λ	λ	PROPN
ejde-390	433	21	>	>	X
ejde-390	433	22	0	0	PROPN
ejde-390	433	23	,	,	PUNCT
ejde-390	433	24	we	we	PRON
ejde-390	433	25	can	can	AUX
ejde-390	433	26	state	state	VERB
ejde-390	433	27	the	the	DET
ejde-390	433	28	following	follow	VERB
ejde-390	433	29	bifurcation	bifurcation	NOUN
ejde-390	433	30	-	-	PUNCT
ejde-390	433	31	type	type	NOUN
ejde-390	433	32	result	result	NOUN
ejde-390	433	33	for	for	ADP
ejde-390	433	34	big	big	ADJ
ejde-390	433	35	values	value	NOUN
ejde-390	433	36	of	of	ADP
ejde-390	433	37	λ	λ	PROPN
ejde-390	433	38	>	>	X
ejde-390	433	39	0	0	PROPN
ejde-390	433	40	.	.	PUNCT
ejde-390	433	41	theorem	theorem	VERB
ejde-390	433	42	3.6	3.6	NUM
ejde-390	433	43	.	.	PUNCT
ejde-390	434	1	if	if	SCONJ
ejde-390	434	2	hypotheses	hypothesis	NOUN
ejde-390	434	3	(	(	PUNCT
ejde-390	434	4	h1)–(h3	h1)–(h3	NOUN
ejde-390	434	5	)	)	PUNCT
ejde-390	434	6	hold	hold	VERB
ejde-390	434	7	,	,	PUNCT
ejde-390	434	8	then	then	ADV
ejde-390	434	9	there	there	PRON
ejde-390	434	10	exists	exist	VERB
ejde-390	434	11	a	a	DET
ejde-390	434	12	critical	critical	ADJ
ejde-390	434	13	parameter	parameter	NOUN
ejde-390	434	14	value	value	NOUN
ejde-390	434	15	λ∗	λ∗	PROPN
ejde-390	434	16	>	>	X
ejde-390	434	17	0	0	NUM
ejde-390	435	1	such	such	ADJ
ejde-390	435	2	that	that	SCONJ
ejde-390	435	3	(	(	PUNCT
ejde-390	435	4	a	a	NOUN
ejde-390	435	5	)	)	PUNCT
ejde-390	435	6	for	for	ADP
ejde-390	435	7	all	all	DET
ejde-390	435	8	λ	λ	PROPN
ejde-390	435	9	>	>	X
ejde-390	435	10	λ∗	λ∗	PROPN
ejde-390	435	11	problem	problem	NOUN
ejde-390	435	12	(	(	PUNCT
ejde-390	435	13	1.1	1.1	NUM
ejde-390	435	14	)	)	PUNCT
ejde-390	435	15	has	have	VERB
ejde-390	435	16	at	at	ADV
ejde-390	435	17	least	least	ADV
ejde-390	435	18	two	two	NUM
ejde-390	435	19	positive	positive	ADJ
ejde-390	435	20	solutions	solution	NOUN
ejde-390	435	21	u0	u0	ADJ
ejde-390	435	22	,	,	PUNCT
ejde-390	435	23	û	û	PROPN
ejde-390	435	24	∈	∈	PROPN
ejde-390	435	25	d+	d+	PUNCT
ejde-390	435	26	,	,	PUNCT
ejde-390	435	27	u0	u0	ADJ
ejde-390	435	28	6=	6=	PROPN
ejde-390	435	29	û	û	NUM
ejde-390	435	30	;	;	PUNCT
ejde-390	435	31	(	(	PUNCT
ejde-390	435	32	b	b	X
ejde-390	435	33	)	)	PUNCT
ejde-390	435	34	for	for	ADP
ejde-390	435	35	λ	λ	PROPN
ejde-390	435	36	=	=	SYM
ejde-390	435	37	λ∗	λ∗	PROPN
ejde-390	435	38	problem	problem	NOUN
ejde-390	435	39	(	(	PUNCT
ejde-390	435	40	1.1	1.1	NUM
ejde-390	435	41	)	)	PUNCT
ejde-390	435	42	has	have	VERB
ejde-390	435	43	at	at	ADV
ejde-390	435	44	least	least	ADV
ejde-390	435	45	one	one	NUM
ejde-390	435	46	positive	positive	ADJ
ejde-390	435	47	solution	solution	NOUN
ejde-390	435	48	u∗	u∗	X
ejde-390	435	49	∈	∈	PROPN
ejde-390	435	50	d+	d+	X
ejde-390	435	51	;	;	PUNCT
ejde-390	435	52	(	(	PUNCT
ejde-390	435	53	c	c	X
ejde-390	435	54	)	)	PUNCT
ejde-390	435	55	for	for	ADP
ejde-390	435	56	all	all	DET
ejde-390	435	57	λ	λ	PROPN
ejde-390	435	58	∈	∈	PROPN
ejde-390	435	59	(	(	PUNCT
ejde-390	435	60	0	0	NUM
ejde-390	435	61	,	,	PUNCT
ejde-390	435	62	λ∗	λ∗	NOUN
ejde-390	435	63	)	)	PUNCT
ejde-390	435	64	problem	problem	NOUN
ejde-390	435	65	(	(	PUNCT
ejde-390	435	66	1.1	1.1	NUM
ejde-390	435	67	)	)	PUNCT
ejde-390	435	68	has	have	VERB
ejde-390	435	69	no	no	DET
ejde-390	435	70	positive	positive	ADJ
ejde-390	435	71	solutions	solution	NOUN
ejde-390	435	72	.	.	PUNCT
ejde-390	436	1	next	next	ADV
ejde-390	436	2	we	we	PRON
ejde-390	436	3	show	show	VERB
ejde-390	436	4	that	that	SCONJ
ejde-390	436	5	for	for	ADP
ejde-390	436	6	every	every	DET
ejde-390	436	7	λ	λ	PROPN
ejde-390	436	8	∈	∈	NOUN
ejde-390	436	9	l	l	NOUN
ejde-390	436	10	=	=	PUNCT
ejde-390	437	1	[	[	X
ejde-390	437	2	λ∗,+∞	λ∗,+∞	X
ejde-390	437	3	)	)	PUNCT
ejde-390	437	4	,	,	PUNCT
ejde-390	437	5	problem	problem	NOUN
ejde-390	437	6	(	(	PUNCT
ejde-390	437	7	1.1	1.1	NUM
ejde-390	437	8	)	)	PUNCT
ejde-390	437	9	has	have	VERB
ejde-390	437	10	a	a	DET
ejde-390	437	11	smallest	small	ADJ
ejde-390	437	12	positive	positive	ADJ
ejde-390	437	13	solution	solution	NOUN
ejde-390	437	14	.	.	PUNCT
ejde-390	438	1	proposition	proposition	NOUN
ejde-390	438	2	3.7	3.7	NUM
ejde-390	438	3	.	.	PUNCT
ejde-390	439	1	if	if	SCONJ
ejde-390	439	2	hypotheses	hypothesis	NOUN
ejde-390	439	3	(	(	PUNCT
ejde-390	439	4	h1)–(h3	h1)–(h3	NOUN
ejde-390	439	5	)	)	PUNCT
ejde-390	439	6	hold	hold	VERB
ejde-390	439	7	and	and	CCONJ
ejde-390	439	8	λ	λ	X
ejde-390	439	9	∈	∈	NOUN
ejde-390	439	10	l	l	NOUN
ejde-390	440	1	=	=	PUNCT
ejde-390	441	1	[	[	X
ejde-390	441	2	λ∗,+∞	λ∗,+∞	X
ejde-390	441	3	)	)	PUNCT
ejde-390	441	4	,	,	PUNCT
ejde-390	441	5	then	then	ADV
ejde-390	441	6	problem	problem	NOUN
ejde-390	441	7	(	(	PUNCT
ejde-390	441	8	1.1	1.1	NUM
ejde-390	441	9	)	)	PUNCT
ejde-390	441	10	has	have	VERB
ejde-390	441	11	a	a	DET
ejde-390	441	12	smallest	small	ADJ
ejde-390	441	13	positive	positive	ADJ
ejde-390	441	14	solution	solution	NOUN
ejde-390	441	15	ûλ	ûλ	NOUN
ejde-390	441	16	∈	∈	PROPN
ejde-390	441	17	d+	d+	PUNCT
ejde-390	441	18	.	.	PUNCT
ejde-390	442	1	proof	proof	NOUN
ejde-390	442	2	.	.	PUNCT
ejde-390	443	1	from	from	ADP
ejde-390	443	2	papageorgiou	papageorgiou	NOUN
ejde-390	443	3	-	-	PUNCT
ejde-390	443	4	rǎdulescu	rǎdulescu	NUM
ejde-390	443	5	-	-	PUNCT
ejde-390	443	6	repovš	repovš	NOUN
ejde-390	443	7	[	[	X
ejde-390	443	8	12	12	NUM
ejde-390	443	9	]	]	PUNCT
ejde-390	443	10	(	(	PUNCT
ejde-390	443	11	see	see	VERB
ejde-390	443	12	the	the	DET
ejde-390	443	13	proof	proof	NOUN
ejde-390	443	14	of	of	ADP
ejde-390	443	15	proposition	proposition	NOUN
ejde-390	443	16	7	7	NUM
ejde-390	443	17	)	)	PUNCT
ejde-390	443	18	,	,	PUNCT
ejde-390	443	19	we	we	PRON
ejde-390	443	20	know	know	VERB
ejde-390	443	21	that	that	SCONJ
ejde-390	443	22	the	the	DET
ejde-390	443	23	solution	solution	NOUN
ejde-390	443	24	set	set	VERB
ejde-390	443	25	sλ	sλ	NOUN
ejde-390	443	26	is	be	AUX
ejde-390	443	27	downward	downward	ADV
ejde-390	443	28	directed	direct	VERB
ejde-390	443	29	(	(	PUNCT
ejde-390	443	30	that	that	PRON
ejde-390	443	31	is	is	ADV
ejde-390	443	32	,	,	PUNCT
ejde-390	443	33	if	if	SCONJ
ejde-390	443	34	u1	u1	NOUN
ejde-390	443	35	,	,	PUNCT
ejde-390	443	36	u2	u2	PROPN
ejde-390	443	37	∈	∈	PROPN
ejde-390	443	38	sλ	sλ	NOUN
ejde-390	443	39	,	,	PUNCT
ejde-390	443	40	then	then	ADV
ejde-390	443	41	we	we	PRON
ejde-390	443	42	can	can	AUX
ejde-390	443	43	find	find	VERB
ejde-390	443	44	u	u	PRON
ejde-390	443	45	∈	∈	NOUN
ejde-390	443	46	sλ	sλ	NOUN
ejde-390	443	47	such	such	ADJ
ejde-390	443	48	that	that	SCONJ
ejde-390	443	49	u	u	PROPN
ejde-390	443	50	≤	≤	NUM
ejde-390	443	51	u1	u1	NOUN
ejde-390	443	52	,	,	PUNCT
ejde-390	443	53	u	u	NOUN
ejde-390	443	54	≤	≤	NOUN
ejde-390	443	55	u2	u2	NOUN
ejde-390	443	56	)	)	PUNCT
ejde-390	443	57	.	.	PUNCT
ejde-390	444	1	then	then	ADV
ejde-390	444	2	invoking	invoke	VERB
ejde-390	444	3	[	[	X
ejde-390	444	4	5	5	NUM
ejde-390	444	5	,	,	PUNCT
ejde-390	444	6	lemma	lemma	PROPN
ejde-390	444	7	3.10	3.10	NUM
ejde-390	444	8	,	,	PUNCT
ejde-390	444	9	p.	p.	NOUN
ejde-390	444	10	178	178	NUM
ejde-390	444	11	]	]	PUNCT
ejde-390	444	12	,	,	PUNCT
ejde-390	444	13	we	we	PRON
ejde-390	444	14	can	can	AUX
ejde-390	444	15	find	find	VERB
ejde-390	444	16	a	a	DET
ejde-390	444	17	decreasing	decrease	VERB
ejde-390	444	18	sequence	sequence	NOUN
ejde-390	444	19	{	{	PUNCT
ejde-390	444	20	un}n≥1	un}n≥1	NOUN
ejde-390	444	21	⊆	⊆	NUM
ejde-390	444	22	sλ	sλ	NOUN
ejde-390	444	23	such	such	ADJ
ejde-390	444	24	that	that	DET
ejde-390	444	25	inf	inf	PROPN
ejde-390	444	26	sλ	sλ	NOUN
ejde-390	444	27	=	=	PUNCT
ejde-390	444	28	inf	inf	PROPN
ejde-390	444	29	n≥1	n≥1	PROPN
ejde-390	444	30	un	un	PROPN
ejde-390	444	31	and	and	CCONJ
ejde-390	444	32	0	0	NUM
ejde-390	444	33	≤	≤	NUM
ejde-390	444	34	un	un	PROPN
ejde-390	444	35	≤	≤	PROPN
ejde-390	444	36	u1	u1	NOUN
ejde-390	444	37	for	for	ADP
ejde-390	444	38	all	all	DET
ejde-390	444	39	n	n	PRON
ejde-390	444	40	∈	∈	PROPN
ejde-390	444	41	n.	n.	NOUN
ejde-390	444	42	(	(	PUNCT
ejde-390	444	43	3.48	3.48	NUM
ejde-390	444	44	)	)	PUNCT
ejde-390	444	45	16	16	NUM
ejde-390	444	46	n.	n.	PROPN
ejde-390	444	47	s.	s.	PROPN
ejde-390	444	48	papageorgiou	papageorgiou	PROPN
ejde-390	444	49	,	,	PUNCT
ejde-390	444	50	c.	c.	PROPN
ejde-390	444	51	vetro	vetro	PROPN
ejde-390	444	52	,	,	PUNCT
ejde-390	444	53	f.	f.	PROPN
ejde-390	444	54	vetro	vetro	PROPN
ejde-390	444	55	ejde-2020/12	ejde-2020/12	NOUN
ejde-390	444	56	we	we	PRON
ejde-390	444	57	have	have	VERB
ejde-390	444	58	〈	〈	PROPN
ejde-390	444	59	a(un	a(un	PROPN
ejde-390	444	60	)	)	PUNCT
ejde-390	444	61	,	,	PUNCT
ejde-390	445	1	h〉+	h〉+	PROPN
ejde-390	445	2	∫	∫	PROPN
ejde-390	445	3	ω	ω	PROPN
ejde-390	446	1	[	[	X
ejde-390	446	2	ξ(z	ξ(z	NOUN
ejde-390	446	3	)	)	PUNCT
ejde-390	447	1	+	+	CCONJ
ejde-390	447	2	λ]up−1	λ]up−1	SYM
ejde-390	447	3	n	n	ADV
ejde-390	447	4	hdz	hdz	NOUN
ejde-390	447	5	=	=	SYM
ejde-390	447	6	∫	∫	PROPN
ejde-390	447	7	ω	ω	NUM
ejde-390	447	8	f(z	f(z	PROPN
ejde-390	447	9	,	,	PUNCT
ejde-390	447	10	un)hdz	un)hdz	VERB
ejde-390	447	11	for	for	ADP
ejde-390	447	12	all	all	DET
ejde-390	447	13	h	h	NOUN
ejde-390	447	14	∈w	∈w	PROPN
ejde-390	447	15	1,p(ω	1,p(ω	NUM
ejde-390	447	16	)	)	PUNCT
ejde-390	447	17	.	.	PUNCT
ejde-390	448	1	(	(	PUNCT
ejde-390	448	2	3.49	3.49	NUM
ejde-390	448	3	)	)	PUNCT
ejde-390	448	4	choosing	choose	VERB
ejde-390	448	5	h	h	NOUN
ejde-390	448	6	=	=	NOUN
ejde-390	448	7	un	un	PROPN
ejde-390	448	8	∈	∈	PROPN
ejde-390	448	9	w	w	PROPN
ejde-390	448	10	1,p(ω	1,p(ω	PROPN
ejde-390	448	11	)	)	PUNCT
ejde-390	448	12	in	in	ADP
ejde-390	448	13	(	(	PUNCT
ejde-390	448	14	3.49	3.49	NUM
ejde-390	448	15	)	)	PUNCT
ejde-390	448	16	and	and	CCONJ
ejde-390	448	17	using	use	VERB
ejde-390	448	18	(	(	PUNCT
ejde-390	448	19	3.48	3.48	NUM
ejde-390	448	20	)	)	PUNCT
ejde-390	448	21	,	,	PUNCT
ejde-390	448	22	we	we	PRON
ejde-390	448	23	infer	infer	VERB
ejde-390	448	24	that	that	SCONJ
ejde-390	448	25	{	{	PUNCT
ejde-390	448	26	un}n≥1	un}n≥1	X
ejde-390	448	27	⊆	⊆	NUM
ejde-390	448	28	w	w	PROPN
ejde-390	448	29	1,p(ω	1,p(ω	NUM
ejde-390	448	30	)	)	PUNCT
ejde-390	448	31	is	be	AUX
ejde-390	448	32	bounded	bound	VERB
ejde-390	448	33	.	.	PUNCT
ejde-390	449	1	proposition	proposition	NOUN
ejde-390	449	2	7	7	NUM
ejde-390	449	3	in	in	ADP
ejde-390	449	4	papageorgiou	papageorgiou	NOUN
ejde-390	449	5	-	-	PUNCT
ejde-390	449	6	rǎdulescu	rǎdulescu	NOUN
ejde-390	449	7	[	[	X
ejde-390	449	8	10	10	NUM
ejde-390	449	9	]	]	PUNCT
ejde-390	449	10	implies	imply	VERB
ejde-390	449	11	that	that	SCONJ
ejde-390	449	12	we	we	PRON
ejde-390	449	13	can	can	AUX
ejde-390	449	14	find	find	VERB
ejde-390	449	15	c16	c16	NOUN
ejde-390	449	16	>	>	X
ejde-390	449	17	0	0	NUM
ejde-390	449	18	such	such	ADJ
ejde-390	449	19	that	that	SCONJ
ejde-390	449	20	un	un	PROPN
ejde-390	449	21	∈	∈	PROPN
ejde-390	449	22	l∞(ω	l∞(ω	PROPN
ejde-390	449	23	)	)	PUNCT
ejde-390	449	24	and	and	CCONJ
ejde-390	449	25	‖un‖∞	‖un‖∞	NUM
ejde-390	449	26	≤	≤	NUM
ejde-390	449	27	c16	c16	NOUN
ejde-390	449	28	for	for	ADP
ejde-390	449	29	all	all	DET
ejde-390	449	30	n	n	PRON
ejde-390	449	31	∈	∈	PROPN
ejde-390	449	32	n.	n.	NOUN
ejde-390	449	33	then	then	ADV
ejde-390	449	34	the	the	DET
ejde-390	449	35	nonlinear	nonlinear	ADJ
ejde-390	449	36	regularity	regularity	NOUN
ejde-390	449	37	theory	theory	NOUN
ejde-390	449	38	of	of	ADP
ejde-390	449	39	lieberman	lieberman	PROPN
ejde-390	450	1	[	[	X
ejde-390	450	2	7	7	NUM
ejde-390	450	3	]	]	PUNCT
ejde-390	450	4	implies	imply	VERB
ejde-390	450	5	that	that	SCONJ
ejde-390	450	6	there	there	PRON
ejde-390	450	7	exist	exist	VERB
ejde-390	450	8	α	α	PRON
ejde-390	450	9	∈	∈	PROPN
ejde-390	450	10	(	(	PUNCT
ejde-390	450	11	0	0	NUM
ejde-390	450	12	,	,	PUNCT
ejde-390	450	13	1	1	NUM
ejde-390	450	14	)	)	PUNCT
ejde-390	450	15	and	and	CCONJ
ejde-390	450	16	c17	c17	NOUN
ejde-390	450	17	>	>	X
ejde-390	450	18	0	0	NUM
ejde-390	450	19	such	such	ADJ
ejde-390	450	20	that	that	SCONJ
ejde-390	450	21	un	un	PROPN
ejde-390	450	22	∈	∈	PROPN
ejde-390	450	23	c1,α(ω	c1,α(ω	NOUN
ejde-390	450	24	)	)	PUNCT
ejde-390	450	25	,	,	PUNCT
ejde-390	450	26	‖un‖c1,α(ω	‖un‖c1,α(ω	NOUN
ejde-390	450	27	)	)	PUNCT
ejde-390	450	28	≤	≤	NOUN
ejde-390	450	29	c17	c17	NOUN
ejde-390	450	30	for	for	ADP
ejde-390	450	31	all	all	DET
ejde-390	450	32	n	n	PRON
ejde-390	450	33	∈	∈	PROPN
ejde-390	450	34	n.	n.	NOUN
ejde-390	450	35	(	(	PUNCT
ejde-390	450	36	3.50	3.50	NUM
ejde-390	450	37	)	)	PUNCT
ejde-390	450	38	from	from	ADP
ejde-390	450	39	(	(	PUNCT
ejde-390	450	40	3.50	3.50	NUM
ejde-390	450	41	)	)	PUNCT
ejde-390	450	42	,	,	PUNCT
ejde-390	450	43	the	the	DET
ejde-390	450	44	compact	compact	ADJ
ejde-390	450	45	embedding	embedding	NOUN
ejde-390	450	46	of	of	ADP
ejde-390	450	47	c1,α(ω	c1,α(ω	NOUN
ejde-390	450	48	)	)	PUNCT
ejde-390	450	49	into	into	ADP
ejde-390	450	50	c1(ω	c1(ω	NOUN
ejde-390	450	51	)	)	PUNCT
ejde-390	450	52	,	,	PUNCT
ejde-390	450	53	and	and	CCONJ
ejde-390	450	54	the	the	DET
ejde-390	450	55	monotonicity	monotonicity	NOUN
ejde-390	450	56	of	of	ADP
ejde-390	450	57	{	{	PUNCT
ejde-390	450	58	un}n≥1	un}n≥1	PROPN
ejde-390	450	59	,	,	PUNCT
ejde-390	450	60	we	we	PRON
ejde-390	450	61	have	have	VERB
ejde-390	450	62	un	un	PROPN
ejde-390	450	63	→	→	X
ejde-390	450	64	ûλ	ûλ	NOUN
ejde-390	450	65	in	in	ADP
ejde-390	450	66	c1(ω	c1(ω	NOUN
ejde-390	450	67	)	)	PUNCT
ejde-390	450	68	.	.	PUNCT
ejde-390	451	1	(	(	PUNCT
ejde-390	451	2	3.51	3.51	NUM
ejde-390	451	3	)	)	PUNCT
ejde-390	451	4	from	from	ADP
ejde-390	451	5	the	the	DET
ejde-390	451	6	proof	proof	NOUN
ejde-390	451	7	of	of	ADP
ejde-390	451	8	proposition	proposition	NOUN
ejde-390	451	9	3.3	3.3	NUM
ejde-390	451	10	,	,	PUNCT
ejde-390	451	11	we	we	PRON
ejde-390	451	12	know	know	VERB
ejde-390	451	13	that	that	SCONJ
ejde-390	451	14	ũ	ũ	PROPN
ejde-390	451	15	≤	≤	PROPN
ejde-390	451	16	un	un	NOUN
ejde-390	451	17	for	for	ADP
ejde-390	451	18	all	all	PRON
ejde-390	451	19	n	n	PRON
ejde-390	451	20	∈	∈	PROPN
ejde-390	451	21	n	n	CCONJ
ejde-390	451	22	,	,	PUNCT
ejde-390	451	23	⇒	⇒	VERB
ejde-390	451	24	ũ	ũ	PROPN
ejde-390	451	25	≤	≤	PROPN
ejde-390	451	26	ûλ	ûλ	NOUN
ejde-390	451	27	(	(	PUNCT
ejde-390	451	28	see	see	VERB
ejde-390	451	29	(	(	PUNCT
ejde-390	451	30	3.51	3.51	NUM
ejde-390	451	31	)	)	PUNCT
ejde-390	451	32	)	)	PUNCT
ejde-390	451	33	,	,	PUNCT
ejde-390	451	34	hence	hence	ADV
ejde-390	451	35	ûλ	ûλ	ADV
ejde-390	451	36	6=	6=	NOUN
ejde-390	451	37	0	0	NUM
ejde-390	451	38	.	.	PUNCT
ejde-390	452	1	if	if	SCONJ
ejde-390	452	2	in	in	ADP
ejde-390	452	3	(	(	PUNCT
ejde-390	452	4	3.49	3.49	NUM
ejde-390	452	5	)	)	PUNCT
ejde-390	452	6	we	we	PRON
ejde-390	452	7	pass	pass	VERB
ejde-390	452	8	to	to	ADP
ejde-390	452	9	the	the	DET
ejde-390	452	10	limit	limit	NOUN
ejde-390	452	11	as	as	ADP
ejde-390	452	12	n→	n→	ADV
ejde-390	452	13	+	+	PROPN
ejde-390	452	14	∞	∞	NOUN
ejde-390	452	15	and	and	CCONJ
ejde-390	452	16	use	use	NOUN
ejde-390	452	17	(	(	PUNCT
ejde-390	452	18	3.51	3.51	NUM
ejde-390	452	19	)	)	PUNCT
ejde-390	452	20	,	,	PUNCT
ejde-390	452	21	we	we	PRON
ejde-390	452	22	obtain	obtain	VERB
ejde-390	452	23	〈	〈	PROPN
ejde-390	452	24	a(ûλ	a(ûλ	NOUN
ejde-390	452	25	)	)	PUNCT
ejde-390	452	26	,	,	PUNCT
ejde-390	453	1	h〉+	h〉+	PROPN
ejde-390	453	2	∫	∫	PROPN
ejde-390	453	3	ω	ω	PROPN
ejde-390	454	1	[	[	X
ejde-390	454	2	ξ(z	ξ(z	NOUN
ejde-390	454	3	)	)	PUNCT
ejde-390	455	1	+	+	PUNCT
ejde-390	455	2	λ]ûp−1	λ]ûp−1	NUM
ejde-390	455	3	λ	λ	X
ejde-390	455	4	hdz	hdz	NOUN
ejde-390	455	5	=	=	SYM
ejde-390	455	6	∫	∫	PROPN
ejde-390	455	7	ω	ω	NUM
ejde-390	455	8	f(z	f(z	PROPN
ejde-390	455	9	,	,	PUNCT
ejde-390	455	10	ûλ)hdz	ûλ)hdz	VERB
ejde-390	455	11	for	for	ADP
ejde-390	455	12	all	all	DET
ejde-390	455	13	h	h	NOUN
ejde-390	455	14	∈w	∈w	PROPN
ejde-390	455	15	1,p(ω	1,p(ω	NUM
ejde-390	455	16	)	)	PUNCT
ejde-390	455	17	,	,	PUNCT
ejde-390	455	18	⇒	⇒	VERB
ejde-390	455	19	ûλ	ûλ	NOUN
ejde-390	455	20	∈	∈	NOUN
ejde-390	455	21	sλ	sλ	NOUN
ejde-390	455	22	⊆	⊆	NUM
ejde-390	455	23	d+	d+	NOUN
ejde-390	455	24	and	and	CCONJ
ejde-390	455	25	ûλ	ûλ	NOUN
ejde-390	455	26	=	=	VERB
ejde-390	455	27	inf	inf	ADJ
ejde-390	455	28	sλ	sλ	NOUN
ejde-390	455	29	.	.	PUNCT
ejde-390	456	1	�	�	PROPN
ejde-390	456	2	next	next	ADV
ejde-390	456	3	we	we	PRON
ejde-390	456	4	examine	examine	VERB
ejde-390	456	5	the	the	DET
ejde-390	456	6	properties	property	NOUN
ejde-390	456	7	of	of	ADP
ejde-390	456	8	the	the	DET
ejde-390	456	9	map	map	NOUN
ejde-390	456	10	l	l	NOUN
ejde-390	456	11	3	3	NUM
ejde-390	456	12	λ→	λ→	PUNCT
ejde-390	456	13	ûλ	ûλ	NOUN
ejde-390	456	14	∈	∈	NOUN
ejde-390	456	15	c1(ω	c1(ω	NUM
ejde-390	456	16	)	)	PUNCT
ejde-390	456	17	.	.	PUNCT
ejde-390	457	1	proposition	proposition	NOUN
ejde-390	457	2	3.8	3.8	NUM
ejde-390	457	3	.	.	PUNCT
ejde-390	458	1	if	if	SCONJ
ejde-390	458	2	hypotheses	hypothesis	NOUN
ejde-390	458	3	(	(	PUNCT
ejde-390	458	4	h1)–(h3	h1)–(h3	NOUN
ejde-390	458	5	)	)	PUNCT
ejde-390	458	6	hold	hold	VERB
ejde-390	458	7	,	,	PUNCT
ejde-390	458	8	then	then	ADV
ejde-390	458	9	the	the	DET
ejde-390	458	10	map	map	NOUN
ejde-390	458	11	σ	σ	X
ejde-390	458	12	:	:	PUNCT
ejde-390	458	13	l	l	X
ejde-390	458	14	→	→	SYM
ejde-390	458	15	c1(ω	c1(ω	NOUN
ejde-390	458	16	)	)	PUNCT
ejde-390	458	17	defined	define	VERB
ejde-390	458	18	by	by	ADP
ejde-390	458	19	σ(λ	σ(λ	PROPN
ejde-390	458	20	)	)	PUNCT
ejde-390	459	1	=	=	VERB
ejde-390	459	2	ûλ	ûλ	ADV
ejde-390	459	3	has	have	VERB
ejde-390	459	4	the	the	DET
ejde-390	459	5	following	follow	VERB
ejde-390	459	6	properties	property	NOUN
ejde-390	459	7	:	:	PUNCT
ejde-390	459	8	(	(	PUNCT
ejde-390	459	9	a	a	X
ejde-390	459	10	)	)	PUNCT
ejde-390	459	11	σ	σ	PROPN
ejde-390	459	12	(	(	PUNCT
ejde-390	459	13	·	·	PUNCT
ejde-390	459	14	)	)	PUNCT
ejde-390	459	15	is	be	AUX
ejde-390	459	16	strictly	strictly	ADV
ejde-390	459	17	decreasing	decrease	VERB
ejde-390	459	18	in	in	ADP
ejde-390	459	19	the	the	DET
ejde-390	459	20	sense	sense	NOUN
ejde-390	459	21	that	that	SCONJ
ejde-390	459	22	λ∗	λ∗	PROPN
ejde-390	459	23	≤	≤	PROPN
ejde-390	459	24	λ	λ	PROPN
ejde-390	459	25	<	<	X
ejde-390	459	26	η	η	PROPN
ejde-390	459	27	implies	imply	VERB
ejde-390	459	28	ûλ	ûλ	ADV
ejde-390	459	29	−	−	NOUN
ejde-390	459	30	ûη	ûη	SYM
ejde-390	459	31	∈	∈	NOUN
ejde-390	459	32	int	int	NOUN
ejde-390	459	33	ĉ+	ĉ+	X
ejde-390	459	34	;	;	PUNCT
ejde-390	459	35	(	(	PUNCT
ejde-390	459	36	b	b	X
ejde-390	459	37	)	)	PUNCT
ejde-390	459	38	σ	σ	PROPN
ejde-390	459	39	(	(	PUNCT
ejde-390	459	40	·	·	PUNCT
ejde-390	459	41	)	)	PUNCT
ejde-390	459	42	is	be	AUX
ejde-390	459	43	right	right	ADV
ejde-390	459	44	continuous	continuous	ADJ
ejde-390	459	45	.	.	PUNCT
ejde-390	460	1	proof	proof	NOUN
ejde-390	460	2	.	.	PUNCT
ejde-390	461	1	(	(	PUNCT
ejde-390	461	2	a	a	X
ejde-390	461	3	)	)	PUNCT
ejde-390	461	4	let	let	VERB
ejde-390	461	5	ûλ	ûλ	PRON
ejde-390	461	6	∈	∈	NOUN
ejde-390	461	7	d+	d+	NOUN
ejde-390	461	8	be	be	AUX
ejde-390	461	9	the	the	DET
ejde-390	461	10	minimal	minimal	ADJ
ejde-390	461	11	positive	positive	ADJ
ejde-390	461	12	solution	solution	NOUN
ejde-390	461	13	of	of	ADP
ejde-390	461	14	(	(	PUNCT
ejde-390	461	15	1.1	1.1	NUM
ejde-390	461	16	)	)	PUNCT
ejde-390	461	17	(	(	PUNCT
ejde-390	461	18	λ	λ	PROPN
ejde-390	461	19	∈	∈	PROPN
ejde-390	461	20	l	l	NOUN
ejde-390	461	21	)	)	PUNCT
ejde-390	461	22	.	.	PUNCT
ejde-390	462	1	according	accord	VERB
ejde-390	462	2	to	to	ADP
ejde-390	462	3	proposition	proposition	NOUN
ejde-390	462	4	3.2	3.2	NUM
ejde-390	462	5	,	,	PUNCT
ejde-390	462	6	we	we	PRON
ejde-390	462	7	can	can	AUX
ejde-390	462	8	find	find	VERB
ejde-390	462	9	uη	uη	ADJ
ejde-390	462	10	∈	∈	PROPN
ejde-390	462	11	sη	sη	VERB
ejde-390	462	12	⊆	⊆	NUM
ejde-390	462	13	d+	d+	NOUN
ejde-390	462	14	such	such	ADJ
ejde-390	462	15	that	that	SCONJ
ejde-390	462	16	ûλ	ûλ	NOUN
ejde-390	462	17	−	−	ADJ
ejde-390	462	18	uη	uη	ADP
ejde-390	462	19	∈	∈	PROPN
ejde-390	462	20	int	int	NOUN
ejde-390	462	21	ĉ+	ĉ+	PROPN
ejde-390	462	22	,	,	PUNCT
ejde-390	462	23	⇒	⇒	VERB
ejde-390	462	24	ûλ	ûλ	ADV
ejde-390	462	25	−	−	PROPN
ejde-390	462	26	ûη	ûη	SYM
ejde-390	462	27	∈	∈	NOUN
ejde-390	462	28	int	int	NOUN
ejde-390	462	29	ĉ+	ĉ+	PROPN
ejde-390	462	30	(	(	PUNCT
ejde-390	462	31	since	since	SCONJ
ejde-390	462	32	ûη	ûη	X
ejde-390	462	33	≤	≤	ADP
ejde-390	462	34	uη	uη	NOUN
ejde-390	462	35	)	)	PUNCT
ejde-390	462	36	⇒	⇒	PROPN
ejde-390	462	37	σ	σ	PROPN
ejde-390	462	38	(	(	PUNCT
ejde-390	462	39	·	·	PUNCT
ejde-390	462	40	)	)	PUNCT
ejde-390	462	41	is	be	AUX
ejde-390	462	42	strictly	strictly	ADV
ejde-390	462	43	decreasing	decrease	VERB
ejde-390	462	44	.	.	PUNCT
ejde-390	463	1	(	(	PUNCT
ejde-390	463	2	b	b	X
ejde-390	463	3	)	)	PUNCT
ejde-390	463	4	let	let	VERB
ejde-390	463	5	λn	λn	VERB
ejde-390	463	6	↓	↓	PROPN
ejde-390	463	7	λ	λ	X
ejde-390	463	8	∈	∈	PROPN
ejde-390	463	9	l.	l.	NOUN
ejde-390	463	10	as	as	ADP
ejde-390	463	11	in	in	ADP
ejde-390	463	12	the	the	DET
ejde-390	463	13	proof	proof	NOUN
ejde-390	463	14	of	of	ADP
ejde-390	463	15	proposition	proposition	NOUN
ejde-390	463	16	3.3	3.3	NUM
ejde-390	463	17	,	,	PUNCT
ejde-390	463	18	we	we	PRON
ejde-390	463	19	can	can	AUX
ejde-390	463	20	find	find	VERB
ejde-390	463	21	un	un	PROPN
ejde-390	463	22	∈w	∈w	PROPN
ejde-390	463	23	1,p(ω	1,p(ω	NUM
ejde-390	463	24	)	)	PUNCT
ejde-390	463	25	such	such	ADJ
ejde-390	463	26	that	that	SCONJ
ejde-390	463	27	un	un	PROPN
ejde-390	463	28	∈	∈	PROPN
ejde-390	463	29	sλn	sλn	NOUN
ejde-390	464	1	⊆	⊆	NUM
ejde-390	464	2	d+	d+	NOUN
ejde-390	464	3	and	and	CCONJ
ejde-390	464	4	ϕλn(un	ϕλn(un	NOUN
ejde-390	464	5	)	)	PUNCT
ejde-390	464	6	≤	≤	NOUN
ejde-390	464	7	c18	c18	NOUN
ejde-390	464	8	for	for	ADP
ejde-390	464	9	some	some	DET
ejde-390	464	10	c18	c18	NOUN
ejde-390	464	11	>	>	X
ejde-390	464	12	0	0	PROPN
ejde-390	464	13	,	,	PUNCT
ejde-390	464	14	all	all	DET
ejde-390	464	15	n	n	PRON
ejde-390	464	16	∈	∈	NOUN
ejde-390	464	17	n.	n.	NOUN
ejde-390	464	18	from	from	ADP
ejde-390	464	19	this	this	PRON
ejde-390	464	20	it	it	PRON
ejde-390	464	21	follows	follow	VERB
ejde-390	464	22	that	that	SCONJ
ejde-390	464	23	{	{	PUNCT
ejde-390	464	24	un}n≥1	un}n≥1	NOUN
ejde-390	464	25	⊆	⊆	NUM
ejde-390	464	26	w	w	PROPN
ejde-390	464	27	1,p(ω	1,p(ω	NUM
ejde-390	464	28	)	)	PUNCT
ejde-390	464	29	is	be	AUX
ejde-390	464	30	bounded	bound	VERB
ejde-390	464	31	(	(	PUNCT
ejde-390	464	32	see	see	VERB
ejde-390	464	33	the	the	DET
ejde-390	464	34	proof	proof	NOUN
ejde-390	464	35	of	of	ADP
ejde-390	464	36	proposition	proposition	NOUN
ejde-390	464	37	3.3	3.3	NUM
ejde-390	464	38	)	)	PUNCT
ejde-390	464	39	.	.	PUNCT
ejde-390	465	1	we	we	PRON
ejde-390	465	2	have	have	VERB
ejde-390	465	3	0	0	NUM
ejde-390	465	4	≤	≤	NUM
ejde-390	465	5	ûλn	ûλn	ADJ
ejde-390	465	6	≤	≤	PUNCT
ejde-390	465	7	un	un	NOUN
ejde-390	465	8	for	for	ADP
ejde-390	465	9	all	all	PRON
ejde-390	465	10	n	n	PRON
ejde-390	465	11	∈	∈	PROPN
ejde-390	465	12	n	n	CCONJ
ejde-390	465	13	,	,	PUNCT
ejde-390	465	14	⇒	⇒	VERB
ejde-390	465	15	{	{	PUNCT
ejde-390	465	16	ûλn}n≥1	ûλn}n≥1	ADJ
ejde-390	465	17	⊆w	⊆w	NOUN
ejde-390	465	18	1,p(ω	1,p(ω	NUM
ejde-390	465	19	)	)	PUNCT
ejde-390	465	20	.	.	PUNCT
ejde-390	466	1	ejde-2020/12	ejde-2020/12	NOUN
ejde-390	466	2	positive	positive	ADJ
ejde-390	466	3	and	and	CCONJ
ejde-390	466	4	nodal	nodal	ADJ
ejde-390	466	5	solutions	solution	NOUN
ejde-390	466	6	17	17	NUM
ejde-390	466	7	from	from	ADP
ejde-390	466	8	this	this	PRON
ejde-390	466	9	and	and	CCONJ
ejde-390	466	10	the	the	DET
ejde-390	466	11	nonlinear	nonlinear	ADJ
ejde-390	466	12	regularity	regularity	NOUN
ejde-390	466	13	theory	theory	NOUN
ejde-390	466	14	of	of	ADP
ejde-390	466	15	lieberman	lieberman	PROPN
ejde-390	466	16	[	[	X
ejde-390	466	17	7	7	NUM
ejde-390	466	18	]	]	PUNCT
ejde-390	466	19	(	(	PUNCT
ejde-390	466	20	see	see	VERB
ejde-390	466	21	the	the	DET
ejde-390	466	22	proof	proof	NOUN
ejde-390	466	23	of	of	ADP
ejde-390	466	24	proposition	proposition	NOUN
ejde-390	466	25	11	11	NUM
ejde-390	466	26	)	)	PUNCT
ejde-390	466	27	,	,	PUNCT
ejde-390	466	28	we	we	PRON
ejde-390	466	29	obtain	obtain	VERB
ejde-390	466	30	(	(	PUNCT
ejde-390	466	31	at	at	ADP
ejde-390	466	32	least	least	ADJ
ejde-390	466	33	for	for	ADP
ejde-390	466	34	a	a	DET
ejde-390	466	35	subsequence	subsequence	NOUN
ejde-390	466	36	)	)	PUNCT
ejde-390	466	37	that	that	PRON
ejde-390	466	38	ûλn	ûλn	NOUN
ejde-390	466	39	→	→	SYM
ejde-390	466	40	ũλ	ũλ	PROPN
ejde-390	466	41	in	in	ADP
ejde-390	466	42	c1(ω	c1(ω	PROPN
ejde-390	466	43	)	)	PUNCT
ejde-390	466	44	.	.	PUNCT
ejde-390	467	1	(	(	PUNCT
ejde-390	467	2	3.52	3.52	NUM
ejde-390	467	3	)	)	PUNCT
ejde-390	467	4	if	if	SCONJ
ejde-390	467	5	ũλ	ũλ	PROPN
ejde-390	467	6	6=	6=	PROPN
ejde-390	467	7	ûλ	ûλ	PROPN
ejde-390	467	8	,	,	PUNCT
ejde-390	467	9	then	then	ADV
ejde-390	467	10	we	we	PRON
ejde-390	467	11	can	can	AUX
ejde-390	467	12	find	find	VERB
ejde-390	467	13	z0	z0	PROPN
ejde-390	467	14	∈	∈	PROPN
ejde-390	467	15	ω	ω	NOUN
ejde-390	467	16	such	such	ADJ
ejde-390	467	17	that	that	SCONJ
ejde-390	467	18	ûλ(z0	ûλ(z0	NOUN
ejde-390	467	19	)	)	PUNCT
ejde-390	467	20	<	<	X
ejde-390	467	21	ũλ(z0	ũλ(z0	ADJ
ejde-390	467	22	)	)	PUNCT
ejde-390	467	23	implies	imply	VERB
ejde-390	467	24	ûλ(z0	ûλ(z0	NOUN
ejde-390	467	25	)	)	PUNCT
ejde-390	467	26	<	<	X
ejde-390	467	27	ûλn(z0	ûλn(z0	NOUN
ejde-390	467	28	)	)	PUNCT
ejde-390	467	29	for	for	ADP
ejde-390	467	30	all	all	PRON
ejde-390	467	31	n	n	DET
ejde-390	467	32	≥	≥	NOUN
ejde-390	467	33	n0	n0	NUM
ejde-390	467	34	(	(	PUNCT
ejde-390	467	35	see	see	INTJ
ejde-390	467	36	(	(	PUNCT
ejde-390	467	37	3.52	3.52	NUM
ejde-390	467	38	)	)	PUNCT
ejde-390	467	39	)	)	PUNCT
ejde-390	467	40	.	.	PUNCT
ejde-390	468	1	this	this	PRON
ejde-390	468	2	contradicts	contradict	VERB
ejde-390	468	3	(	(	PUNCT
ejde-390	468	4	a	a	NOUN
ejde-390	468	5	)	)	PUNCT
ejde-390	468	6	.	.	PUNCT
ejde-390	469	1	therefore	therefore	ADV
ejde-390	469	2	by	by	ADP
ejde-390	469	3	urysohn	urysohn	PROPN
ejde-390	469	4	’s	’s	PART
ejde-390	469	5	criterion	criterion	NOUN
ejde-390	469	6	,	,	PUNCT
ejde-390	469	7	for	for	ADP
ejde-390	469	8	the	the	DET
ejde-390	469	9	original	original	ADJ
ejde-390	469	10	sequence	sequence	NOUN
ejde-390	469	11	we	we	PRON
ejde-390	469	12	have	have	VERB
ejde-390	469	13	ûλn	ûλn	NOUN
ejde-390	469	14	→	→	SYM
ejde-390	469	15	ûλ	ûλ	NOUN
ejde-390	469	16	in	in	ADP
ejde-390	469	17	c1(ω	c1(ω	NOUN
ejde-390	469	18	)	)	PUNCT
ejde-390	469	19	⇒	⇒	NOUN
ejde-390	469	20	σ	σ	PROPN
ejde-390	469	21	(	(	PUNCT
ejde-390	469	22	·	·	PUNCT
ejde-390	469	23	)	)	PUNCT
ejde-390	469	24	is	be	AUX
ejde-390	469	25	right	right	ADV
ejde-390	469	26	continuous	continuous	ADJ
ejde-390	469	27	.	.	PUNCT
ejde-390	470	1	�	�	PROPN
ejde-390	470	2	if	if	SCONJ
ejde-390	470	3	we	we	PRON
ejde-390	470	4	impose	impose	VERB
ejde-390	470	5	on	on	ADP
ejde-390	470	6	f(z	f(z	PROPN
ejde-390	470	7	,	,	PUNCT
ejde-390	470	8	·	·	PUNCT
ejde-390	470	9	)	)	PUNCT
ejde-390	470	10	similar	similar	ADJ
ejde-390	470	11	conditions	condition	NOUN
ejde-390	470	12	valid	valid	ADJ
ejde-390	470	13	on	on	ADP
ejde-390	470	14	the	the	DET
ejde-390	470	15	negative	negative	ADJ
ejde-390	470	16	semiaxis	semiaxis	NOUN
ejde-390	470	17	r−	r−	PROPN
ejde-390	470	18	=	=	SYM
ejde-390	470	19	(	(	PUNCT
ejde-390	470	20	−∞	−∞	NOUN
ejde-390	470	21	,	,	PUNCT
ejde-390	470	22	0	0	NUM
ejde-390	470	23	]	]	PUNCT
ejde-390	470	24	,	,	PUNCT
ejde-390	470	25	we	we	PRON
ejde-390	470	26	can	can	AUX
ejde-390	470	27	have	have	VERB
ejde-390	470	28	analogous	analogous	ADJ
ejde-390	470	29	results	result	NOUN
ejde-390	470	30	for	for	ADP
ejde-390	470	31	the	the	DET
ejde-390	470	32	negative	negative	ADJ
ejde-390	470	33	solutions	solution	NOUN
ejde-390	470	34	.	.	PUNCT
ejde-390	471	1	now	now	ADV
ejde-390	471	2	the	the	DET
ejde-390	471	3	hypotheses	hypothesis	NOUN
ejde-390	471	4	on	on	ADP
ejde-390	471	5	the	the	DET
ejde-390	471	6	reaction	reaction	NOUN
ejde-390	471	7	f(z	f(z	NOUN
ejde-390	471	8	,	,	PUNCT
ejde-390	471	9	x	x	X
ejde-390	471	10	)	)	PUNCT
ejde-390	471	11	are	be	AUX
ejde-390	471	12	as	as	SCONJ
ejde-390	471	13	follows	follow	VERB
ejde-390	471	14	(	(	PUNCT
ejde-390	471	15	h3	h3	NOUN
ejde-390	471	16	’	'	PUNCT
ejde-390	471	17	)	)	PUNCT
ejde-390	472	1	f	f	NOUN
ejde-390	472	2	:	:	PUNCT
ejde-390	473	1	ω	ω	NUM
ejde-390	473	2	×	×	NOUN
ejde-390	473	3	r	r	NOUN
ejde-390	473	4	→	→	SYM
ejde-390	473	5	r	r	NOUN
ejde-390	473	6	is	be	AUX
ejde-390	473	7	a	a	DET
ejde-390	473	8	carathéodory	carathéodory	NOUN
ejde-390	473	9	function	function	NOUN
ejde-390	473	10	such	such	ADJ
ejde-390	473	11	that	that	DET
ejde-390	473	12	f(z	f(z	PROPN
ejde-390	473	13	,	,	PUNCT
ejde-390	473	14	0	0	NUM
ejde-390	473	15	)	)	PUNCT
ejde-390	473	16	=	=	SYM
ejde-390	473	17	0	0	NUM
ejde-390	473	18	for	for	ADP
ejde-390	473	19	a.a	a.a	PROPN
ejde-390	473	20	.	.	PROPN
ejde-390	473	21	z	z	PROPN
ejde-390	473	22	∈	∈	PROPN
ejde-390	473	23	ω	ω	PROPN
ejde-390	473	24	and	and	CCONJ
ejde-390	473	25	(	(	PUNCT
ejde-390	473	26	i	i	NOUN
ejde-390	473	27	)	)	PUNCT
ejde-390	473	28	η(z)|x|p	η(z)|x|p	VERB
ejde-390	473	29	≤	≤	NOUN
ejde-390	473	30	f(z	f(z	PROPN
ejde-390	473	31	,	,	PUNCT
ejde-390	473	32	x)x	x)x	PUNCT
ejde-390	473	33	≤	≤	X
ejde-390	474	1	α(z)[1	α(z)[1	PRON
ejde-390	475	1	+	+	CCONJ
ejde-390	475	2	|x|r	|x|r	X
ejde-390	475	3	]	]	PUNCT
ejde-390	475	4	for	for	ADP
ejde-390	475	5	a.a	a.a	PROPN
ejde-390	475	6	.	.	PROPN
ejde-390	475	7	z	z	PROPN
ejde-390	475	8	∈	∈	PROPN
ejde-390	475	9	ω	ω	PROPN
ejde-390	475	10	,	,	PUNCT
ejde-390	475	11	all	all	PRON
ejde-390	475	12	x	x	SYM
ejde-390	475	13	≤	≤	NOUN
ejde-390	475	14	0	0	NUM
ejde-390	475	15	,	,	PUNCT
ejde-390	475	16	with	with	ADP
ejde-390	475	17	η	η	PROPN
ejde-390	475	18	,	,	PUNCT
ejde-390	475	19	α	α	PROPN
ejde-390	475	20	∈	∈	PROPN
ejde-390	475	21	l∞(ω	l∞(ω	NOUN
ejde-390	475	22	)	)	PUNCT
ejde-390	475	23	,	,	PUNCT
ejde-390	475	24	ξ	ξ	PROPN
ejde-390	475	25	�	�	PROPN
ejde-390	475	26	η	η	PROPN
ejde-390	475	27	and	and	CCONJ
ejde-390	475	28	p	p	X
ejde-390	475	29	<	<	X
ejde-390	475	30	r	r	X
ejde-390	475	31	<	<	X
ejde-390	475	32	p∗	p∗	PROPN
ejde-390	475	33	;	;	PUNCT
ejde-390	475	34	(	(	PUNCT
ejde-390	475	35	ii	ii	NOUN
ejde-390	475	36	)	)	PUNCT
ejde-390	475	37	if	if	SCONJ
ejde-390	475	38	f	f	PROPN
ejde-390	475	39	(	(	PUNCT
ejde-390	475	40	z	z	NOUN
ejde-390	475	41	,	,	PUNCT
ejde-390	475	42	x	x	NOUN
ejde-390	475	43	)	)	PUNCT
ejde-390	476	1	=	=	SYM
ejde-390	476	2	∫	∫	PROPN
ejde-390	476	3	x	x	SYM
ejde-390	476	4	0	0	NUM
ejde-390	476	5	f(z	f(z	PROPN
ejde-390	476	6	,	,	PUNCT
ejde-390	476	7	s)ds	s)ds	PROPN
ejde-390	476	8	,	,	PUNCT
ejde-390	476	9	then	then	ADV
ejde-390	476	10	limx→−∞	limx→−∞	PROPN
ejde-390	476	11	f	f	PROPN
ejde-390	476	12	(	(	PUNCT
ejde-390	476	13	z	z	NOUN
ejde-390	476	14	,	,	PUNCT
ejde-390	476	15	x	x	NOUN
ejde-390	476	16	)	)	PUNCT
ejde-390	476	17	|x|p	|x|p	PROPN
ejde-390	476	18	=	=	PUNCT
ejde-390	477	1	+	+	NOUN
ejde-390	477	2	∞	∞	NOUN
ejde-390	477	3	uniformly	uniformly	ADJ
ejde-390	477	4	for	for	ADP
ejde-390	477	5	a.a	a.a	PROPN
ejde-390	477	6	.	.	PROPN
ejde-390	477	7	z	z	PROPN
ejde-390	477	8	∈	∈	PROPN
ejde-390	477	9	ω	ω	PROPN
ejde-390	477	10	;	;	PUNCT
ejde-390	477	11	(	(	PUNCT
ejde-390	477	12	iii	iii	X
ejde-390	477	13	)	)	PUNCT
ejde-390	477	14	if	if	SCONJ
ejde-390	477	15	d(z	d(z	NOUN
ejde-390	477	16	,	,	PUNCT
ejde-390	477	17	x	x	NOUN
ejde-390	477	18	)	)	PUNCT
ejde-390	477	19	=	=	SYM
ejde-390	477	20	f(z	f(z	PROPN
ejde-390	477	21	,	,	PUNCT
ejde-390	477	22	x)x−	x)x−	NOUN
ejde-390	477	23	pf	pf	PROPN
ejde-390	477	24	(	(	PUNCT
ejde-390	477	25	z	z	PROPN
ejde-390	477	26	,	,	PUNCT
ejde-390	477	27	x	x	NOUN
ejde-390	477	28	)	)	PUNCT
ejde-390	477	29	,	,	PUNCT
ejde-390	477	30	then	then	ADV
ejde-390	477	31	there	there	PRON
ejde-390	477	32	exists	exist	VERB
ejde-390	477	33	e	e	PROPN
ejde-390	477	34	∈	∈	PROPN
ejde-390	477	35	l1(ω	l1(ω	PROPN
ejde-390	477	36	)	)	PUNCT
ejde-390	478	1	such	such	ADJ
ejde-390	478	2	that	that	SCONJ
ejde-390	478	3	d(z	d(z	PROPN
ejde-390	478	4	,	,	PUNCT
ejde-390	478	5	x	x	NOUN
ejde-390	478	6	)	)	PUNCT
ejde-390	478	7	≤	≤	NOUN
ejde-390	478	8	d(z	d(z	PROPN
ejde-390	478	9	,	,	PUNCT
ejde-390	478	10	y	y	NOUN
ejde-390	478	11	)	)	PUNCT
ejde-390	478	12	+	+	PUNCT
ejde-390	478	13	e(z	e(z	NOUN
ejde-390	478	14	)	)	PUNCT
ejde-390	478	15	for	for	ADP
ejde-390	478	16	a.a	a.a	PROPN
ejde-390	478	17	.	.	PROPN
ejde-390	478	18	z	z	PROPN
ejde-390	478	19	∈	∈	PROPN
ejde-390	478	20	ω	ω	PROPN
ejde-390	478	21	,	,	PUNCT
ejde-390	478	22	all	all	PRON
ejde-390	479	1	y	y	PROPN
ejde-390	479	2	<	<	X
ejde-390	479	3	x	x	SYM
ejde-390	479	4	≤	≤	NUM
ejde-390	479	5	0	0	NUM
ejde-390	479	6	and	and	CCONJ
ejde-390	479	7	d(z	d(z	PROPN
ejde-390	479	8	,	,	PUNCT
ejde-390	480	1	x)→	x)→	PUNCT
ejde-390	481	1	+	+	ADJ
ejde-390	481	2	∞	∞	PROPN
ejde-390	481	3	for	for	ADP
ejde-390	481	4	a.a	a.a	PROPN
ejde-390	481	5	.	.	PROPN
ejde-390	481	6	z	z	PROPN
ejde-390	481	7	∈	∈	PROPN
ejde-390	481	8	ω	ω	PROPN
ejde-390	481	9	as	as	ADP
ejde-390	481	10	x→	x→	PROPN
ejde-390	481	11	−∞	−∞	NOUN
ejde-390	481	12	;	;	PUNCT
ejde-390	481	13	(	(	PUNCT
ejde-390	481	14	iv	iv	X
ejde-390	481	15	)	)	PUNCT
ejde-390	481	16	with	with	ADP
ejde-390	481	17	q	q	PROPN
ejde-390	481	18	∈	∈	PROPN
ejde-390	481	19	(	(	PUNCT
ejde-390	481	20	1	1	NUM
ejde-390	481	21	,	,	PUNCT
ejde-390	481	22	p	p	NOUN
ejde-390	481	23	)	)	PUNCT
ejde-390	481	24	as	as	ADP
ejde-390	481	25	in	in	ADP
ejde-390	481	26	hypothesis	hypothesis	NOUN
ejde-390	481	27	(	(	PUNCT
ejde-390	481	28	h1	h1	PROPN
ejde-390	481	29	)	)	PUNCT
ejde-390	481	30	(	(	PUNCT
ejde-390	481	31	iv	iv	X
ejde-390	481	32	)	)	PUNCT
ejde-390	481	33	,	,	PUNCT
ejde-390	481	34	we	we	PRON
ejde-390	481	35	have	have	VERB
ejde-390	481	36	limx→0−	limx→0−	ADV
ejde-390	481	37	f(z	f(z	NOUN
ejde-390	481	38	,	,	PUNCT
ejde-390	481	39	x	x	NOUN
ejde-390	481	40	)	)	PUNCT
ejde-390	481	41	|x|q−2x	|x|q−2x	NOUN
ejde-390	481	42	=	=	SYM
ejde-390	482	1	+	+	NOUN
ejde-390	482	2	∞	∞	NOUN
ejde-390	482	3	uniformly	uniformly	ADJ
ejde-390	482	4	for	for	ADP
ejde-390	482	5	a.a	a.a	PROPN
ejde-390	482	6	.	.	PROPN
ejde-390	482	7	z	z	PROPN
ejde-390	482	8	∈	∈	PROPN
ejde-390	482	9	ω	ω	PROPN
ejde-390	482	10	;	;	PUNCT
ejde-390	482	11	(	(	PUNCT
ejde-390	482	12	v	v	NOUN
ejde-390	482	13	)	)	PUNCT
ejde-390	482	14	for	for	ADP
ejde-390	482	15	every	every	DET
ejde-390	482	16	ρ	ρ	PROPN
ejde-390	482	17	>	>	X
ejde-390	482	18	0	0	PUNCT
ejde-390	482	19	there	there	PRON
ejde-390	482	20	exists	exist	VERB
ejde-390	482	21	ξ̂ρ	ξ̂ρ	NOUN
ejde-390	482	22	>	>	X
ejde-390	482	23	0	0	NUM
ejde-390	482	24	such	such	ADJ
ejde-390	482	25	that	that	PRON
ejde-390	482	26	for	for	ADP
ejde-390	482	27	a.a	a.a	PROPN
ejde-390	482	28	.	.	PROPN
ejde-390	482	29	z	z	PROPN
ejde-390	482	30	∈	∈	PROPN
ejde-390	482	31	ω	ω	NUM
ejde-390	482	32	the	the	DET
ejde-390	482	33	function	function	NOUN
ejde-390	482	34	x→	x→	PUNCT
ejde-390	482	35	f(z	f(z	PROPN
ejde-390	482	36	,	,	PUNCT
ejde-390	482	37	x	x	NOUN
ejde-390	482	38	)	)	PUNCT
ejde-390	483	1	+	+	CCONJ
ejde-390	483	2	ξ̂ρ|x|p−2x	ξ̂ρ|x|p−2x	NOUN
ejde-390	483	3	is	be	AUX
ejde-390	483	4	nondecreasing	nondecrease	VERB
ejde-390	483	5	on	on	ADP
ejde-390	483	6	[	[	X
ejde-390	483	7	−ρ	−ρ	NOUN
ejde-390	483	8	,	,	PUNCT
ejde-390	483	9	0	0	NUM
ejde-390	483	10	]	]	PUNCT
ejde-390	483	11	.	.	PUNCT
ejde-390	484	1	we	we	PRON
ejde-390	484	2	introduce	introduce	VERB
ejde-390	484	3	the	the	DET
ejde-390	484	4	two	two	NUM
ejde-390	484	5	sets	set	NOUN
ejde-390	484	6	:	:	PUNCT
ejde-390	484	7	l′	l′	PROPN
ejde-390	484	8	=	=	PUNCT
ejde-390	484	9	{	{	PUNCT
ejde-390	484	10	λ	λ	X
ejde-390	484	11	>	>	X
ejde-390	484	12	0	0	PUNCT
ejde-390	484	13	:	:	PUNCT
ejde-390	484	14	problem	problem	NOUN
ejde-390	484	15	(	(	PUNCT
ejde-390	484	16	1.1	1.1	NUM
ejde-390	484	17	)	)	PUNCT
ejde-390	484	18	has	have	VERB
ejde-390	484	19	a	a	DET
ejde-390	484	20	negative	negative	ADJ
ejde-390	484	21	solution	solution	NOUN
ejde-390	484	22	}	}	PUNCT
ejde-390	484	23	,	,	PUNCT
ejde-390	484	24	s′λ	s′λ	ADJ
ejde-390	484	25	=	=	PUNCT
ejde-390	484	26	set	set	NOUN
ejde-390	484	27	of	of	ADP
ejde-390	484	28	negative	negative	ADJ
ejde-390	484	29	solutions	solution	NOUN
ejde-390	484	30	of	of	ADP
ejde-390	484	31	(	(	PUNCT
ejde-390	484	32	1.1	1.1	NUM
ejde-390	484	33	)	)	PUNCT
ejde-390	484	34	.	.	PUNCT
ejde-390	485	1	reasoning	reasoning	NOUN
ejde-390	485	2	as	as	SCONJ
ejde-390	485	3	we	we	PRON
ejde-390	485	4	did	do	VERB
ejde-390	485	5	above	above	ADV
ejde-390	485	6	for	for	ADP
ejde-390	485	7	positive	positive	ADJ
ejde-390	485	8	solutions	solution	NOUN
ejde-390	485	9	,	,	PUNCT
ejde-390	485	10	we	we	PRON
ejde-390	485	11	have	have	VERB
ejde-390	485	12	the	the	DET
ejde-390	485	13	following	follow	VERB
ejde-390	485	14	bifurcationtype	bifurcationtype	NOUN
ejde-390	485	15	result	result	NOUN
ejde-390	485	16	describing	describe	VERB
ejde-390	485	17	the	the	DET
ejde-390	485	18	dependence	dependence	NOUN
ejde-390	485	19	of	of	ADP
ejde-390	485	20	the	the	DET
ejde-390	485	21	set	set	NOUN
ejde-390	485	22	of	of	ADP
ejde-390	485	23	negative	negative	ADJ
ejde-390	485	24	solutions	solution	NOUN
ejde-390	485	25	on	on	ADP
ejde-390	485	26	the	the	DET
ejde-390	485	27	parameter	parameter	NOUN
ejde-390	486	1	λ	λ	PROPN
ejde-390	486	2	>	>	X
ejde-390	486	3	0	0	X
ejde-390	486	4	.	.	PUNCT
ejde-390	486	5	theorem	theorem	VERB
ejde-390	486	6	3.9	3.9	NUM
ejde-390	486	7	.	.	PUNCT
ejde-390	487	1	if	if	SCONJ
ejde-390	487	2	hypotheses	hypothesis	NOUN
ejde-390	487	3	(	(	PUNCT
ejde-390	487	4	h1	h1	PROPN
ejde-390	487	5	)	)	PUNCT
ejde-390	487	6	,	,	PUNCT
ejde-390	487	7	(	(	PUNCT
ejde-390	487	8	h2	h2	NOUN
ejde-390	487	9	)	)	PUNCT
ejde-390	487	10	,	,	PUNCT
ejde-390	487	11	(	(	PUNCT
ejde-390	487	12	h3′	h3′	NOUN
ejde-390	487	13	)	)	PUNCT
ejde-390	487	14	hold	hold	VERB
ejde-390	487	15	,	,	PUNCT
ejde-390	487	16	then	then	ADV
ejde-390	487	17	there	there	PRON
ejde-390	487	18	exists	exist	VERB
ejde-390	487	19	a	a	DET
ejde-390	487	20	critical	critical	ADJ
ejde-390	487	21	parameter	parameter	NOUN
ejde-390	487	22	value	value	NOUN
ejde-390	487	23	λ′∗	λ′∗	NOUN
ejde-390	487	24	>	>	X
ejde-390	487	25	0	0	NUM
ejde-390	488	1	such	such	ADJ
ejde-390	488	2	that	that	SCONJ
ejde-390	488	3	(	(	PUNCT
ejde-390	488	4	a	a	NOUN
ejde-390	488	5	)	)	PUNCT
ejde-390	488	6	for	for	ADP
ejde-390	488	7	all	all	DET
ejde-390	488	8	λ	λ	PROPN
ejde-390	488	9	>	>	X
ejde-390	488	10	λ′∗	λ′∗	PROPN
ejde-390	488	11	problem	problem	NOUN
ejde-390	488	12	(	(	PUNCT
ejde-390	488	13	1.1	1.1	NUM
ejde-390	488	14	)	)	PUNCT
ejde-390	488	15	has	have	VERB
ejde-390	488	16	at	at	ADV
ejde-390	488	17	least	least	ADV
ejde-390	488	18	two	two	NUM
ejde-390	488	19	negative	negative	ADJ
ejde-390	488	20	solutions	solution	NOUN
ejde-390	488	21	v0	v0	NOUN
ejde-390	488	22	,	,	PUNCT
ejde-390	488	23	v̂	v̂	ADP
ejde-390	488	24	∈	∈	PROPN
ejde-390	488	25	−d+	−d+	NOUN
ejde-390	488	26	,	,	PUNCT
ejde-390	488	27	v0	v0	PROPN
ejde-390	488	28	6=	6=	ADP
ejde-390	488	29	v̂	v̂	NOUN
ejde-390	488	30	;	;	PUNCT
ejde-390	488	31	(	(	PUNCT
ejde-390	488	32	b	b	X
ejde-390	488	33	)	)	PUNCT
ejde-390	488	34	for	for	ADP
ejde-390	488	35	λ	λ	NOUN
ejde-390	488	36	=	=	SYM
ejde-390	488	37	λ′∗	λ′∗	PROPN
ejde-390	488	38	problem	problem	NOUN
ejde-390	488	39	(	(	PUNCT
ejde-390	488	40	1.1	1.1	NUM
ejde-390	488	41	)	)	PUNCT
ejde-390	488	42	has	have	VERB
ejde-390	488	43	at	at	ADV
ejde-390	488	44	least	least	ADV
ejde-390	488	45	one	one	NUM
ejde-390	488	46	negative	negative	ADJ
ejde-390	488	47	solution	solution	NOUN
ejde-390	488	48	v∗	v∗	PROPN
ejde-390	488	49	∈	∈	PROPN
ejde-390	488	50	−d+	−d+	NOUN
ejde-390	488	51	;	;	PUNCT
ejde-390	488	52	(	(	PUNCT
ejde-390	488	53	c	c	X
ejde-390	488	54	)	)	PUNCT
ejde-390	488	55	for	for	ADP
ejde-390	488	56	all	all	DET
ejde-390	488	57	λ	λ	PROPN
ejde-390	488	58	∈	∈	PROPN
ejde-390	488	59	(	(	PUNCT
ejde-390	488	60	0	0	NUM
ejde-390	488	61	,	,	PUNCT
ejde-390	488	62	λ′∗	λ′∗	NOUN
ejde-390	488	63	)	)	PUNCT
ejde-390	488	64	problem	problem	NOUN
ejde-390	488	65	(	(	PUNCT
ejde-390	488	66	1.1	1.1	NUM
ejde-390	488	67	)	)	PUNCT
ejde-390	488	68	has	have	VERB
ejde-390	488	69	no	no	DET
ejde-390	488	70	negative	negative	ADJ
ejde-390	488	71	solutions	solution	NOUN
ejde-390	488	72	.	.	PUNCT
ejde-390	489	1	we	we	PRON
ejde-390	489	2	can	can	AUX
ejde-390	489	3	generate	generate	VERB
ejde-390	489	4	extremal	extremal	ADJ
ejde-390	489	5	negative	negative	ADJ
ejde-390	489	6	solutions	solution	NOUN
ejde-390	489	7	.	.	PUNCT
ejde-390	490	1	in	in	ADP
ejde-390	490	2	this	this	DET
ejde-390	490	3	case	case	NOUN
ejde-390	490	4	s′λ	s′λ	ADJ
ejde-390	490	5	is	be	AUX
ejde-390	490	6	upward	upward	ADV
ejde-390	490	7	directed	direct	VERB
ejde-390	490	8	,	,	PUNCT
ejde-390	490	9	that	that	ADV
ejde-390	490	10	is	is	ADV
ejde-390	490	11	,	,	PUNCT
ejde-390	490	12	if	if	SCONJ
ejde-390	490	13	v1	v1	NOUN
ejde-390	490	14	,	,	PUNCT
ejde-390	490	15	v2	v2	PROPN
ejde-390	490	16	∈	∈	PROPN
ejde-390	490	17	s′λ	s′λ	ADJ
ejde-390	490	18	⊆	⊆	NUM
ejde-390	490	19	−d+	−d+	NOUN
ejde-390	490	20	,	,	PUNCT
ejde-390	490	21	we	we	PRON
ejde-390	490	22	can	can	AUX
ejde-390	490	23	find	find	VERB
ejde-390	490	24	v	v	ADP
ejde-390	490	25	∈	∈	NOUN
ejde-390	490	26	s′λ	s′λ	ADJ
ejde-390	490	27	such	such	ADJ
ejde-390	490	28	that	that	DET
ejde-390	490	29	v1	v1	PROPN
ejde-390	490	30	≤	≤	NUM
ejde-390	490	31	v	v	NOUN
ejde-390	490	32	,	,	PUNCT
ejde-390	490	33	v2	v2	PROPN
ejde-390	490	34	≤	≤	NUM
ejde-390	490	35	v	v	NOUN
ejde-390	490	36	(	(	PUNCT
ejde-390	490	37	see	see	VERB
ejde-390	490	38	[	[	X
ejde-390	490	39	12	12	NUM
ejde-390	490	40	]	]	NUM
ejde-390	490	41	)	)	PUNCT
ejde-390	490	42	.	.	PUNCT
ejde-390	491	1	so	so	ADV
ejde-390	491	2	,	,	PUNCT
ejde-390	491	3	in	in	ADP
ejde-390	491	4	this	this	DET
ejde-390	491	5	case	case	NOUN
ejde-390	491	6	we	we	PRON
ejde-390	491	7	produce	produce	VERB
ejde-390	491	8	the	the	DET
ejde-390	491	9	biggest	big	ADJ
ejde-390	491	10	negative	negative	ADJ
ejde-390	491	11	solution	solution	NOUN
ejde-390	491	12	for	for	ADP
ejde-390	491	13	problem	problem	NOUN
ejde-390	491	14	(	(	PUNCT
ejde-390	491	15	1.1	1.1	NUM
ejde-390	491	16	)	)	PUNCT
ejde-390	491	17	.	.	PUNCT
ejde-390	492	1	proposition	proposition	NOUN
ejde-390	492	2	3.10	3.10	NUM
ejde-390	492	3	.	.	PUNCT
ejde-390	493	1	if	if	SCONJ
ejde-390	493	2	hypotheses	hypothesis	NOUN
ejde-390	493	3	(	(	PUNCT
ejde-390	493	4	h1	h1	PROPN
ejde-390	493	5	)	)	PUNCT
ejde-390	493	6	,	,	PUNCT
ejde-390	493	7	(	(	PUNCT
ejde-390	493	8	h2	h2	NOUN
ejde-390	493	9	)	)	PUNCT
ejde-390	493	10	,	,	PUNCT
ejde-390	493	11	(	(	PUNCT
ejde-390	493	12	h3	h3	NOUN
ejde-390	493	13	’	'	PUNCT
ejde-390	493	14	)	)	PUNCT
ejde-390	493	15	hold	hold	VERB
ejde-390	493	16	and	and	CCONJ
ejde-390	493	17	λ	λ	X
ejde-390	493	18	∈	∈	NOUN
ejde-390	493	19	l′	l′	NOUN
ejde-390	493	20	=	=	PUNCT
ejde-390	494	1	[	[	X
ejde-390	494	2	λ′∗,+∞	λ′∗,+∞	NOUN
ejde-390	494	3	)	)	PUNCT
ejde-390	494	4	,	,	PUNCT
ejde-390	494	5	then	then	ADV
ejde-390	494	6	problem	problem	NOUN
ejde-390	494	7	(	(	PUNCT
ejde-390	494	8	1.1	1.1	NUM
ejde-390	494	9	)	)	PUNCT
ejde-390	494	10	has	have	VERB
ejde-390	494	11	a	a	DET
ejde-390	494	12	biggest	big	ADJ
ejde-390	494	13	negative	negative	ADJ
ejde-390	494	14	solution	solution	NOUN
ejde-390	494	15	v̂λ	v̂λ	DET
ejde-390	494	16	∈	∈	NOUN
ejde-390	494	17	−d+	−d+	NOUN
ejde-390	494	18	and	and	CCONJ
ejde-390	494	19	the	the	DET
ejde-390	494	20	map	map	NOUN
ejde-390	494	21	σ′	σ′	PROPN
ejde-390	494	22	:	:	PUNCT
ejde-390	494	23	l′	l′	X
ejde-390	494	24	→	→	SYM
ejde-390	494	25	c1(ω	c1(ω	X
ejde-390	494	26	)	)	PUNCT
ejde-390	494	27	defined	define	VERB
ejde-390	494	28	by	by	ADP
ejde-390	494	29	σ′(λ	σ′(λ	NOUN
ejde-390	494	30	)	)	PUNCT
ejde-390	494	31	=	=	PUNCT
ejde-390	494	32	v̂λ	v̂λ	X
ejde-390	494	33	is	be	AUX
ejde-390	494	34	strictly	strictly	ADV
ejde-390	494	35	increasing	increase	VERB
ejde-390	494	36	in	in	ADP
ejde-390	494	37	the	the	DET
ejde-390	494	38	sense	sense	NOUN
ejde-390	494	39	that	that	SCONJ
ejde-390	494	40	λ′∗	λ′∗	NOUN
ejde-390	494	41	≤	≤	X
ejde-390	494	42	λ	λ	PROPN
ejde-390	494	43	<	<	X
ejde-390	494	44	η	η	PROPN
ejde-390	494	45	implies	imply	VERB
ejde-390	494	46	v̂η	v̂η	NOUN
ejde-390	494	47	−	−	PROPN
ejde-390	494	48	v̂λ	v̂λ	DET
ejde-390	494	49	∈	∈	NOUN
ejde-390	494	50	int	int	NOUN
ejde-390	494	51	ĉ+	ĉ+	PUNCT
ejde-390	494	52	and	and	CCONJ
ejde-390	494	53	σ′	σ′	PROPN
ejde-390	494	54	(	(	PUNCT
ejde-390	494	55	·	·	PUNCT
ejde-390	494	56	)	)	PUNCT
ejde-390	494	57	is	be	AUX
ejde-390	494	58	also	also	ADV
ejde-390	494	59	right	right	ADV
ejde-390	494	60	continuous	continuous	ADJ
ejde-390	494	61	.	.	PUNCT
ejde-390	494	62	18	18	NUM
ejde-390	494	63	n.	n.	PROPN
ejde-390	494	64	s.	s.	PROPN
ejde-390	494	65	papageorgiou	papageorgiou	PROPN
ejde-390	494	66	,	,	PUNCT
ejde-390	494	67	c.	c.	PROPN
ejde-390	494	68	vetro	vetro	PROPN
ejde-390	494	69	,	,	PUNCT
ejde-390	494	70	f.	f.	PROPN
ejde-390	494	71	vetro	vetro	PROPN
ejde-390	494	72	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	494	73	4	4	NUM
ejde-390	494	74	.	.	PUNCT
ejde-390	494	75	nodal	nodal	NOUN
ejde-390	494	76	solutions	solution	NOUN
ejde-390	494	77	let	let	VERB
ejde-390	494	78	λ̂∗	λ̂∗	X
ejde-390	494	79	=	=	PUNCT
ejde-390	494	80	max{λ∗	max{λ∗	ADJ
ejde-390	494	81	,	,	PUNCT
ejde-390	494	82	λ′∗	λ′∗	NOUN
ejde-390	494	83	}	}	PUNCT
ejde-390	494	84	.	.	PUNCT
ejde-390	495	1	suppose	suppose	VERB
ejde-390	495	2	that	that	SCONJ
ejde-390	495	3	the	the	DET
ejde-390	495	4	conditions	condition	NOUN
ejde-390	495	5	of	of	ADP
ejde-390	495	6	f(z	f(z	PROPN
ejde-390	495	7	,	,	PUNCT
ejde-390	495	8	·	·	PUNCT
ejde-390	495	9	)	)	PUNCT
ejde-390	495	10	are	be	AUX
ejde-390	495	11	bilateral	bilateral	ADJ
ejde-390	495	12	(	(	PUNCT
ejde-390	495	13	that	that	ADV
ejde-390	495	14	is	is	ADV
ejde-390	495	15	,	,	PUNCT
ejde-390	495	16	valid	valid	ADJ
ejde-390	495	17	on	on	ADP
ejde-390	495	18	all	all	PRON
ejde-390	495	19	of	of	ADP
ejde-390	495	20	r	r	NOUN
ejde-390	495	21	)	)	PUNCT
ejde-390	495	22	.	.	PUNCT
ejde-390	496	1	then	then	ADV
ejde-390	496	2	proposition	proposition	VERB
ejde-390	496	3	3.8	3.8	NUM
ejde-390	496	4	and	and	CCONJ
ejde-390	496	5	3.10	3.10	NUM
ejde-390	496	6	guarantee	guarantee	NOUN
ejde-390	496	7	that	that	SCONJ
ejde-390	496	8	for	for	ADP
ejde-390	496	9	all	all	DET
ejde-390	496	10	λ	λ	PROPN
ejde-390	496	11	≥	≥	PRON
ejde-390	496	12	λ̂∗	λ̂∗	X
ejde-390	496	13	problem	problem	NOUN
ejde-390	496	14	(	(	PUNCT
ejde-390	496	15	1.1	1.1	NUM
ejde-390	496	16	)	)	PUNCT
ejde-390	496	17	has	have	VERB
ejde-390	496	18	a	a	DET
ejde-390	496	19	smallest	small	ADJ
ejde-390	496	20	positive	positive	ADJ
ejde-390	496	21	solution	solution	NOUN
ejde-390	496	22	ûλ	ûλ	NOUN
ejde-390	496	23	∈	∈	NOUN
ejde-390	496	24	d+	d+	PUNCT
ejde-390	496	25	and	and	CCONJ
ejde-390	496	26	a	a	DET
ejde-390	496	27	biggest	big	ADJ
ejde-390	496	28	negative	negative	ADJ
ejde-390	496	29	solution	solution	NOUN
ejde-390	496	30	v̂λ	v̂λ	PRON
ejde-390	496	31	∈	∈	PROPN
ejde-390	496	32	−d+	−d+	NOUN
ejde-390	496	33	.	.	PUNCT
ejde-390	497	1	using	use	VERB
ejde-390	497	2	these	these	DET
ejde-390	497	3	two	two	NUM
ejde-390	497	4	extremal	extremal	ADJ
ejde-390	497	5	constant	constant	ADJ
ejde-390	497	6	sign	sign	NOUN
ejde-390	497	7	solutions	solution	NOUN
ejde-390	497	8	of	of	ADP
ejde-390	497	9	(	(	PUNCT
ejde-390	497	10	1.1	1.1	NUM
ejde-390	497	11	)	)	PUNCT
ejde-390	497	12	,	,	PUNCT
ejde-390	497	13	we	we	PRON
ejde-390	497	14	can	can	AUX
ejde-390	497	15	produce	produce	VERB
ejde-390	497	16	a	a	DET
ejde-390	497	17	nodal	nodal	NOUN
ejde-390	497	18	(	(	PUNCT
ejde-390	497	19	sign	sign	NOUN
ejde-390	497	20	-	-	PUNCT
ejde-390	497	21	changing	change	VERB
ejde-390	497	22	)	)	PUNCT
ejde-390	497	23	solution	solution	NOUN
ejde-390	497	24	.	.	PUNCT
ejde-390	498	1	now	now	ADV
ejde-390	498	2	the	the	DET
ejde-390	498	3	hypotheses	hypothesis	NOUN
ejde-390	498	4	on	on	ADP
ejde-390	498	5	the	the	DET
ejde-390	498	6	reaction	reaction	NOUN
ejde-390	498	7	f(z	f(z	NOUN
ejde-390	498	8	,	,	PUNCT
ejde-390	498	9	x	x	X
ejde-390	498	10	)	)	PUNCT
ejde-390	498	11	are	be	AUX
ejde-390	498	12	as	as	SCONJ
ejde-390	498	13	follows	follow	VERB
ejde-390	498	14	:	:	PUNCT
ejde-390	498	15	(	(	PUNCT
ejde-390	498	16	h3	h3	NOUN
ejde-390	498	17	”	"	PUNCT
ejde-390	498	18	)	)	PUNCT
ejde-390	498	19	f	f	NOUN
ejde-390	499	1	:	:	PUNCT
ejde-390	499	2	ω	ω	NUM
ejde-390	499	3	×	×	NOUN
ejde-390	499	4	r	r	NOUN
ejde-390	499	5	→	→	SYM
ejde-390	499	6	r	r	NOUN
ejde-390	499	7	is	be	AUX
ejde-390	499	8	a	a	DET
ejde-390	499	9	carathéodory	carathéodory	NOUN
ejde-390	499	10	function	function	NOUN
ejde-390	499	11	such	such	ADJ
ejde-390	499	12	that	that	DET
ejde-390	499	13	f(z	f(z	PROPN
ejde-390	499	14	,	,	PUNCT
ejde-390	499	15	0	0	NUM
ejde-390	499	16	)	)	PUNCT
ejde-390	499	17	=	=	SYM
ejde-390	499	18	0	0	NUM
ejde-390	499	19	for	for	ADP
ejde-390	499	20	a.a	a.a	PROPN
ejde-390	499	21	.	.	PROPN
ejde-390	499	22	z	z	PROPN
ejde-390	499	23	∈	∈	PROPN
ejde-390	499	24	ω	ω	PROPN
ejde-390	499	25	and	and	CCONJ
ejde-390	499	26	(	(	PUNCT
ejde-390	499	27	i	i	NOUN
ejde-390	499	28	)	)	PUNCT
ejde-390	499	29	η(z)|x|p	η(z)|x|p	VERB
ejde-390	499	30	≤	≤	NOUN
ejde-390	499	31	f(z	f(z	PROPN
ejde-390	499	32	,	,	PUNCT
ejde-390	499	33	x)x	x)x	PUNCT
ejde-390	499	34	≤	≤	X
ejde-390	500	1	α(z)[1	α(z)[1	PRON
ejde-390	501	1	+	+	CCONJ
ejde-390	501	2	|x|r	|x|r	X
ejde-390	501	3	]	]	PUNCT
ejde-390	501	4	for	for	ADP
ejde-390	501	5	a.a	a.a	PROPN
ejde-390	501	6	.	.	PROPN
ejde-390	501	7	z	z	PROPN
ejde-390	501	8	∈	∈	PROPN
ejde-390	501	9	ω	ω	PROPN
ejde-390	501	10	,	,	PUNCT
ejde-390	501	11	all	all	PRON
ejde-390	501	12	x	x	SYM
ejde-390	501	13	∈	∈	NOUN
ejde-390	501	14	r	r	NOUN
ejde-390	501	15	,	,	PUNCT
ejde-390	501	16	with	with	ADP
ejde-390	501	17	η	η	PROPN
ejde-390	501	18	,	,	PUNCT
ejde-390	501	19	α	α	PROPN
ejde-390	501	20	∈	∈	PROPN
ejde-390	501	21	l∞(ω	l∞(ω	NOUN
ejde-390	501	22	)	)	PUNCT
ejde-390	501	23	,	,	PUNCT
ejde-390	501	24	ξ	ξ	PROPN
ejde-390	501	25	�	�	PROPN
ejde-390	501	26	η	η	PROPN
ejde-390	501	27	and	and	CCONJ
ejde-390	501	28	p	p	X
ejde-390	501	29	<	<	X
ejde-390	501	30	r	r	X
ejde-390	501	31	<	<	X
ejde-390	501	32	p∗	p∗	PROPN
ejde-390	501	33	;	;	PUNCT
ejde-390	501	34	(	(	PUNCT
ejde-390	501	35	ii	ii	NOUN
ejde-390	501	36	)	)	PUNCT
ejde-390	501	37	if	if	SCONJ
ejde-390	501	38	f	f	PROPN
ejde-390	501	39	(	(	PUNCT
ejde-390	501	40	z	z	NOUN
ejde-390	501	41	,	,	PUNCT
ejde-390	501	42	x	x	NOUN
ejde-390	501	43	)	)	PUNCT
ejde-390	502	1	=	=	SYM
ejde-390	502	2	∫	∫	PROPN
ejde-390	502	3	x	x	SYM
ejde-390	502	4	0	0	NUM
ejde-390	502	5	f(z	f(z	PROPN
ejde-390	502	6	,	,	PUNCT
ejde-390	502	7	s)ds	s)ds	PROPN
ejde-390	502	8	,	,	PUNCT
ejde-390	502	9	then	then	ADV
ejde-390	502	10	limx→±∞	limx→±∞	PROPN
ejde-390	502	11	f	f	PROPN
ejde-390	502	12	(	(	PUNCT
ejde-390	502	13	z	z	NOUN
ejde-390	502	14	,	,	PUNCT
ejde-390	502	15	x	x	NOUN
ejde-390	502	16	)	)	PUNCT
ejde-390	503	1	|x|p	|x|p	PROPN
ejde-390	503	2	=	=	PUNCT
ejde-390	504	1	+	+	NOUN
ejde-390	504	2	∞	∞	NOUN
ejde-390	504	3	uniformly	uniformly	ADJ
ejde-390	504	4	for	for	ADP
ejde-390	504	5	a.a	a.a	PROPN
ejde-390	504	6	.	.	PROPN
ejde-390	504	7	z	z	PROPN
ejde-390	504	8	∈	∈	PROPN
ejde-390	504	9	ω	ω	PROPN
ejde-390	504	10	;	;	PUNCT
ejde-390	504	11	(	(	PUNCT
ejde-390	504	12	iii	iii	X
ejde-390	504	13	)	)	PUNCT
ejde-390	504	14	if	if	SCONJ
ejde-390	504	15	d(z	d(z	NOUN
ejde-390	504	16	,	,	PUNCT
ejde-390	504	17	x	x	NOUN
ejde-390	504	18	)	)	PUNCT
ejde-390	504	19	=	=	SYM
ejde-390	504	20	f(z	f(z	PROPN
ejde-390	504	21	,	,	PUNCT
ejde-390	504	22	x)x−	x)x−	NOUN
ejde-390	504	23	pf	pf	PROPN
ejde-390	504	24	(	(	PUNCT
ejde-390	504	25	z	z	PROPN
ejde-390	504	26	,	,	PUNCT
ejde-390	504	27	x	x	NOUN
ejde-390	504	28	)	)	PUNCT
ejde-390	504	29	,	,	PUNCT
ejde-390	504	30	then	then	ADV
ejde-390	504	31	there	there	PRON
ejde-390	504	32	exists	exist	VERB
ejde-390	504	33	e	e	PROPN
ejde-390	504	34	∈	∈	PROPN
ejde-390	504	35	l∞(ω	l∞(ω	ADV
ejde-390	504	36	)	)	PUNCT
ejde-390	504	37	such	such	ADJ
ejde-390	504	38	that	that	SCONJ
ejde-390	504	39	d(z	d(z	PROPN
ejde-390	504	40	,	,	PUNCT
ejde-390	504	41	x	x	NOUN
ejde-390	504	42	)	)	PUNCT
ejde-390	504	43	≤	≤	NOUN
ejde-390	504	44	d(z	d(z	PROPN
ejde-390	504	45	,	,	PUNCT
ejde-390	504	46	y	y	NOUN
ejde-390	504	47	)	)	PUNCT
ejde-390	504	48	+	+	PUNCT
ejde-390	505	1	e(z	e(z	NOUN
ejde-390	505	2	)	)	PUNCT
ejde-390	505	3	for	for	ADP
ejde-390	505	4	a.a	a.a	PROPN
ejde-390	505	5	.	.	PROPN
ejde-390	505	6	z	z	PROPN
ejde-390	505	7	∈	∈	PROPN
ejde-390	505	8	ω	ω	PROPN
ejde-390	505	9	,	,	PUNCT
ejde-390	505	10	all	all	PRON
ejde-390	505	11	0	0	NUM
ejde-390	505	12	≤	≤	NUM
ejde-390	505	13	x	x	PUNCT
ejde-390	505	14	≤	≤	NUM
ejde-390	505	15	y	y	PROPN
ejde-390	505	16	or	or	CCONJ
ejde-390	505	17	y	y	PROPN
ejde-390	505	18	≤	≤	NUM
ejde-390	505	19	x	x	PUNCT
ejde-390	505	20	≤	≤	NUM
ejde-390	505	21	0	0	NUM
ejde-390	505	22	and	and	CCONJ
ejde-390	505	23	d(z	d(z	PROPN
ejde-390	505	24	,	,	PUNCT
ejde-390	505	25	x)→	x)→	PUNCT
ejde-390	506	1	+	+	ADJ
ejde-390	506	2	∞	∞	PROPN
ejde-390	506	3	for	for	ADP
ejde-390	506	4	a.a	a.a	PROPN
ejde-390	506	5	.	.	PROPN
ejde-390	506	6	z	z	PROPN
ejde-390	506	7	∈	∈	PROPN
ejde-390	506	8	ω	ω	PROPN
ejde-390	506	9	as	as	ADP
ejde-390	506	10	x→	x→	PROPN
ejde-390	506	11	±∞	±∞	PROPN
ejde-390	506	12	;	;	PUNCT
ejde-390	506	13	(	(	PUNCT
ejde-390	506	14	iv	iv	X
ejde-390	506	15	)	)	PUNCT
ejde-390	506	16	with	with	ADP
ejde-390	506	17	q	q	NOUN
ejde-390	506	18	<	<	X
ejde-390	506	19	p	p	NOUN
ejde-390	506	20	as	as	ADP
ejde-390	506	21	in	in	ADP
ejde-390	506	22	hypothesis	hypothesis	NOUN
ejde-390	506	23	(	(	PUNCT
ejde-390	506	24	h1	h1	PROPN
ejde-390	506	25	)	)	PUNCT
ejde-390	506	26	(	(	PUNCT
ejde-390	506	27	iv	iv	X
ejde-390	506	28	)	)	PUNCT
ejde-390	506	29	,	,	PUNCT
ejde-390	506	30	there	there	PRON
ejde-390	506	31	exists	exist	VERB
ejde-390	506	32	τ	τ	PROPN
ejde-390	506	33	∈	∈	PROPN
ejde-390	506	34	(	(	PUNCT
ejde-390	506	35	1	1	NUM
ejde-390	506	36	,	,	PUNCT
ejde-390	506	37	q	q	NOUN
ejde-390	506	38	)	)	PUNCT
ejde-390	506	39	and	and	CCONJ
ejde-390	506	40	δ0	δ0	VERB
ejde-390	506	41	>	>	X
ejde-390	506	42	0	0	NUM
ejde-390	506	43	such	such	ADJ
ejde-390	506	44	that	that	SCONJ
ejde-390	506	45	ĉ0|x|τ	ĉ0|x|τ	VERB
ejde-390	506	46	≤	≤	NUM
ejde-390	506	47	f(z	f(z	PROPN
ejde-390	506	48	,	,	PUNCT
ejde-390	506	49	x)x	x)x	PUNCT
ejde-390	506	50	≤	≤	NUM
ejde-390	507	1	τf	τf	ADP
ejde-390	507	2	(	(	PUNCT
ejde-390	507	3	z	z	NOUN
ejde-390	507	4	,	,	PUNCT
ejde-390	507	5	x	x	NOUN
ejde-390	507	6	)	)	PUNCT
ejde-390	507	7	for	for	ADP
ejde-390	507	8	a.a	a.a	PROPN
ejde-390	507	9	.	.	PROPN
ejde-390	507	10	z	z	PROPN
ejde-390	507	11	∈	∈	PROPN
ejde-390	507	12	ω	ω	PROPN
ejde-390	507	13	,	,	PUNCT
ejde-390	507	14	all	all	DET
ejde-390	507	15	|x|	|x|	PROPN
ejde-390	507	16	≤	≤	NUM
ejde-390	507	17	δ0	δ0	NOUN
ejde-390	507	18	,	,	PUNCT
ejde-390	507	19	some	some	DET
ejde-390	507	20	ĉ0	ĉ0	PROPN
ejde-390	507	21	>	>	X
ejde-390	507	22	0	0	NUM
ejde-390	507	23	;	;	PUNCT
ejde-390	507	24	(	(	PUNCT
ejde-390	507	25	v	v	NOUN
ejde-390	507	26	)	)	PUNCT
ejde-390	507	27	for	for	ADP
ejde-390	507	28	every	every	DET
ejde-390	507	29	ρ	ρ	PROPN
ejde-390	507	30	>	>	X
ejde-390	507	31	0	0	PROPN
ejde-390	507	32	,	,	PUNCT
ejde-390	507	33	there	there	PRON
ejde-390	507	34	exists	exist	VERB
ejde-390	507	35	ξ̂ρ	ξ̂ρ	NOUN
ejde-390	507	36	>	>	X
ejde-390	507	37	0	0	NUM
ejde-390	507	38	such	such	ADJ
ejde-390	507	39	that	that	PRON
ejde-390	507	40	for	for	ADP
ejde-390	507	41	a.a	a.a	PROPN
ejde-390	507	42	.	.	PROPN
ejde-390	507	43	z	z	PROPN
ejde-390	507	44	∈	∈	PROPN
ejde-390	507	45	ω	ω	PROPN
ejde-390	507	46	,	,	PUNCT
ejde-390	507	47	the	the	DET
ejde-390	507	48	function	function	NOUN
ejde-390	507	49	x→	x→	PUNCT
ejde-390	507	50	f(z	f(z	PROPN
ejde-390	507	51	,	,	PUNCT
ejde-390	507	52	x	x	NOUN
ejde-390	507	53	)	)	PUNCT
ejde-390	508	1	+	+	CCONJ
ejde-390	508	2	ξ̂ρ|x|p−2x	ξ̂ρ|x|p−2x	NOUN
ejde-390	508	3	is	be	AUX
ejde-390	508	4	nondecreasing	nondecrease	VERB
ejde-390	508	5	on	on	ADP
ejde-390	508	6	[	[	X
ejde-390	508	7	−ρ	−ρ	NOUN
ejde-390	508	8	,	,	PUNCT
ejde-390	508	9	ρ	ρ	NOUN
ejde-390	508	10	]	]	PUNCT
ejde-390	508	11	.	.	PUNCT
ejde-390	509	1	note	note	VERB
ejde-390	509	2	that	that	SCONJ
ejde-390	509	3	now	now	ADV
ejde-390	509	4	our	our	PRON
ejde-390	509	5	condition	condition	NOUN
ejde-390	509	6	on	on	ADP
ejde-390	509	7	f(z	f(z	PROPN
ejde-390	509	8	,	,	PUNCT
ejde-390	509	9	·	·	PUNCT
ejde-390	509	10	)	)	PUNCT
ejde-390	509	11	near	near	ADP
ejde-390	509	12	zero	zero	NUM
ejde-390	509	13	is	be	AUX
ejde-390	509	14	stronger	strong	ADJ
ejde-390	509	15	than	than	ADP
ejde-390	509	16	before	before	ADV
ejde-390	509	17	.	.	PUNCT
ejde-390	510	1	proposition	proposition	NOUN
ejde-390	510	2	4.1	4.1	NUM
ejde-390	510	3	.	.	PUNCT
ejde-390	511	1	if	if	SCONJ
ejde-390	511	2	hypotheses	hypothesis	NOUN
ejde-390	511	3	(	(	PUNCT
ejde-390	511	4	h1	h1	PROPN
ejde-390	511	5	)	)	PUNCT
ejde-390	511	6	,	,	PUNCT
ejde-390	511	7	(	(	PUNCT
ejde-390	511	8	h2	h2	NOUN
ejde-390	511	9	)	)	PUNCT
ejde-390	511	10	,	,	PUNCT
ejde-390	511	11	(	(	PUNCT
ejde-390	511	12	h3	h3	NOUN
ejde-390	511	13	”	"	PUNCT
ejde-390	511	14	)	)	PUNCT
ejde-390	511	15	hold	hold	VERB
ejde-390	511	16	and	and	CCONJ
ejde-390	511	17	λ	λ	X
ejde-390	511	18	≥	≥	X
ejde-390	511	19	λ̂∗	λ̂∗	PROPN
ejde-390	511	20	,	,	PUNCT
ejde-390	511	21	then	then	ADV
ejde-390	511	22	problem	problem	NOUN
ejde-390	511	23	(	(	PUNCT
ejde-390	511	24	1.1	1.1	NUM
ejde-390	511	25	)	)	PUNCT
ejde-390	511	26	admits	admit	VERB
ejde-390	511	27	a	a	DET
ejde-390	511	28	nodal	nodal	NOUN
ejde-390	511	29	solution	solution	NOUN
ejde-390	511	30	yλ	yλ	PRON
ejde-390	511	31	∈	∈	PROPN
ejde-390	511	32	c1(ω	c1(ω	PROPN
ejde-390	511	33	)	)	PUNCT
ejde-390	511	34	.	.	PUNCT
ejde-390	512	1	proof	proof	NOUN
ejde-390	512	2	.	.	PUNCT
ejde-390	513	1	using	use	VERB
ejde-390	513	2	the	the	DET
ejde-390	513	3	extremal	extremal	ADJ
ejde-390	513	4	constant	constant	ADJ
ejde-390	513	5	sign	sign	NOUN
ejde-390	513	6	solutions	solution	NOUN
ejde-390	513	7	ûλ	ûλ	NOUN
ejde-390	513	8	∈	∈	NOUN
ejde-390	513	9	d+	d+	PUNCT
ejde-390	513	10	and	and	CCONJ
ejde-390	513	11	v̂λ	v̂λ	PRON
ejde-390	513	12	∈	∈	NOUN
ejde-390	513	13	−d+	−d+	NOUN
ejde-390	513	14	,	,	PUNCT
ejde-390	513	15	we	we	PRON
ejde-390	513	16	introduce	introduce	VERB
ejde-390	513	17	the	the	DET
ejde-390	513	18	carathéodory	carathéodory	NOUN
ejde-390	513	19	function	function	NOUN
ejde-390	513	20	γ̂(z	γ̂(z	NOUN
ejde-390	513	21	,	,	PUNCT
ejde-390	513	22	x	x	NOUN
ejde-390	513	23	)	)	PUNCT
ejde-390	513	24	=	=	SYM
ejde-390	514	1			PROPN
ejde-390	514	2	f(z	f(z	PROPN
ejde-390	514	3	,	,	PUNCT
ejde-390	514	4	v̂λ(z	v̂λ(z	NUM
ejde-390	514	5	)	)	PUNCT
ejde-390	514	6	)	)	PUNCT
ejde-390	515	1	+	+	CCONJ
ejde-390	515	2	µ̂|v̂λ(z)|p−2v̂λ(z	µ̂|v̂λ(z)|p−2v̂λ(z	X
ejde-390	515	3	)	)	PUNCT
ejde-390	515	4	if	if	SCONJ
ejde-390	515	5	x	x	X
ejde-390	515	6	<	<	X
ejde-390	515	7	v̂λ(z	v̂λ(z	PROPN
ejde-390	515	8	)	)	PUNCT
ejde-390	515	9	,	,	PUNCT
ejde-390	515	10	f(z	f(z	PROPN
ejde-390	515	11	,	,	PUNCT
ejde-390	515	12	x	x	NOUN
ejde-390	515	13	)	)	PUNCT
ejde-390	515	14	+	+	PUNCT
ejde-390	515	15	µ̂|x|p−2x	µ̂|x|p−2x	NOUN
ejde-390	515	16	if	if	SCONJ
ejde-390	515	17	v̂λ(z	v̂λ(z	NOUN
ejde-390	515	18	)	)	PUNCT
ejde-390	515	19	≤	≤	NUM
ejde-390	515	20	x	x	SYM
ejde-390	515	21	≤	≤	ADJ
ejde-390	515	22	ûλ(z	ûλ(z	NOUN
ejde-390	515	23	)	)	PUNCT
ejde-390	515	24	,	,	PUNCT
ejde-390	515	25	f(z	f(z	PROPN
ejde-390	515	26	,	,	PUNCT
ejde-390	515	27	ûλ(z	ûλ(z	PROPN
ejde-390	515	28	)	)	PUNCT
ejde-390	515	29	)	)	PUNCT
ejde-390	516	1	+	+	CCONJ
ejde-390	516	2	µ̂ûλ(z)p−1	µ̂ûλ(z)p−1	NUM
ejde-390	516	3	if	if	SCONJ
ejde-390	516	4	ûλ(z	ûλ(z	NOUN
ejde-390	516	5	)	)	PUNCT
ejde-390	516	6	<	<	X
ejde-390	516	7	x	x	X
ejde-390	516	8	,	,	PUNCT
ejde-390	516	9	(	(	PUNCT
ejde-390	516	10	4.1	4.1	NUM
ejde-390	516	11	)	)	PUNCT
ejde-390	516	12	with	with	ADP
ejde-390	516	13	µ̂	µ̂	DET
ejde-390	516	14	≥	≥	NOUN
ejde-390	516	15	‖ξ‖∞.	‖ξ‖∞.	NUM
ejde-390	516	16	also	also	ADV
ejde-390	516	17	we	we	PRON
ejde-390	516	18	consider	consider	VERB
ejde-390	516	19	the	the	DET
ejde-390	516	20	positive	positive	ADJ
ejde-390	516	21	and	and	CCONJ
ejde-390	516	22	negative	negative	ADJ
ejde-390	516	23	truncations	truncation	NOUN
ejde-390	516	24	of	of	ADP
ejde-390	516	25	γ̂(z	γ̂(z	NOUN
ejde-390	516	26	,	,	PUNCT
ejde-390	516	27	·	·	PUNCT
ejde-390	516	28	)	)	PUNCT
ejde-390	516	29	,	,	PUNCT
ejde-390	516	30	namely	namely	ADV
ejde-390	516	31	the	the	DET
ejde-390	516	32	carathéodory	carathéodory	PROPN
ejde-390	516	33	functions	function	NOUN
ejde-390	516	34	γ̂±(z	γ̂±(z	NOUN
ejde-390	516	35	,	,	PUNCT
ejde-390	516	36	x	x	X
ejde-390	516	37	)	)	PUNCT
ejde-390	516	38	=	=	SYM
ejde-390	516	39	γ̂(z,±x±	γ̂(z,±x±	ADJ
ejde-390	516	40	)	)	PUNCT
ejde-390	516	41	.	.	PUNCT
ejde-390	517	1	(	(	PUNCT
ejde-390	517	2	4.2	4.2	NUM
ejde-390	517	3	)	)	PUNCT
ejde-390	517	4	we	we	PRON
ejde-390	517	5	set	set	VERB
ejde-390	517	6	γ̂(z	γ̂(z	NOUN
ejde-390	517	7	,	,	PUNCT
ejde-390	517	8	x	x	NOUN
ejde-390	517	9	)	)	PUNCT
ejde-390	517	10	=	=	SYM
ejde-390	518	1	∫	∫	PROPN
ejde-390	518	2	x	x	SYM
ejde-390	518	3	0	0	NUM
ejde-390	518	4	γ̂(z	γ̂(z	NOUN
ejde-390	518	5	,	,	PUNCT
ejde-390	518	6	s)ds	s)ds	PROPN
ejde-390	518	7	and	and	CCONJ
ejde-390	518	8	γ̂±(z	γ̂±(z	ADJ
ejde-390	518	9	,	,	PUNCT
ejde-390	518	10	x	x	X
ejde-390	518	11	)	)	PUNCT
ejde-390	518	12	=	=	SYM
ejde-390	519	1	∫	∫	PROPN
ejde-390	519	2	x	x	SYM
ejde-390	519	3	0	0	NUM
ejde-390	519	4	γ̂±(z	γ̂±(z	PROPN
ejde-390	519	5	,	,	PUNCT
ejde-390	519	6	s)ds	s)ds	PROPN
ejde-390	519	7	and	and	CCONJ
ejde-390	519	8	consider	consider	VERB
ejde-390	519	9	the	the	DET
ejde-390	519	10	c1functionals	c1functional	NOUN
ejde-390	519	11	σ̂	σ̂	NUM
ejde-390	519	12	,	,	PUNCT
ejde-390	519	13	σ̂±	σ̂±	VERB
ejde-390	519	14	:	:	PUNCT
ejde-390	520	1	w	w	PROPN
ejde-390	520	2	1,p(ω)→	1,p(ω)→	NUM
ejde-390	520	3	r	r	NOUN
ejde-390	520	4	defined	define	VERB
ejde-390	520	5	by	by	ADP
ejde-390	520	6	σ̂(u	σ̂(u	NUM
ejde-390	520	7	)	)	PUNCT
ejde-390	520	8	=	=	SYM
ejde-390	520	9	1	1	NUM
ejde-390	520	10	p	p	NOUN
ejde-390	520	11	γ(u	γ(u	PROPN
ejde-390	520	12	)	)	PUNCT
ejde-390	521	1	+	+	CCONJ
ejde-390	521	2	λ+	λ+	PUNCT
ejde-390	521	3	µ̂	µ̂	PRON
ejde-390	521	4	p	p	PRON
ejde-390	521	5	‖u‖pp	‖u‖pp	NOUN
ejde-390	521	6	−	−	PROPN
ejde-390	521	7	∫	∫	PROPN
ejde-390	521	8	ω	ω	PROPN
ejde-390	521	9	γ̂(z	γ̂(z	PROPN
ejde-390	521	10	,	,	PUNCT
ejde-390	521	11	u)dz	u)dz	PROPN
ejde-390	521	12	σ̂±(u	σ̂±(u	NUM
ejde-390	521	13	)	)	PUNCT
ejde-390	521	14	=	=	SYM
ejde-390	522	1	1	1	NUM
ejde-390	522	2	p	p	NOUN
ejde-390	522	3	γ(u	γ(u	PROPN
ejde-390	522	4	)	)	PUNCT
ejde-390	523	1	+	+	CCONJ
ejde-390	523	2	λ+	λ+	PUNCT
ejde-390	523	3	µ̂	µ̂	PRON
ejde-390	523	4	p	p	PRON
ejde-390	523	5	‖u‖pp	‖u‖pp	NOUN
ejde-390	523	6	−	−	PROPN
ejde-390	523	7	∫	∫	PROPN
ejde-390	523	8	ω	ω	PROPN
ejde-390	523	9	γ̂±(z	γ̂±(z	PROPN
ejde-390	523	10	,	,	PUNCT
ejde-390	523	11	u)dz	u)dz	PROPN
ejde-390	523	12	for	for	ADP
ejde-390	523	13	all	all	DET
ejde-390	523	14	u	u	NOUN
ejde-390	523	15	∈w	∈w	NOUN
ejde-390	523	16	1,p(ω	1,p(ω	NUM
ejde-390	523	17	)	)	PUNCT
ejde-390	523	18	.	.	PUNCT
ejde-390	524	1	using	use	VERB
ejde-390	524	2	(	(	PUNCT
ejde-390	524	3	4.1	4.1	NUM
ejde-390	524	4	)	)	PUNCT
ejde-390	524	5	and	and	CCONJ
ejde-390	524	6	(	(	PUNCT
ejde-390	524	7	4.2	4.2	NUM
ejde-390	524	8	)	)	PUNCT
ejde-390	524	9	,	,	PUNCT
ejde-390	524	10	we	we	PRON
ejde-390	524	11	can	can	AUX
ejde-390	524	12	easily	easily	ADV
ejde-390	524	13	show	show	VERB
ejde-390	524	14	that	that	SCONJ
ejde-390	524	15	kσ̂	kσ̂	VERB
ejde-390	524	16	⊆	⊆	NUM
ejde-390	524	17	[	[	X
ejde-390	524	18	v̂λ	v̂λ	X
ejde-390	524	19	,	,	PUNCT
ejde-390	524	20	ûλ	ûλ	NOUN
ejde-390	524	21	]	]	PUNCT
ejde-390	524	22	∩	∩	X
ejde-390	524	23	c1(ω	c1(ω	X
ejde-390	524	24	)	)	PUNCT
ejde-390	524	25	,	,	PUNCT
ejde-390	524	26	kσ̂+	kσ̂+	VERB
ejde-390	524	27	⊆	⊆	NUM
ejde-390	524	28	[	[	X
ejde-390	524	29	0	0	NUM
ejde-390	524	30	,	,	PUNCT
ejde-390	524	31	ûλ	ûλ	NOUN
ejde-390	524	32	]	]	PUNCT
ejde-390	524	33	∩	∩	NOUN
ejde-390	524	34	c+,kσ̂−	c+,kσ̂−	PRON
ejde-390	524	35	⊆	⊆	NUM
ejde-390	524	36	[	[	X
ejde-390	524	37	v̂λ	v̂λ	X
ejde-390	524	38	,	,	PUNCT
ejde-390	524	39	0	0	NUM
ejde-390	524	40	]	]	X
ejde-390	524	41	∩	∩	NOUN
ejde-390	524	42	(	(	PUNCT
ejde-390	524	43	−c+	−c+	NOUN
ejde-390	524	44	)	)	PUNCT
ejde-390	524	45	.	.	PUNCT
ejde-390	525	1	the	the	DET
ejde-390	525	2	extremality	extremality	NOUN
ejde-390	525	3	of	of	ADP
ejde-390	525	4	ûλ	ûλ	NOUN
ejde-390	525	5	and	and	CCONJ
ejde-390	525	6	v̂λ	v̂λ	PRON
ejde-390	525	7	implies	implie	NOUN
ejde-390	525	8	that	that	PRON
ejde-390	525	9	kσ̂	kσ̂	VERB
ejde-390	525	10	⊆	⊆	NUM
ejde-390	525	11	[	[	X
ejde-390	525	12	v̂λ	v̂λ	X
ejde-390	525	13	,	,	PUNCT
ejde-390	525	14	ûλ	ûλ	NOUN
ejde-390	525	15	]	]	PUNCT
ejde-390	525	16	∩	∩	X
ejde-390	525	17	c1(ω	c1(ω	X
ejde-390	525	18	)	)	PUNCT
ejde-390	525	19	,	,	PUNCT
ejde-390	525	20	kσ̂+	kσ̂+	PROPN
ejde-390	525	21	=	=	PUNCT
ejde-390	525	22	{	{	PUNCT
ejde-390	525	23	0	0	NUM
ejde-390	525	24	,	,	PUNCT
ejde-390	525	25	ûλ	ûλ	NOUN
ejde-390	525	26	}	}	PUNCT
ejde-390	525	27	,	,	PUNCT
ejde-390	525	28	kσ̂−	kσ̂−	PROPN
ejde-390	525	29	=	=	PUNCT
ejde-390	525	30	{	{	PUNCT
ejde-390	525	31	0	0	NUM
ejde-390	525	32	,	,	PUNCT
ejde-390	525	33	v̂λ	v̂λ	NOUN
ejde-390	525	34	}	}	PUNCT
ejde-390	525	35	.	.	PUNCT
ejde-390	526	1	(	(	PUNCT
ejde-390	526	2	4.3	4.3	NUM
ejde-390	526	3	)	)	PUNCT
ejde-390	526	4	ejde-2020/12	ejde-2020/12	NOUN
ejde-390	526	5	positive	positive	ADJ
ejde-390	526	6	and	and	CCONJ
ejde-390	526	7	nodal	nodal	ADJ
ejde-390	526	8	solutions	solution	NOUN
ejde-390	526	9	19	19	NUM
ejde-390	526	10	from	from	ADP
ejde-390	526	11	(	(	PUNCT
ejde-390	526	12	4.1	4.1	NUM
ejde-390	526	13	)	)	PUNCT
ejde-390	526	14	and	and	CCONJ
ejde-390	526	15	(	(	PUNCT
ejde-390	526	16	4.2	4.2	NUM
ejde-390	526	17	)	)	PUNCT
ejde-390	526	18	it	it	PRON
ejde-390	526	19	is	be	AUX
ejde-390	526	20	clear	clear	ADJ
ejde-390	526	21	that	that	SCONJ
ejde-390	526	22	σ̂+	σ̂+	PROPN
ejde-390	526	23	(	(	PUNCT
ejde-390	526	24	·	·	PUNCT
ejde-390	526	25	)	)	PUNCT
ejde-390	526	26	is	be	AUX
ejde-390	526	27	coercive	coercive	ADJ
ejde-390	526	28	.	.	PUNCT
ejde-390	527	1	also	also	ADV
ejde-390	527	2	,	,	PUNCT
ejde-390	527	3	it	it	PRON
ejde-390	527	4	is	be	AUX
ejde-390	527	5	sequentially	sequentially	ADV
ejde-390	527	6	weakly	weakly	ADV
ejde-390	527	7	lower	low	ADJ
ejde-390	527	8	semicontinuous	semicontinuous	ADJ
ejde-390	527	9	.	.	PUNCT
ejde-390	528	1	so	so	ADV
ejde-390	528	2	,	,	PUNCT
ejde-390	528	3	we	we	PRON
ejde-390	528	4	can	can	AUX
ejde-390	528	5	find	find	VERB
ejde-390	528	6	ũλ	ũλ	PRON
ejde-390	528	7	∈w	∈w	VERB
ejde-390	528	8	1,p(ω	1,p(ω	NUM
ejde-390	528	9	)	)	PUNCT
ejde-390	528	10	such	such	ADJ
ejde-390	528	11	that	that	SCONJ
ejde-390	528	12	σ̂+(ũλ	σ̂+(ũλ	NUM
ejde-390	528	13	)	)	PUNCT
ejde-390	528	14	=	=	SYM
ejde-390	529	1	inf[σ̂+(u	inf[σ̂+(u	X
ejde-390	529	2	)	)	PUNCT
ejde-390	529	3	:	:	PUNCT
ejde-390	529	4	u	u	NOUN
ejde-390	529	5	∈w	∈w	VERB
ejde-390	529	6	1,p(ω	1,p(ω	NUM
ejde-390	529	7	)	)	PUNCT
ejde-390	529	8	]	]	PUNCT
ejde-390	529	9	.	.	PUNCT
ejde-390	530	1	(	(	PUNCT
ejde-390	530	2	4.4	4.4	NUM
ejde-390	530	3	)	)	PUNCT
ejde-390	530	4	by	by	ADP
ejde-390	530	5	hypothesis	hypothesis	NOUN
ejde-390	530	6	(	(	PUNCT
ejde-390	530	7	h3”)(iv	h3”)(iv	PROPN
ejde-390	530	8	)	)	PUNCT
ejde-390	530	9	,	,	PUNCT
ejde-390	530	10	we	we	PRON
ejde-390	530	11	have	have	VERB
ejde-390	530	12	σ̂+(ũλ	σ̂+(ũλ	NUM
ejde-390	530	13	)	)	PUNCT
ejde-390	530	14	<	<	X
ejde-390	530	15	0	0	PUNCT
ejde-390	530	16	=	=	SYM
ejde-390	530	17	σ̂+(0	σ̂+(0	NOUN
ejde-390	530	18	)	)	PUNCT
ejde-390	530	19	,	,	PUNCT
ejde-390	530	20	⇒	⇒	VERB
ejde-390	530	21	ũλ	ũλ	PROPN
ejde-390	530	22	6=	6=	PROPN
ejde-390	530	23	0	0	NUM
ejde-390	530	24	,	,	PUNCT
ejde-390	530	25	⇒	⇒	VERB
ejde-390	530	26	ũλ	ũλ	NOUN
ejde-390	531	1	=	=	PUNCT
ejde-390	531	2	ûλ	ûλ	NOUN
ejde-390	531	3	∈	∈	NOUN
ejde-390	531	4	d+	d+	PUNCT
ejde-390	531	5	(	(	PUNCT
ejde-390	531	6	see	see	VERB
ejde-390	531	7	(	(	PUNCT
ejde-390	531	8	4.3	4.3	NUM
ejde-390	531	9	)	)	PUNCT
ejde-390	531	10	,	,	PUNCT
ejde-390	531	11	(	(	PUNCT
ejde-390	531	12	4.4	4.4	NUM
ejde-390	531	13	)	)	PUNCT
ejde-390	531	14	)	)	PUNCT
ejde-390	531	15	.	.	PUNCT
ejde-390	532	1	since	since	SCONJ
ejde-390	532	2	σ̂+	σ̂+	PROPN
ejde-390	532	3	∣∣	∣∣	NUM
ejde-390	532	4	c+	c+	X
ejde-390	532	5	=	=	SYM
ejde-390	532	6	σ̂	σ̂	X
ejde-390	532	7	∣∣	∣∣	NUM
ejde-390	532	8	c+	c+	VERB
ejde-390	532	9	it	it	PRON
ejde-390	532	10	follows	follow	VERB
ejde-390	532	11	that	that	SCONJ
ejde-390	532	12	ûλ	ûλ	NOUN
ejde-390	532	13	∈	∈	NOUN
ejde-390	532	14	d+	d+	NOUN
ejde-390	532	15	is	be	AUX
ejde-390	532	16	a	a	DET
ejde-390	532	17	local	local	ADJ
ejde-390	532	18	c1(ω)-minimizer	c1(ω)-minimizer	NOUN
ejde-390	532	19	of	of	ADP
ejde-390	532	20	σ̂	σ̂	PROPN
ejde-390	532	21	(	(	PUNCT
ejde-390	532	22	·	·	PUNCT
ejde-390	532	23	)	)	PUNCT
ejde-390	532	24	,	,	PUNCT
ejde-390	532	25	⇒	⇒	VERB
ejde-390	532	26	ûλ	ûλ	NOUN
ejde-390	532	27	∈	∈	NOUN
ejde-390	532	28	d+	d+	NOUN
ejde-390	532	29	is	be	AUX
ejde-390	532	30	a	a	DET
ejde-390	532	31	local	local	ADJ
ejde-390	532	32	w	w	NOUN
ejde-390	532	33	1,p(ω)-minimizer	1,p(ω)-minimizer	NUM
ejde-390	532	34	of	of	ADP
ejde-390	532	35	σ̂	σ̂	PROPN
ejde-390	532	36	(	(	PUNCT
ejde-390	532	37	·	·	PUNCT
ejde-390	532	38	)	)	PUNCT
ejde-390	532	39	(	(	PUNCT
ejde-390	532	40	4.5	4.5	NUM
ejde-390	532	41	)	)	PUNCT
ejde-390	532	42	(	(	PUNCT
ejde-390	532	43	see	see	VERB
ejde-390	532	44	papageorgiou	papageorgiou	NOUN
ejde-390	532	45	-	-	PUNCT
ejde-390	532	46	rǎdulescu	rǎdulescu	NOUN
ejde-390	532	47	[	[	X
ejde-390	532	48	10	10	NUM
ejde-390	532	49	]	]	NUM
ejde-390	532	50	)	)	PUNCT
ejde-390	532	51	.	.	PUNCT
ejde-390	533	1	similarly	similarly	ADV
ejde-390	533	2	,	,	PUNCT
ejde-390	533	3	using	use	VERB
ejde-390	533	4	this	this	DET
ejde-390	533	5	time	time	NOUN
ejde-390	533	6	σ̂−	σ̂−	PROPN
ejde-390	533	7	(	(	PUNCT
ejde-390	533	8	·	·	PUNCT
ejde-390	533	9	)	)	PUNCT
ejde-390	533	10	,	,	PUNCT
ejde-390	533	11	we	we	PRON
ejde-390	533	12	show	show	VERB
ejde-390	533	13	that	that	SCONJ
ejde-390	533	14	v̂λ	v̂λ	PRON
ejde-390	533	15	∈	∈	PROPN
ejde-390	533	16	−d+	−d+	NOUN
ejde-390	533	17	is	be	AUX
ejde-390	533	18	a	a	DET
ejde-390	533	19	local	local	ADJ
ejde-390	533	20	w	w	NOUN
ejde-390	533	21	1,p(ω)-minimizer	1,p(ω)-minimizer	NUM
ejde-390	533	22	of	of	ADP
ejde-390	533	23	σ̂	σ̂	PROPN
ejde-390	533	24	(	(	PUNCT
ejde-390	533	25	·	·	PUNCT
ejde-390	533	26	)	)	PUNCT
ejde-390	533	27	.	.	PUNCT
ejde-390	534	1	(	(	PUNCT
ejde-390	534	2	4.6	4.6	X
ejde-390	534	3	)	)	PUNCT
ejde-390	534	4	we	we	PRON
ejde-390	534	5	can	can	AUX
ejde-390	534	6	assume	assume	VERB
ejde-390	534	7	that	that	SCONJ
ejde-390	534	8	σ̂(v̂λ	σ̂(v̂λ	PROPN
ejde-390	534	9	)	)	PUNCT
ejde-390	534	10	≤	≤	NUM
ejde-390	534	11	σ̂(ûλ	σ̂(ûλ	PROPN
ejde-390	534	12	)	)	PUNCT
ejde-390	534	13	.	.	PUNCT
ejde-390	535	1	the	the	DET
ejde-390	535	2	reasoning	reasoning	NOUN
ejde-390	535	3	is	be	AUX
ejde-390	535	4	the	the	DET
ejde-390	535	5	same	same	ADJ
ejde-390	535	6	if	if	SCONJ
ejde-390	535	7	the	the	DET
ejde-390	535	8	opposite	opposite	ADJ
ejde-390	535	9	inequality	inequality	NOUN
ejde-390	535	10	holds	hold	VERB
ejde-390	535	11	,	,	PUNCT
ejde-390	535	12	using	use	VERB
ejde-390	535	13	(	(	PUNCT
ejde-390	535	14	4.6	4.6	NUM
ejde-390	535	15	)	)	PUNCT
ejde-390	535	16	instead	instead	ADV
ejde-390	535	17	of	of	ADP
ejde-390	535	18	(	(	PUNCT
ejde-390	535	19	4.5	4.5	NUM
ejde-390	535	20	)	)	PUNCT
ejde-390	535	21	.	.	PUNCT
ejde-390	536	1	by	by	ADP
ejde-390	536	2	(	(	PUNCT
ejde-390	536	3	4.3	4.3	NUM
ejde-390	536	4	)	)	PUNCT
ejde-390	536	5	and	and	CCONJ
ejde-390	536	6	the	the	DET
ejde-390	536	7	extremality	extremality	NOUN
ejde-390	536	8	of	of	ADP
ejde-390	536	9	ûλ	ûλ	NOUN
ejde-390	536	10	and	and	CCONJ
ejde-390	536	11	v̂λ	v̂λ	NOUN
ejde-390	536	12	,	,	PUNCT
ejde-390	536	13	we	we	PRON
ejde-390	536	14	see	see	VERB
ejde-390	536	15	that	that	SCONJ
ejde-390	536	16	we	we	PRON
ejde-390	536	17	can	can	AUX
ejde-390	536	18	assume	assume	VERB
ejde-390	536	19	that	that	SCONJ
ejde-390	536	20	kσ̂	kσ̂	VERB
ejde-390	536	21	⊆	⊆	NUM
ejde-390	536	22	c1(ω	c1(ω	SYM
ejde-390	536	23	)	)	PUNCT
ejde-390	536	24	is	be	AUX
ejde-390	536	25	finite	finite	PROPN
ejde-390	536	26	.	.	PUNCT
ejde-390	537	1	(	(	PUNCT
ejde-390	537	2	4.7	4.7	NUM
ejde-390	537	3	)	)	PUNCT
ejde-390	537	4	otherwise	otherwise	ADV
ejde-390	537	5	we	we	PRON
ejde-390	537	6	already	already	ADV
ejde-390	537	7	have	have	VERB
ejde-390	537	8	an	an	DET
ejde-390	537	9	infinity	infinity	NOUN
ejde-390	537	10	of	of	ADP
ejde-390	537	11	smooth	smooth	ADJ
ejde-390	537	12	nodal	nodal	NOUN
ejde-390	537	13	solutions	solution	NOUN
ejde-390	537	14	and	and	CCONJ
ejde-390	537	15	so	so	ADV
ejde-390	537	16	we	we	PRON
ejde-390	537	17	are	be	AUX
ejde-390	537	18	done	do	VERB
ejde-390	537	19	.	.	PUNCT
ejde-390	538	1	by	by	ADP
ejde-390	538	2	(	(	PUNCT
ejde-390	538	3	4.5	4.5	NUM
ejde-390	538	4	)	)	PUNCT
ejde-390	538	5	,	,	PUNCT
ejde-390	538	6	(	(	PUNCT
ejde-390	538	7	4.7	4.7	NUM
ejde-390	538	8	)	)	PUNCT
ejde-390	538	9	and	and	CCONJ
ejde-390	538	10	[	[	X
ejde-390	538	11	14	14	NUM
ejde-390	538	12	,	,	PUNCT
ejde-390	538	13	theorem	theorem	VERB
ejde-390	538	14	5.7.6	5.7.6	NUM
ejde-390	538	15	,	,	PUNCT
ejde-390	538	16	p.	p.	NOUN
ejde-390	538	17	367	367	NUM
ejde-390	538	18	,	,	PUNCT
ejde-390	538	19	]	]	PUNCT
ejde-390	538	20	,	,	PUNCT
ejde-390	538	21	we	we	PRON
ejde-390	538	22	can	can	AUX
ejde-390	538	23	find	find	VERB
ejde-390	538	24	ρ	ρ	NOUN
ejde-390	538	25	∈	∈	PROPN
ejde-390	538	26	(	(	PUNCT
ejde-390	538	27	0	0	NUM
ejde-390	538	28	,	,	PUNCT
ejde-390	538	29	1	1	X
ejde-390	538	30	)	)	PUNCT
ejde-390	538	31	small	small	ADJ
ejde-390	538	32	such	such	ADJ
ejde-390	538	33	that	that	SCONJ
ejde-390	538	34	σ̂(v̂λ	σ̂(v̂λ	X
ejde-390	538	35	)	)	PUNCT
ejde-390	538	36	≤	≤	NUM
ejde-390	538	37	σ̂(ûλ	σ̂(ûλ	PROPN
ejde-390	538	38	)	)	PUNCT
ejde-390	538	39	<	<	X
ejde-390	538	40	inf[σ̂(u	inf[σ̂(u	PROPN
ejde-390	538	41	)	)	PUNCT
ejde-390	538	42	:	:	PUNCT
ejde-390	539	1	‖u−	‖u−	X
ejde-390	539	2	ûλ‖	ûλ‖	PROPN
ejde-390	539	3	=	=	SYM
ejde-390	539	4	ρ	ρ	PROPN
ejde-390	539	5	]	]	X
ejde-390	539	6	=	=	SYM
ejde-390	539	7	m̂λ	m̂λ	PROPN
ejde-390	539	8	,	,	PUNCT
ejde-390	539	9	‖v̂λ	‖v̂λ	ADJ
ejde-390	539	10	−	−	X
ejde-390	539	11	ûλ‖	ûλ‖	PROPN
ejde-390	539	12	>	>	X
ejde-390	539	13	ρ	ρ	PROPN
ejde-390	539	14	.	.	PUNCT
ejde-390	539	15	(	(	PUNCT
ejde-390	539	16	4.8	4.8	NUM
ejde-390	539	17	)	)	PUNCT
ejde-390	539	18	from	from	ADP
ejde-390	539	19	(	(	PUNCT
ejde-390	539	20	4.1	4.1	NUM
ejde-390	539	21	)	)	PUNCT
ejde-390	539	22	and	and	CCONJ
ejde-390	539	23	since	since	SCONJ
ejde-390	539	24	µ̂	µ̂	DET
ejde-390	539	25	≥	≥	NOUN
ejde-390	539	26	‖ξ‖∞	‖ξ‖∞	NUM
ejde-390	539	27	,	,	PUNCT
ejde-390	539	28	we	we	PRON
ejde-390	539	29	see	see	VERB
ejde-390	539	30	that	that	SCONJ
ejde-390	539	31	σ̂	σ̂	PROPN
ejde-390	539	32	(	(	PUNCT
ejde-390	539	33	·	·	PUNCT
ejde-390	539	34	)	)	PUNCT
ejde-390	539	35	is	be	AUX
ejde-390	539	36	coercive	coercive	ADJ
ejde-390	539	37	.	.	PUNCT
ejde-390	540	1	hence	hence	ADV
ejde-390	540	2	σ̂	σ̂	X
ejde-390	540	3	(	(	PUNCT
ejde-390	540	4	·	·	PUNCT
ejde-390	540	5	)	)	PUNCT
ejde-390	540	6	satisfies	satisfy	VERB
ejde-390	540	7	the	the	DET
ejde-390	540	8	c	c	NOUN
ejde-390	540	9	-	-	NOUN
ejde-390	540	10	condition	condition	NOUN
ejde-390	540	11	.	.	PUNCT
ejde-390	541	1	(	(	PUNCT
ejde-390	541	2	4.9	4.9	NUM
ejde-390	541	3	)	)	PUNCT
ejde-390	541	4	then	then	ADV
ejde-390	541	5	(	(	PUNCT
ejde-390	541	6	4.8	4.8	NUM
ejde-390	541	7	)	)	PUNCT
ejde-390	541	8	and	and	CCONJ
ejde-390	541	9	(	(	PUNCT
ejde-390	541	10	4.9	4.9	NUM
ejde-390	541	11	)	)	PUNCT
ejde-390	541	12	permit	permit	VERB
ejde-390	541	13	the	the	DET
ejde-390	541	14	use	use	NOUN
ejde-390	541	15	of	of	ADP
ejde-390	541	16	the	the	DET
ejde-390	541	17	mountain	mountain	NOUN
ejde-390	541	18	pass	pass	NOUN
ejde-390	541	19	theorem	theorem	NOUN
ejde-390	541	20	.	.	PUNCT
ejde-390	542	1	so	so	ADV
ejde-390	542	2	,	,	PUNCT
ejde-390	542	3	we	we	PRON
ejde-390	542	4	can	can	AUX
ejde-390	542	5	find	find	VERB
ejde-390	542	6	yλ	yλ	PRON
ejde-390	542	7	∈w	∈w	NOUN
ejde-390	542	8	1,p(ω	1,p(ω	NUM
ejde-390	542	9	)	)	PUNCT
ejde-390	542	10	such	such	ADJ
ejde-390	542	11	that	that	SCONJ
ejde-390	542	12	yλ	yλ	PROPN
ejde-390	542	13	∈	∈	PROPN
ejde-390	542	14	kσ̂	kσ̂	X
ejde-390	542	15	and	and	CCONJ
ejde-390	542	16	m̂λ	m̂λ	ADJ
ejde-390	542	17	≤	≤	ADJ
ejde-390	542	18	σ̂(yλ	σ̂(yλ	NOUN
ejde-390	542	19	)	)	PUNCT
ejde-390	542	20	,	,	PUNCT
ejde-390	542	21	⇒	⇒	VERB
ejde-390	542	22	yλ	yλ	PRON
ejde-390	542	23	∈	∈	PROPN
ejde-390	542	24	c1(ω	c1(ω	PROPN
ejde-390	542	25	)	)	PUNCT
ejde-390	542	26	and	and	CCONJ
ejde-390	542	27	yλ	yλ	DET
ejde-390	542	28	6∈	6∈	PROPN
ejde-390	542	29	{	{	PUNCT
ejde-390	542	30	ûλ	ûλ	ADV
ejde-390	542	31	,	,	PUNCT
ejde-390	542	32	v̂λ}(see	v̂λ}(see	PROPN
ejde-390	542	33	(	(	PUNCT
ejde-390	542	34	4.7	4.7	NUM
ejde-390	542	35	)	)	PUNCT
ejde-390	542	36	,	,	PUNCT
ejde-390	542	37	(	(	PUNCT
ejde-390	542	38	4.8	4.8	NUM
ejde-390	542	39	)	)	PUNCT
ejde-390	542	40	)	)	PUNCT
ejde-390	542	41	.	.	PUNCT
ejde-390	543	1	(	(	PUNCT
ejde-390	543	2	4.10	4.10	NUM
ejde-390	543	3	)	)	PUNCT
ejde-390	543	4	also	also	ADV
ejde-390	543	5	.	.	PUNCT
ejde-390	544	1	from	from	ADP
ejde-390	544	2	papageorgiou	papageorgiou	NOUN
ejde-390	544	3	-	-	PUNCT
ejde-390	544	4	rǎdulescu	rǎdulescu	NUM
ejde-390	544	5	-	-	PUNCT
ejde-390	544	6	repovš	repovš	NOUN
ejde-390	544	7	[	[	X
ejde-390	544	8	14	14	NUM
ejde-390	544	9	,	,	PUNCT
ejde-390	544	10	theorem	theorem	VERB
ejde-390	544	11	6.5.8	6.5.8	ADP
ejde-390	544	12	,	,	PUNCT
ejde-390	544	13	p.	p.	NOUN
ejde-390	544	14	431	431	NUM
ejde-390	544	15	]	]	PUNCT
ejde-390	544	16	,	,	PUNCT
ejde-390	544	17	we	we	PRON
ejde-390	544	18	have	have	VERB
ejde-390	544	19	c1(σ̂	c1(σ̂	NOUN
ejde-390	544	20	,	,	PUNCT
ejde-390	544	21	yλ	yλ	PROPN
ejde-390	544	22	)	)	PUNCT
ejde-390	544	23	6=	6=	ADP
ejde-390	544	24	0	0	NUM
ejde-390	544	25	.	.	PUNCT
ejde-390	545	1	(	(	PUNCT
ejde-390	545	2	4.11	4.11	NUM
ejde-390	545	3	)	)	PUNCT
ejde-390	545	4	on	on	ADP
ejde-390	545	5	the	the	DET
ejde-390	545	6	other	other	ADJ
ejde-390	545	7	hand	hand	NOUN
ejde-390	545	8	by	by	ADP
ejde-390	545	9	(	(	PUNCT
ejde-390	545	10	h3”)(iv	h3”)(iv	PROPN
ejde-390	545	11	)	)	PUNCT
ejde-390	545	12	and	and	CCONJ
ejde-390	545	13	papageorgiou	papageorgiou	NOUN
ejde-390	545	14	-	-	PUNCT
ejde-390	545	15	rǎdulescu	rǎdulescu	NOUN
ejde-390	545	16	[	[	X
ejde-390	545	17	9	9	NUM
ejde-390	545	18	,	,	PUNCT
ejde-390	545	19	proposition	proposition	NOUN
ejde-390	545	20	3.7	3.7	NUM
ejde-390	545	21	]	]	PUNCT
ejde-390	545	22	,	,	PUNCT
ejde-390	545	23	we	we	PRON
ejde-390	545	24	have	have	VERB
ejde-390	545	25	ck(σ̂	ck(σ̂	NOUN
ejde-390	545	26	,	,	PUNCT
ejde-390	545	27	0	0	NUM
ejde-390	545	28	)	)	PUNCT
ejde-390	545	29	=	=	SYM
ejde-390	545	30	0	0	NUM
ejde-390	546	1	for	for	ADP
ejde-390	546	2	all	all	DET
ejde-390	546	3	k	k	PROPN
ejde-390	546	4	∈	∈	PROPN
ejde-390	546	5	n0	n0	PROPN
ejde-390	546	6	.	.	PUNCT
ejde-390	547	1	(	(	PUNCT
ejde-390	547	2	4.12	4.12	NUM
ejde-390	547	3	)	)	PUNCT
ejde-390	547	4	comparing	compare	VERB
ejde-390	547	5	(	(	PUNCT
ejde-390	547	6	4.11	4.11	NUM
ejde-390	547	7	)	)	PUNCT
ejde-390	547	8	and	and	CCONJ
ejde-390	547	9	(	(	PUNCT
ejde-390	547	10	4.12	4.12	NUM
ejde-390	547	11	)	)	PUNCT
ejde-390	547	12	,	,	PUNCT
ejde-390	547	13	we	we	PRON
ejde-390	547	14	infer	infer	VERB
ejde-390	547	15	that	that	SCONJ
ejde-390	547	16	yλ	yλ	PROPN
ejde-390	547	17	6=	6=	PROPN
ejde-390	547	18	0	0	NUM
ejde-390	547	19	.	.	PUNCT
ejde-390	548	1	therefore	therefore	ADV
ejde-390	548	2	from	from	ADP
ejde-390	548	3	(	(	PUNCT
ejde-390	548	4	4.3	4.3	NUM
ejde-390	548	5	)	)	PUNCT
ejde-390	548	6	and	and	CCONJ
ejde-390	548	7	(	(	PUNCT
ejde-390	548	8	4.10	4.10	NUM
ejde-390	548	9	)	)	PUNCT
ejde-390	548	10	,	,	PUNCT
ejde-390	548	11	we	we	PRON
ejde-390	548	12	have	have	VERB
ejde-390	548	13	that	that	PRON
ejde-390	548	14	yλ	yλ	PROPN
ejde-390	548	15	∈	∈	PROPN
ejde-390	548	16	c1(ω	c1(ω	X
ejde-390	548	17	)	)	PUNCT
ejde-390	548	18	is	be	AUX
ejde-390	548	19	a	a	DET
ejde-390	548	20	nodal	nodal	ADJ
ejde-390	548	21	solution	solution	NOUN
ejde-390	548	22	of	of	ADP
ejde-390	548	23	(	(	PUNCT
ejde-390	548	24	1.1	1.1	NUM
ejde-390	548	25	)	)	PUNCT
ejde-390	548	26	.	.	PUNCT
ejde-390	549	1	�	�	PROPN
ejde-390	549	2	now	now	ADV
ejde-390	549	3	we	we	PRON
ejde-390	549	4	can	can	AUX
ejde-390	549	5	state	state	VERB
ejde-390	549	6	a	a	DET
ejde-390	549	7	multiplicity	multiplicity	NOUN
ejde-390	549	8	theorem	theorem	VERB
ejde-390	549	9	for	for	ADP
ejde-390	549	10	problem	problem	NOUN
ejde-390	549	11	(	(	PUNCT
ejde-390	549	12	1.1	1.1	NUM
ejde-390	549	13	)	)	PUNCT
ejde-390	549	14	.	.	PUNCT
ejde-390	550	1	theorem	theorem	VERB
ejde-390	550	2	4.2	4.2	NUM
ejde-390	550	3	.	.	PUNCT
ejde-390	551	1	if	if	SCONJ
ejde-390	551	2	hypotheses	hypothesis	NOUN
ejde-390	551	3	(	(	PUNCT
ejde-390	551	4	h1	h1	PROPN
ejde-390	551	5	)	)	PUNCT
ejde-390	551	6	,	,	PUNCT
ejde-390	551	7	(	(	PUNCT
ejde-390	551	8	h2	h2	NOUN
ejde-390	551	9	)	)	PUNCT
ejde-390	551	10	,	,	PUNCT
ejde-390	551	11	(	(	PUNCT
ejde-390	551	12	h3	h3	NOUN
ejde-390	551	13	”	"	PUNCT
ejde-390	551	14	)	)	PUNCT
ejde-390	551	15	hold	hold	VERB
ejde-390	551	16	,	,	PUNCT
ejde-390	551	17	then	then	ADV
ejde-390	551	18	there	there	PRON
ejde-390	551	19	exists	exist	VERB
ejde-390	551	20	a	a	DET
ejde-390	551	21	λ̂∗	λ̂∗	X
ejde-390	551	22	>	>	X
ejde-390	551	23	0	0	NUM
ejde-390	551	24	such	such	ADJ
ejde-390	551	25	that	that	SCONJ
ejde-390	551	26	(	(	PUNCT
ejde-390	551	27	a	a	NOUN
ejde-390	551	28	)	)	PUNCT
ejde-390	551	29	for	for	ADP
ejde-390	551	30	all	all	DET
ejde-390	551	31	λ	λ	PROPN
ejde-390	551	32	>	>	X
ejde-390	551	33	λ̂∗	λ̂∗	PROPN
ejde-390	551	34	problem	problem	NOUN
ejde-390	551	35	(	(	PUNCT
ejde-390	551	36	1.1	1.1	NUM
ejde-390	551	37	)	)	PUNCT
ejde-390	551	38	has	have	AUX
ejde-390	551	39	at	at	ADV
ejde-390	551	40	least	least	ADJ
ejde-390	551	41	five	five	NUM
ejde-390	551	42	nontrivial	nontrivial	ADJ
ejde-390	551	43	smooth	smooth	ADJ
ejde-390	551	44	solutions	solution	NOUN
ejde-390	551	45	u0	u0	ADJ
ejde-390	551	46	,	,	PUNCT
ejde-390	551	47	û	û	PROPN
ejde-390	551	48	∈	∈	PROPN
ejde-390	551	49	d+	d+	X
ejde-390	551	50	,	,	PUNCT
ejde-390	551	51	v0	v0	NOUN
ejde-390	551	52	,	,	PUNCT
ejde-390	551	53	v̂	v̂	ADP
ejde-390	551	54	∈	∈	PROPN
ejde-390	551	55	−d+	−d+	NOUN
ejde-390	551	56	,	,	PUNCT
ejde-390	551	57	yλ	yλ	PROPN
ejde-390	551	58	∈	∈	PROPN
ejde-390	551	59	c1(ω	c1(ω	NOUN
ejde-390	551	60	)	)	PUNCT
ejde-390	551	61	nodal	nodal	NOUN
ejde-390	551	62	;	;	PUNCT
ejde-390	551	63	20	20	NUM
ejde-390	551	64	n.	n.	NOUN
ejde-390	551	65	s.	s.	PROPN
ejde-390	551	66	papageorgiou	papageorgiou	PROPN
ejde-390	551	67	,	,	PUNCT
ejde-390	551	68	c.	c.	PROPN
ejde-390	551	69	vetro	vetro	PROPN
ejde-390	551	70	,	,	PUNCT
ejde-390	551	71	f.	f.	PROPN
ejde-390	551	72	vetro	vetro	PROPN
ejde-390	551	73	ejde-2020/12	ejde-2020/12	PROPN
ejde-390	551	74	(	(	PUNCT
ejde-390	551	75	b	b	NOUN
ejde-390	551	76	)	)	PUNCT
ejde-390	551	77	for	for	ADP
ejde-390	551	78	λ	λ	NOUN
ejde-390	551	79	=	=	PRON
ejde-390	551	80	λ̂∗	λ̂∗	PROPN
ejde-390	551	81	problem	problem	NOUN
ejde-390	551	82	(	(	PUNCT
ejde-390	551	83	1.1	1.1	NUM
ejde-390	551	84	)	)	PUNCT
ejde-390	551	85	has	have	VERB
ejde-390	551	86	at	at	ADV
ejde-390	551	87	least	least	ADV
ejde-390	551	88	three	three	NUM
ejde-390	551	89	nontrivial	nontrivial	ADJ
ejde-390	551	90	smooth	smooth	ADJ
ejde-390	551	91	solutions	solution	NOUN
ejde-390	551	92	u0	u0	NOUN
ejde-390	551	93	∈	∈	PROPN
ejde-390	551	94	d+	d+	PUNCT
ejde-390	551	95	,	,	PUNCT
ejde-390	551	96	v0	v0	PROPN
ejde-390	551	97	∈	∈	PROPN
ejde-390	551	98	−d+	−d+	NOUN
ejde-390	551	99	,	,	PUNCT
ejde-390	551	100	yλ	yλ	PROPN
ejde-390	551	101	∈	∈	PROPN
ejde-390	551	102	c1(ω	c1(ω	NOUN
ejde-390	551	103	)	)	PUNCT
ejde-390	551	104	nodal	nodal	NOUN
ejde-390	551	105	.	.	PUNCT
ejde-390	552	1	references	reference	NOUN
ejde-390	552	2	[	[	X
ejde-390	552	3	1	1	NUM
ejde-390	552	4	]	]	PUNCT
ejde-390	552	5	d.	d.	PROPN
ejde-390	552	6	averna	averna	PROPN
ejde-390	552	7	,	,	PUNCT
ejde-390	552	8	n.	n.	PROPN
ejde-390	552	9	s.	s.	PROPN
ejde-390	552	10	papageorgiou	papageorgiou	PROPN
ejde-390	552	11	,	,	PUNCT
ejde-390	552	12	e.	e.	PROPN
ejde-390	552	13	tornatore	tornatore	PROPN
ejde-390	552	14	;	;	PUNCT
ejde-390	552	15	positive	positive	ADJ
ejde-390	552	16	solutions	solution	NOUN
ejde-390	552	17	for	for	ADP
ejde-390	552	18	the	the	DET
ejde-390	552	19	neumann	neumann	PROPN
ejde-390	552	20	plaplacian	plaplacian	PROPN
ejde-390	552	21	,	,	PUNCT
ejde-390	552	22	monatsh	monatsh	PROPN
ejde-390	552	23	.	.	PUNCT
ejde-390	552	24	math	math	NOUN
ejde-390	552	25	.	.	PUNCT
ejde-390	553	1	,	,	PUNCT
ejde-390	553	2	185	185	NUM
ejde-390	553	3	(	(	PUNCT
ejde-390	553	4	2018	2018	NUM
ejde-390	553	5	)	)	PUNCT
ejde-390	553	6	,	,	PUNCT
ejde-390	554	1	no	no	INTJ
ejde-390	554	2	.	.	NOUN
ejde-390	554	3	6	6	NUM
ejde-390	554	4	,	,	PUNCT
ejde-390	554	5	557–573	557–573	NUM
ejde-390	554	6	.	.	PUNCT
ejde-390	555	1	[	[	X
ejde-390	555	2	2	2	NUM
ejde-390	555	3	]	]	PUNCT
ejde-390	555	4	l.	l.	PROPN
ejde-390	555	5	cherfils	cherfils	PROPN
ejde-390	555	6	,	,	PUNCT
ejde-390	555	7	y.	y.	PROPN
ejde-390	555	8	il′yasov	il′yasov	PROPN
ejde-390	555	9	;	;	PUNCT
ejde-390	555	10	on	on	ADP
ejde-390	555	11	the	the	DET
ejde-390	555	12	stationary	stationary	ADJ
ejde-390	555	13	solutions	solution	NOUN
ejde-390	555	14	of	of	ADP
ejde-390	555	15	generalized	generalized	ADJ
ejde-390	555	16	reaction	reaction	NOUN
ejde-390	555	17	diffusion	diffusion	NOUN
ejde-390	555	18	equations	equation	NOUN
ejde-390	555	19	with	with	ADP
ejde-390	555	20	p&q	p&q	PROPN
ejde-390	555	21	-	-	PUNCT
ejde-390	555	22	laplacian	laplacian	ADJ
ejde-390	555	23	,	,	PUNCT
ejde-390	555	24	commun	commun	PROPN
ejde-390	555	25	.	.	PUNCT
ejde-390	556	1	pure	pure	ADJ
ejde-390	556	2	appl	appl	PROPN
ejde-390	556	3	.	.	PUNCT
ejde-390	557	1	anal	anal	PROPN
ejde-390	557	2	.	.	PROPN
ejde-390	557	3	,	,	PUNCT
ejde-390	557	4	4	4	NUM
ejde-390	557	5	(	(	PUNCT
ejde-390	557	6	2005	2005	NUM
ejde-390	557	7	)	)	PUNCT
ejde-390	557	8	,	,	PUNCT
ejde-390	557	9	no	no	INTJ
ejde-390	557	10	.	.	NOUN
ejde-390	557	11	1	1	NUM
ejde-390	557	12	,	,	PUNCT
ejde-390	557	13	9–22	9–22	NOUN
ejde-390	557	14	.	.	PUNCT
ejde-390	558	1	[	[	X
ejde-390	558	2	3	3	X
ejde-390	558	3	]	]	PUNCT
ejde-390	558	4	m.	m.	NOUN
ejde-390	558	5	fuchs	fuchs	PROPN
ejde-390	558	6	,	,	PUNCT
ejde-390	558	7	g.	g.	PROPN
ejde-390	558	8	li	li	PROPN
ejde-390	558	9	;	;	PUNCT
ejde-390	558	10	variational	variational	ADJ
ejde-390	558	11	inequalities	inequality	NOUN
ejde-390	558	12	for	for	ADP
ejde-390	558	13	energy	energy	NOUN
ejde-390	558	14	functionals	functional	NOUN
ejde-390	558	15	with	with	ADP
ejde-390	558	16	nonstandard	nonstandard	ADJ
ejde-390	558	17	growth	growth	NOUN
ejde-390	558	18	conditions	condition	NOUN
ejde-390	558	19	,	,	PUNCT
ejde-390	558	20	abstr	abstr	PROPN
ejde-390	558	21	.	.	PUNCT
ejde-390	558	22	appl	appl	PROPN
ejde-390	558	23	.	.	PUNCT
ejde-390	559	1	anal	anal	PROPN
ejde-390	559	2	.	.	PROPN
ejde-390	559	3	,	,	PUNCT
ejde-390	559	4	3	3	NUM
ejde-390	559	5	(	(	PUNCT
ejde-390	559	6	1998	1998	NUM
ejde-390	559	7	)	)	PUNCT
ejde-390	559	8	,	,	PUNCT
ejde-390	559	9	495907	495907	NUM
ejde-390	559	10	,	,	PUNCT
ejde-390	559	11	41–64	41–64	NUM
ejde-390	559	12	.	.	PUNCT
ejde-390	560	1	[	[	X
ejde-390	560	2	4	4	X
ejde-390	560	3	]	]	PUNCT
ejde-390	560	4	l.	l.	PROPN
ejde-390	560	5	gasiński	gasiński	PROPN
ejde-390	560	6	,	,	PUNCT
ejde-390	560	7	n.	n.	PROPN
ejde-390	560	8	s.	s.	PROPN
ejde-390	560	9	papageorgiou	papageorgiou	PROPN
ejde-390	560	10	;	;	PUNCT
ejde-390	560	11	exercises	exercise	NOUN
ejde-390	560	12	in	in	ADP
ejde-390	560	13	analysis	analysis	NOUN
ejde-390	560	14	.	.	PUNCT
ejde-390	561	1	part	part	NOUN
ejde-390	561	2	2	2	NUM
ejde-390	561	3	.	.	PUNCT
ejde-390	561	4	nonlinear	nonlinear	ADJ
ejde-390	561	5	analysis	analysis	NOUN
ejde-390	561	6	,	,	PUNCT
ejde-390	561	7	problem	problem	NOUN
ejde-390	561	8	books	book	NOUN
ejde-390	561	9	in	in	ADP
ejde-390	561	10	mathematics	mathematic	NOUN
ejde-390	561	11	,	,	PUNCT
ejde-390	561	12	springer	springer	NOUN
ejde-390	561	13	,	,	PUNCT
ejde-390	561	14	cham	cham	NOUN
ejde-390	561	15	,	,	PUNCT
ejde-390	561	16	2016	2016	NUM
ejde-390	561	17	.	.	PUNCT
ejde-390	562	1	[	[	X
ejde-390	562	2	5	5	X
ejde-390	562	3	]	]	PUNCT
ejde-390	562	4	s.	s.	PROPN
ejde-390	562	5	hu	hu	PROPN
ejde-390	562	6	,	,	PUNCT
ejde-390	562	7	n.	n.	PROPN
ejde-390	562	8	s.	s.	PROPN
ejde-390	562	9	papageorgiou	papageorgiou	PROPN
ejde-390	562	10	;	;	PUNCT
ejde-390	562	11	handbook	handbook	NOUN
ejde-390	562	12	of	of	ADP
ejde-390	562	13	multivalued	multivalued	ADJ
ejde-390	562	14	analysis	analysis	NOUN
ejde-390	562	15	.	.	PUNCT
ejde-390	563	1	volume	volume	NOUN
ejde-390	563	2	i	i	PRON
ejde-390	563	3	:	:	PUNCT
ejde-390	563	4	theory	theory	NOUN
ejde-390	563	5	,	,	PUNCT
ejde-390	563	6	kluwer	kluwer	NOUN
ejde-390	563	7	academic	academic	ADJ
ejde-390	563	8	publishers	publisher	NOUN
ejde-390	563	9	,	,	PUNCT
ejde-390	563	10	dordrecht	dordrecht	PROPN
ejde-390	563	11	,	,	PUNCT
ejde-390	563	12	the	the	DET
ejde-390	563	13	netherlands	netherlands	PROPN
ejde-390	563	14	,	,	PUNCT
ejde-390	563	15	1997	1997	NUM
ejde-390	563	16	.	.	PUNCT
ejde-390	564	1	[	[	X
ejde-390	564	2	6	6	NUM
ejde-390	564	3	]	]	PUNCT
ejde-390	564	4	g.	g.	PROPN
ejde-390	564	5	li	li	PROPN
ejde-390	564	6	,	,	PUNCT
ejde-390	564	7	c.	c.	PROPN
ejde-390	564	8	yang	yang	PROPN
ejde-390	564	9	;	;	PUNCT
ejde-390	564	10	the	the	DET
ejde-390	564	11	existence	existence	NOUN
ejde-390	564	12	of	of	ADP
ejde-390	564	13	a	a	DET
ejde-390	564	14	nontrivial	nontrivial	ADJ
ejde-390	564	15	solution	solution	NOUN
ejde-390	564	16	to	to	ADP
ejde-390	564	17	a	a	DET
ejde-390	564	18	nonlinear	nonlinear	ADJ
ejde-390	564	19	elliptic	elliptic	ADJ
ejde-390	564	20	boundary	boundary	ADJ
ejde-390	564	21	value	value	NOUN
ejde-390	564	22	problem	problem	NOUN
ejde-390	564	23	of	of	ADP
ejde-390	564	24	p	p	NOUN
ejde-390	564	25	-	-	PUNCT
ejde-390	564	26	laplacian	laplacian	ADJ
ejde-390	564	27	type	type	NOUN
ejde-390	564	28	without	without	ADP
ejde-390	564	29	the	the	DET
ejde-390	564	30	ambrosetti	ambrosetti	NOUN
ejde-390	564	31	-	-	PUNCT
ejde-390	564	32	rabinowitz	rabinowitz	NOUN
ejde-390	564	33	condition	condition	NOUN
ejde-390	564	34	,	,	PUNCT
ejde-390	564	35	nonlinear	nonlinear	ADJ
ejde-390	564	36	anal	anal	NOUN
ejde-390	564	37	.	.	PUNCT
ejde-390	564	38	,	,	PUNCT
ejde-390	564	39	72	72	NUM
ejde-390	564	40	(	(	PUNCT
ejde-390	564	41	2010	2010	NUM
ejde-390	564	42	)	)	PUNCT
ejde-390	564	43	,	,	PUNCT
ejde-390	564	44	no	no	INTJ
ejde-390	564	45	.	.	NOUN
ejde-390	564	46	12	12	NUM
ejde-390	564	47	,	,	PUNCT
ejde-390	564	48	4602–4613	4602–4613	NUM
ejde-390	564	49	.	.	PUNCT
ejde-390	565	1	[	[	X
ejde-390	565	2	7	7	X
ejde-390	565	3	]	]	X
ejde-390	565	4	g.	g.	PROPN
ejde-390	565	5	m.	m.	PROPN
ejde-390	565	6	lieberman	lieberman	PROPN
ejde-390	565	7	;	;	PUNCT
ejde-390	565	8	the	the	DET
ejde-390	565	9	natural	natural	ADJ
ejde-390	565	10	generalization	generalization	NOUN
ejde-390	565	11	of	of	ADP
ejde-390	565	12	the	the	DET
ejde-390	565	13	natural	natural	ADJ
ejde-390	565	14	conditions	condition	NOUN
ejde-390	565	15	of	of	ADP
ejde-390	565	16	ladyzhenskaya	ladyzhenskaya	NOUN
ejde-390	565	17	and	and	CCONJ
ejde-390	565	18	ural’tseva	ural’tseva	ADJ
ejde-390	565	19	for	for	ADP
ejde-390	565	20	elliptic	elliptic	ADJ
ejde-390	565	21	equations	equation	NOUN
ejde-390	565	22	,	,	PUNCT
ejde-390	565	23	comm	comm	NOUN
ejde-390	565	24	.	.	PUNCT
ejde-390	566	1	partial	partial	ADJ
ejde-390	566	2	differential	differential	NOUN
ejde-390	566	3	equations	equation	NOUN
ejde-390	566	4	,	,	PUNCT
ejde-390	566	5	16	16	NUM
ejde-390	566	6	(	(	PUNCT
ejde-390	566	7	1991	1991	NUM
ejde-390	566	8	)	)	PUNCT
ejde-390	566	9	,	,	PUNCT
ejde-390	566	10	no	no	INTJ
ejde-390	566	11	.	.	NOUN
ejde-390	567	1	2	2	NUM
ejde-390	567	2	-	-	SYM
ejde-390	567	3	3	3	NUM
ejde-390	567	4	,	,	PUNCT
ejde-390	567	5	311–361	311–361	NUM
ejde-390	567	6	.	.	PUNCT
ejde-390	568	1	[	[	X
ejde-390	568	2	8	8	NUM
ejde-390	568	3	]	]	X
ejde-390	568	4	d.	d.	NOUN
ejde-390	568	5	motreanu	motreanu	PROPN
ejde-390	568	6	,	,	PUNCT
ejde-390	568	7	v.	v.	ADP
ejde-390	568	8	motreanu	motreanu	NOUN
ejde-390	568	9	,	,	PUNCT
ejde-390	568	10	n.	n.	PROPN
ejde-390	568	11	s.	s.	PROPN
ejde-390	568	12	papageorgiou	papageorgiou	PROPN
ejde-390	568	13	;	;	PUNCT
ejde-390	568	14	multiple	multiple	ADJ
ejde-390	568	15	constant	constant	ADJ
ejde-390	568	16	sign	sign	NOUN
ejde-390	568	17	and	and	CCONJ
ejde-390	568	18	nodal	nodal	ADJ
ejde-390	568	19	solutions	solution	NOUN
ejde-390	568	20	for	for	ADP
ejde-390	568	21	nonlinear	nonlinear	ADJ
ejde-390	568	22	neumann	neumann	PROPN
ejde-390	568	23	eigenvalue	eigenvalue	PROPN
ejde-390	568	24	problems	problem	NOUN
ejde-390	568	25	,	,	PUNCT
ejde-390	568	26	ann	ann	PROPN
ejde-390	568	27	.	.	PROPN
ejde-390	568	28	sc	sc	PROPN
ejde-390	568	29	.	.	PROPN
ejde-390	568	30	norm	norm	PROPN
ejde-390	568	31	.	.	PUNCT
ejde-390	569	1	super	super	ADJ
ejde-390	569	2	.	.	PUNCT
ejde-390	569	3	pisa	pisa	PROPN
ejde-390	569	4	cl	cl	PROPN
ejde-390	569	5	.	.	PUNCT
ejde-390	570	1	sci	sci	PROPN
ejde-390	570	2	.	.	PUNCT
ejde-390	571	1	(	(	PUNCT
ejde-390	571	2	5	5	NUM
ejde-390	571	3	)	)	PUNCT
ejde-390	571	4	,	,	PUNCT
ejde-390	571	5	x	x	X
ejde-390	571	6	(	(	PUNCT
ejde-390	571	7	2011	2011	NUM
ejde-390	571	8	)	)	PUNCT
ejde-390	571	9	,	,	PUNCT
ejde-390	572	1	no	no	INTJ
ejde-390	572	2	.	.	NOUN
ejde-390	572	3	3	3	NUM
ejde-390	572	4	,	,	PUNCT
ejde-390	572	5	729–755	729–755	NUM
ejde-390	572	6	.	.	PUNCT
ejde-390	573	1	[	[	X
ejde-390	573	2	9	9	NUM
ejde-390	573	3	]	]	X
ejde-390	573	4	n.	n.	PROPN
ejde-390	573	5	s.	s.	PROPN
ejde-390	573	6	papageorgiou	papageorgiou	PROPN
ejde-390	573	7	,	,	PUNCT
ejde-390	573	8	v.	v.	PROPN
ejde-390	573	9	d.	d.	PROPN
ejde-390	573	10	rǎdulescu	rǎdulescu	PROPN
ejde-390	573	11	;	;	PUNCT
ejde-390	573	12	coercive	coercive	ADJ
ejde-390	573	13	and	and	CCONJ
ejde-390	573	14	noncoercive	noncoercive	ADJ
ejde-390	573	15	nonlinear	nonlinear	ADJ
ejde-390	573	16	neumann	neumann	PROPN
ejde-390	573	17	problems	problem	NOUN
ejde-390	573	18	with	with	ADP
ejde-390	573	19	indefinite	indefinite	ADJ
ejde-390	573	20	potential	potential	NOUN
ejde-390	573	21	,	,	PUNCT
ejde-390	573	22	forum	forum	NOUN
ejde-390	573	23	math	math	PROPN
ejde-390	573	24	.	.	PUNCT
ejde-390	573	25	,	,	PUNCT
ejde-390	573	26	28	28	NUM
ejde-390	573	27	(	(	PUNCT
ejde-390	573	28	2016	2016	NUM
ejde-390	573	29	)	)	PUNCT
ejde-390	573	30	,	,	PUNCT
ejde-390	573	31	no	no	INTJ
ejde-390	573	32	.	.	NOUN
ejde-390	573	33	3	3	NUM
ejde-390	573	34	,	,	PUNCT
ejde-390	573	35	545–571	545–571	NUM
ejde-390	573	36	.	.	PUNCT
ejde-390	574	1	[	[	X
ejde-390	574	2	10	10	NUM
ejde-390	574	3	]	]	X
ejde-390	574	4	n.	n.	PROPN
ejde-390	574	5	s.	s.	PROPN
ejde-390	574	6	papageorgiou	papageorgiou	PROPN
ejde-390	574	7	,	,	PUNCT
ejde-390	574	8	v.	v.	PROPN
ejde-390	574	9	d.	d.	PROPN
ejde-390	574	10	rǎdulescu	rǎdulescu	PROPN
ejde-390	574	11	;	;	PUNCT
ejde-390	574	12	nonlinear	nonlinear	PROPN
ejde-390	574	13	nonhomogeneous	nonhomogeneous	ADJ
ejde-390	574	14	robin	robin	PROPN
ejde-390	574	15	problems	problem	NOUN
ejde-390	574	16	with	with	ADP
ejde-390	574	17	superlinear	superlinear	ADJ
ejde-390	574	18	reaction	reaction	NOUN
ejde-390	574	19	term	term	NOUN
ejde-390	574	20	,	,	PUNCT
ejde-390	574	21	adv	adv	PROPN
ejde-390	574	22	.	.	PUNCT
ejde-390	574	23	nonlinear	nonlinear	PROPN
ejde-390	574	24	.	.	PUNCT
ejde-390	574	25	stud	stud	PROPN
ejde-390	574	26	.	.	PUNCT
ejde-390	574	27	,	,	PUNCT
ejde-390	574	28	16	16	NUM
ejde-390	574	29	(	(	PUNCT
ejde-390	574	30	2016	2016	NUM
ejde-390	574	31	)	)	PUNCT
ejde-390	574	32	,	,	PUNCT
ejde-390	574	33	no	no	INTJ
ejde-390	574	34	.	.	NOUN
ejde-390	574	35	4	4	NUM
ejde-390	574	36	,	,	PUNCT
ejde-390	574	37	737–764	737–764	NUM
ejde-390	574	38	.	.	PUNCT
ejde-390	575	1	[	[	X
ejde-390	575	2	11	11	NUM
ejde-390	575	3	]	]	X
ejde-390	575	4	n.	n.	PROPN
ejde-390	575	5	s.	s.	PROPN
ejde-390	575	6	papageorgiou	papageorgiou	PROPN
ejde-390	575	7	,	,	PUNCT
ejde-390	575	8	v.	v.	PROPN
ejde-390	575	9	d.	d.	PROPN
ejde-390	575	10	rǎdulescu	rǎdulescu	PROPN
ejde-390	575	11	;	;	PUNCT
ejde-390	575	12	positive	positive	ADJ
ejde-390	575	13	solutions	solution	NOUN
ejde-390	575	14	for	for	ADP
ejde-390	575	15	parametric	parametric	ADJ
ejde-390	575	16	semilinear	semilinear	PROPN
ejde-390	575	17	robin	robin	PROPN
ejde-390	575	18	problems	problem	VERB
ejde-390	575	19	with	with	ADP
ejde-390	575	20	indefinite	indefinite	ADJ
ejde-390	575	21	and	and	CCONJ
ejde-390	575	22	unbounded	unbounded	ADJ
ejde-390	575	23	potential	potential	NOUN
ejde-390	575	24	,	,	PUNCT
ejde-390	575	25	math	math	NOUN
ejde-390	575	26	.	.	PUNCT
ejde-390	576	1	scand	scand	PROPN
ejde-390	576	2	.	.	PROPN
ejde-390	576	3	,	,	PUNCT
ejde-390	576	4	121	121	NUM
ejde-390	576	5	(	(	PUNCT
ejde-390	576	6	2017	2017	NUM
ejde-390	576	7	)	)	PUNCT
ejde-390	576	8	,	,	PUNCT
ejde-390	576	9	no	no	INTJ
ejde-390	576	10	.	.	NOUN
ejde-390	576	11	2	2	NUM
ejde-390	576	12	,	,	PUNCT
ejde-390	576	13	263–292	263–292	NUM
ejde-390	576	14	.	.	PUNCT
ejde-390	577	1	[	[	X
ejde-390	577	2	12	12	NUM
ejde-390	577	3	]	]	X
ejde-390	577	4	n.	n.	PROPN
ejde-390	577	5	s.	s.	PROPN
ejde-390	577	6	papageorgiou	papageorgiou	PROPN
ejde-390	577	7	,	,	PUNCT
ejde-390	577	8	v.	v.	PROPN
ejde-390	577	9	d.	d.	PROPN
ejde-390	577	10	rǎdulescu	rǎdulescu	PROPN
ejde-390	577	11	,	,	PUNCT
ejde-390	577	12	d.	d.	PROPN
ejde-390	577	13	d.	d.	PROPN
ejde-390	577	14	repovš	repovš	VERB
ejde-390	577	15	;	;	PUNCT
ejde-390	577	16	positive	positive	ADJ
ejde-390	577	17	solutions	solution	NOUN
ejde-390	577	18	for	for	ADP
ejde-390	577	19	perturbations	perturbation	NOUN
ejde-390	577	20	of	of	ADP
ejde-390	577	21	the	the	DET
ejde-390	577	22	robin	robin	PROPN
ejde-390	577	23	eigenvalue	eigenvalue	PROPN
ejde-390	577	24	problem	problem	NOUN
ejde-390	577	25	plus	plus	CCONJ
ejde-390	577	26	an	an	DET
ejde-390	577	27	indefinite	indefinite	ADJ
ejde-390	577	28	potential	potential	NOUN
ejde-390	577	29	,	,	PUNCT
ejde-390	577	30	discrete	discrete	ADJ
ejde-390	577	31	contin	contin	NOUN
ejde-390	577	32	.	.	PUNCT
ejde-390	578	1	dyn	dyn	NOUN
ejde-390	578	2	.	.	PUNCT
ejde-390	579	1	syst	syst	PROPN
ejde-390	579	2	.	.	PROPN
ejde-390	579	3	,	,	PUNCT
ejde-390	579	4	37	37	NUM
ejde-390	579	5	(	(	PUNCT
ejde-390	579	6	2017	2017	NUM
ejde-390	579	7	)	)	PUNCT
ejde-390	579	8	,	,	PUNCT
ejde-390	579	9	no	no	INTJ
ejde-390	579	10	.	.	NOUN
ejde-390	579	11	5	5	NUM
ejde-390	579	12	,	,	PUNCT
ejde-390	579	13	2589–2618	2589–2618	NUM
ejde-390	579	14	.	.	PUNCT
ejde-390	580	1	[	[	X
ejde-390	580	2	13	13	NUM
ejde-390	580	3	]	]	X
ejde-390	580	4	n.	n.	PROPN
ejde-390	580	5	s.	s.	PROPN
ejde-390	580	6	papageorgiou	papageorgiou	PROPN
ejde-390	580	7	,	,	PUNCT
ejde-390	580	8	v.	v.	PROPN
ejde-390	580	9	d.	d.	PROPN
ejde-390	580	10	rǎdulescu	rǎdulescu	PROPN
ejde-390	580	11	,	,	PUNCT
ejde-390	580	12	d.	d.	PROPN
ejde-390	580	13	d.	d.	PROPN
ejde-390	580	14	repovš	repovš	VERB
ejde-390	580	15	;	;	PUNCT
ejde-390	580	16	positive	positive	ADJ
ejde-390	580	17	solutions	solution	NOUN
ejde-390	580	18	for	for	ADP
ejde-390	580	19	nonlinear	nonlinear	ADJ
ejde-390	580	20	nonhomogeneous	nonhomogeneous	ADJ
ejde-390	580	21	robin	robin	PROPN
ejde-390	580	22	problems	problem	NOUN
ejde-390	580	23	,	,	PUNCT
ejde-390	580	24	forum	forum	PROPN
ejde-390	580	25	math	math	NOUN
ejde-390	580	26	,	,	PUNCT
ejde-390	580	27	30	30	NUM
ejde-390	580	28	(	(	PUNCT
ejde-390	580	29	2016	2016	NUM
ejde-390	580	30	)	)	PUNCT
ejde-390	580	31	,	,	PUNCT
ejde-390	580	32	no	no	INTJ
ejde-390	580	33	.	.	NOUN
ejde-390	580	34	3	3	NUM
ejde-390	580	35	,	,	PUNCT
ejde-390	580	36	553–580	553–580	NUM
ejde-390	580	37	.	.	PUNCT
ejde-390	581	1	[	[	X
ejde-390	581	2	14	14	NUM
ejde-390	581	3	]	]	X
ejde-390	581	4	n.	n.	PROPN
ejde-390	581	5	s.	s.	PROPN
ejde-390	581	6	papageorgiou	papageorgiou	PROPN
ejde-390	581	7	,	,	PUNCT
ejde-390	581	8	v.	v.	PROPN
ejde-390	581	9	d.	d.	PROPN
ejde-390	581	10	rǎdulescu	rǎdulescu	PROPN
ejde-390	581	11	,	,	PUNCT
ejde-390	581	12	d.	d.	PROPN
ejde-390	581	13	d.	d.	PROPN
ejde-390	581	14	repovš	repovš	VERB
ejde-390	581	15	;	;	PUNCT
ejde-390	581	16	modern	modern	ADJ
ejde-390	581	17	nonlinear	nonlinear	ADJ
ejde-390	581	18	analysis	analysis	NOUN
ejde-390	581	19	theory	theory	NOUN
ejde-390	581	20	,	,	PUNCT
ejde-390	581	21	springer	springer	NOUN
ejde-390	581	22	,	,	PUNCT
ejde-390	581	23	heidelberg	heidelberg	NOUN
ejde-390	581	24	,	,	PUNCT
ejde-390	581	25	2019	2019	NUM
ejde-390	581	26	.	.	PUNCT
ejde-390	582	1	[	[	X
ejde-390	582	2	15	15	NUM
ejde-390	582	3	]	]	X
ejde-390	582	4	p.	p.	NOUN
ejde-390	582	5	pucci	pucci	PROPN
ejde-390	582	6	,	,	PUNCT
ejde-390	582	7	j.	j.	PROPN
ejde-390	582	8	serrin	serrin	PROPN
ejde-390	582	9	;	;	PUNCT
ejde-390	582	10	the	the	DET
ejde-390	582	11	maximum	maximum	ADJ
ejde-390	582	12	principle	principle	NOUN
ejde-390	582	13	,	,	PUNCT
ejde-390	582	14	birkhäuser	birkhäuser	X
ejde-390	582	15	verlag	verlag	PROPN
ejde-390	582	16	,	,	PUNCT
ejde-390	582	17	basel	basel	PROPN
ejde-390	582	18	,	,	PUNCT
ejde-390	582	19	2007	2007	NUM
ejde-390	582	20	.	.	PUNCT
ejde-390	583	1	[	[	X
ejde-390	583	2	16	16	X
ejde-390	583	3	]	]	X
ejde-390	583	4	v.	v.	PROPN
ejde-390	583	5	v.	v.	PROPN
ejde-390	583	6	zhikov	zhikov	PROPN
ejde-390	583	7	;	;	PUNCT
ejde-390	583	8	averaging	average	VERB
ejde-390	583	9	of	of	ADP
ejde-390	583	10	functionals	functional	NOUN
ejde-390	583	11	of	of	ADP
ejde-390	583	12	the	the	DET
ejde-390	583	13	calculus	calculus	NOUN
ejde-390	583	14	of	of	ADP
ejde-390	583	15	variations	variation	NOUN
ejde-390	583	16	and	and	CCONJ
ejde-390	583	17	elasticity	elasticity	NOUN
ejde-390	583	18	theory	theory	NOUN
ejde-390	583	19	,	,	PUNCT
ejde-390	583	20	math	math	NOUN
ejde-390	583	21	.	.	PUNCT
ejde-390	584	1	ussr	ussr	PROPN
ejde-390	584	2	izv	izv	PROPN
ejde-390	584	3	.	.	PROPN
ejde-390	584	4	,	,	PUNCT
ejde-390	584	5	29	29	NUM
ejde-390	584	6	(	(	PUNCT
ejde-390	584	7	1987	1987	NUM
ejde-390	584	8	)	)	PUNCT
ejde-390	584	9	,	,	PUNCT
ejde-390	585	1	no	no	INTJ
ejde-390	585	2	.	.	NOUN
ejde-390	585	3	1	1	NUM
ejde-390	585	4	,	,	PUNCT
ejde-390	585	5	33–66	33–66	NUM
ejde-390	585	6	.	.	PUNCT
ejde-390	586	1	nikolaos	nikolaos	PROPN
ejde-390	586	2	s.	s.	PROPN
ejde-390	586	3	papageorgiou	papageorgiou	PROPN
ejde-390	586	4	national	national	PROPN
ejde-390	586	5	technical	technical	PROPN
ejde-390	586	6	university	university	PROPN
ejde-390	586	7	,	,	PUNCT
ejde-390	586	8	department	department	NOUN
ejde-390	586	9	of	of	ADP
ejde-390	586	10	mathematics	mathematics	PROPN
ejde-390	586	11	,	,	PUNCT
ejde-390	586	12	zografou	zografou	PROPN
ejde-390	586	13	campus	campus	PROPN
ejde-390	586	14	,	,	PUNCT
ejde-390	586	15	15780	15780	NUM
ejde-390	586	16	,	,	PUNCT
ejde-390	586	17	athens	athens	PROPN
ejde-390	586	18	,	,	PUNCT
ejde-390	586	19	greece	greece	PROPN
ejde-390	586	20	email	email	NOUN
ejde-390	586	21	address	address	NOUN
ejde-390	586	22	:	:	PUNCT
ejde-390	586	23	npapg@math.ntua.gr	npapg@math.ntua.gr	ADP
ejde-390	586	24	calogero	calogero	PROPN
ejde-390	586	25	vetro	vetro	PROPN
ejde-390	586	26	university	university	PROPN
ejde-390	586	27	of	of	ADP
ejde-390	586	28	palermo	palermo	PROPN
ejde-390	586	29	,	,	PUNCT
ejde-390	586	30	department	department	NOUN
ejde-390	586	31	of	of	ADP
ejde-390	586	32	mathematics	mathematics	PROPN
ejde-390	586	33	and	and	CCONJ
ejde-390	586	34	computer	computer	NOUN
ejde-390	586	35	science	science	NOUN
ejde-390	586	36	,	,	PUNCT
ejde-390	586	37	via	via	ADP
ejde-390	586	38	archirafi	archirafi	NOUN
ejde-390	586	39	34	34	NUM
ejde-390	586	40	,	,	PUNCT
ejde-390	586	41	90123	90123	NUM
ejde-390	586	42	,	,	PUNCT
ejde-390	586	43	palermo	palermo	PROPN
ejde-390	586	44	,	,	PUNCT
ejde-390	586	45	italy	italy	PROPN
ejde-390	586	46	email	email	NOUN
ejde-390	586	47	address	address	NOUN
ejde-390	586	48	:	:	PUNCT
ejde-390	586	49	calogero.vetro@unipa.it	calogero.vetro@unipa.it	PROPN
ejde-390	586	50	francesca	francesca	PROPN
ejde-390	586	51	vetro	vetro	PROPN
ejde-390	586	52	(	(	PUNCT
ejde-390	586	53	corresponding	corresponding	ADJ
ejde-390	586	54	author	author	NOUN
ejde-390	586	55	)	)	PUNCT
ejde-390	586	56	nonlinear	nonlinear	ADJ
ejde-390	586	57	analysis	analysis	NOUN
ejde-390	586	58	research	research	NOUN
ejde-390	586	59	group	group	NOUN
ejde-390	586	60	,	,	PUNCT
ejde-390	586	61	faculty	faculty	NOUN
ejde-390	586	62	of	of	ADP
ejde-390	586	63	mathematics	mathematic	NOUN
ejde-390	586	64	and	and	CCONJ
ejde-390	586	65	statistics	statistic	NOUN
ejde-390	586	66	,	,	PUNCT
ejde-390	586	67	ton	ton	PROPN
ejde-390	586	68	duc	duc	PROPN
ejde-390	586	69	thang	thang	PROPN
ejde-390	586	70	university	university	PROPN
ejde-390	586	71	,	,	PUNCT
ejde-390	586	72	ho	ho	PROPN
ejde-390	586	73	chi	chi	PROPN
ejde-390	586	74	minh	minh	PROPN
ejde-390	586	75	city	city	PROPN
ejde-390	586	76	,	,	PUNCT
ejde-390	586	77	vietnam	vietnam	PROPN
ejde-390	586	78	email	email	NOUN
ejde-390	586	79	address	address	NOUN
ejde-390	586	80	:	:	PUNCT
ejde-390	586	81	francescavetro@tdtu.edu.vn	francescavetro@tdtu.edu.vn	NOUN
ejde-390	586	82	1	1	NUM
ejde-390	586	83	.	.	PUNCT
ejde-390	587	1	introduction	introduction	NOUN
ejde-390	587	2	2	2	NUM
ejde-390	587	3	.	.	PUNCT
ejde-390	587	4	mathematical	mathematical	ADJ
ejde-390	587	5	background	background	NOUN
ejde-390	587	6	hypotheses	hypothese	VERB
ejde-390	587	7	3	3	NUM
ejde-390	587	8	.	.	X
ejde-390	587	9	positive	positive	ADJ
ejde-390	587	10	solutions	solution	NOUN
ejde-390	587	11	4	4	NUM
ejde-390	587	12	.	.	PUNCT
ejde-390	587	13	nodal	nodal	NOUN
ejde-390	587	14	solutions	solution	NOUN
ejde-390	587	15	references	reference	NOUN