id	sid	tid	token	lemma	pos
ejde-681	1	1	electronic	electronic	ADJ
ejde-681	1	2	journal	journal	NOUN
ejde-681	1	3	of	of	ADP
ejde-681	1	4	differential	differential	ADJ
ejde-681	1	5	equations	equation	NOUN
ejde-681	1	6	,	,	PUNCT
ejde-681	1	7	vol	vol	NOUN
ejde-681	1	8	.	.	NOUN
ejde-681	1	9	2024	2024	NUM
ejde-681	1	10	(	(	PUNCT
ejde-681	1	11	2024	2024	NUM
ejde-681	1	12	)	)	PUNCT
ejde-681	1	13	,	,	PUNCT
ejde-681	1	14	no	no	INTJ
ejde-681	1	15	.	.	NOUN
ejde-681	1	16	32	32	NUM
ejde-681	1	17	,	,	PUNCT
ejde-681	1	18	pp	pp	ADJ
ejde-681	1	19	.	.	PUNCT
ejde-681	2	1	1–9	1–9	NOUN
ejde-681	2	2	.	.	PUNCT
ejde-681	2	3	issn	issn	PROPN
ejde-681	2	4	:	:	PUNCT
ejde-681	2	5	1072	1072	NUM
ejde-681	2	6	-	-	SYM
ejde-681	2	7	6691	6691	NUM
ejde-681	2	8	.	.	PUNCT
ejde-681	3	1	url	url	PROPN
ejde-681	3	2	:	:	PUNCT
ejde-681	3	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-681	3	4	,	,	PUNCT
ejde-681	3	5	https://ejde.math.unt.edu	https://ejde.math.unt.edu	PROPN
ejde-681	3	6	doi	doi	PROPN
ejde-681	3	7	:	:	PUNCT
ejde-681	3	8	10.58997	10.58997	NUM
ejde-681	3	9	/	/	SYM
ejde-681	3	10	ejde.2024.32	ejde.2024.32	NOUN
ejde-681	3	11	existence	existence	NOUN
ejde-681	3	12	of	of	ADP
ejde-681	3	13	semi	semi	ADJ
ejde-681	3	14	-	-	ADJ
ejde-681	3	15	nodal	nodal	ADJ
ejde-681	3	16	solutions	solution	NOUN
ejde-681	3	17	for	for	ADP
ejde-681	3	18	elliptic	elliptic	ADJ
ejde-681	3	19	systems	system	NOUN
ejde-681	3	20	related	relate	VERB
ejde-681	3	21	to	to	ADP
ejde-681	3	22	gross	gross	ADJ
ejde-681	3	23	-	-	PUNCT
ejde-681	3	24	pitaevskii	pitaevskii	ADJ
ejde-681	3	25	equations	equation	NOUN
ejde-681	3	26	joão	joão	PROPN
ejde-681	3	27	pablo	pablo	PROPN
ejde-681	3	28	pinheiro	pinheiro	PROPN
ejde-681	3	29	da	da	PROPN
ejde-681	3	30	silva	silva	PROPN
ejde-681	3	31	,	,	PUNCT
ejde-681	3	32	edcarlos	edcarlo	VERB
ejde-681	3	33	domingos	domingos	PROPN
ejde-681	3	34	da	da	PROPN
ejde-681	3	35	silva	silva	PROPN
ejde-681	3	36	communicated	communicate	VERB
ejde-681	3	37	by	by	ADP
ejde-681	3	38	claudianor	claudianor	PROPN
ejde-681	3	39	o.	o.	PROPN
ejde-681	3	40	alves	alves	PROPN
ejde-681	3	41	abstract	abstract	PROPN
ejde-681	3	42	.	.	PUNCT
ejde-681	4	1	in	in	ADP
ejde-681	4	2	this	this	DET
ejde-681	4	3	work	work	NOUN
ejde-681	4	4	we	we	PRON
ejde-681	4	5	consider	consider	VERB
ejde-681	4	6	existence	existence	NOUN
ejde-681	4	7	of	of	ADP
ejde-681	4	8	semi	semi	ADJ
ejde-681	4	9	-	-	ADJ
ejde-681	4	10	nodal	nodal	ADJ
ejde-681	4	11	solutions	solution	NOUN
ejde-681	4	12	,	,	PUNCT
ejde-681	4	13	i.e.	i.e.	X
ejde-681	4	14	,	,	PUNCT
ejde-681	4	15	solutions	solution	NOUN
ejde-681	4	16	of	of	ADP
ejde-681	4	17	the	the	DET
ejde-681	4	18	form	form	NOUN
ejde-681	4	19	(	(	PUNCT
ejde-681	4	20	u	u	NOUN
ejde-681	4	21	,	,	PUNCT
ejde-681	4	22	v	v	NOUN
ejde-681	4	23	)	)	PUNCT
ejde-681	4	24	with	with	ADP
ejde-681	4	25	u	u	PROPN
ejde-681	4	26	>	>	X
ejde-681	4	27	0	0	PUNCT
ejde-681	4	28	and	and	CCONJ
ejde-681	4	29	v±	v±	NUM
ejde-681	4	30	:	:	PUNCT
ejde-681	4	31	=	=	SYM
ejde-681	4	32	max{0,±v	max{0,±v	PROPN
ejde-681	4	33	}	}	PUNCT
ejde-681	4	34	̸≡	̸≡	NOUN
ejde-681	4	35	0	0	NUM
ejde-681	4	36	for	for	ADP
ejde-681	4	37	a	a	DET
ejde-681	4	38	class	class	NOUN
ejde-681	4	39	of	of	ADP
ejde-681	4	40	elliptic	elliptic	ADJ
ejde-681	4	41	systems	system	NOUN
ejde-681	4	42	related	relate	VERB
ejde-681	4	43	to	to	ADP
ejde-681	4	44	the	the	DET
ejde-681	4	45	gross	gross	ADJ
ejde-681	4	46	-	-	PUNCT
ejde-681	4	47	pitaevskii	pitaevskii	ADJ
ejde-681	4	48	equation	equation	NOUN
ejde-681	4	49	.	.	PUNCT
ejde-681	5	1	1	1	X
ejde-681	5	2	.	.	X
ejde-681	5	3	introduction	introduction	NOUN
ejde-681	5	4	this	this	DET
ejde-681	5	5	work	work	NOUN
ejde-681	5	6	concerns	concern	VERB
ejde-681	5	7	the	the	DET
ejde-681	5	8	elliptic	elliptic	ADJ
ejde-681	5	9	system	system	NOUN
ejde-681	5	10	−∆u	−∆u	X
ejde-681	6	1	=	=	PUNCT
ejde-681	6	2	λ1u+	λ1u+	INTJ
ejde-681	6	3	µ1|u|2p−2u+	µ1|u|2p−2u+	PROPN
ejde-681	7	1	β|u|p−2u|v|q	β|u|p−2u|v|q	PROPN
ejde-681	7	2	,	,	PUNCT
ejde-681	7	3	in	in	ADP
ejde-681	7	4	ω	ω	NUM
ejde-681	7	5	−∆v	−∆v	PUNCT
ejde-681	7	6	=	=	PUNCT
ejde-681	8	1	λ2v	λ2v	PUNCT
ejde-681	8	2	+	+	NUM
ejde-681	8	3	µ2|v|2q−2v	µ2|v|2q−2v	ADV
ejde-681	8	4	+	+	X
ejde-681	8	5	β|u|p|v|q−2v	β|u|p|v|q−2v	PROPN
ejde-681	8	6	,	,	PUNCT
ejde-681	8	7	in	in	ADP
ejde-681	8	8	ω	ω	NUM
ejde-681	8	9	u	u	NOUN
ejde-681	8	10	=	=	X
ejde-681	8	11	v	v	NOUN
ejde-681	8	12	=	=	SYM
ejde-681	8	13	0	0	NUM
ejde-681	8	14	,	,	PUNCT
ejde-681	8	15	on	on	ADP
ejde-681	8	16	∂ω	∂ω	PROPN
ejde-681	8	17	.	.	PUNCT
ejde-681	9	1	(	(	PUNCT
ejde-681	9	2	1.1	1.1	NUM
ejde-681	9	3	)	)	PUNCT
ejde-681	9	4	for	for	ADP
ejde-681	9	5	p	p	NOUN
ejde-681	9	6	=	=	NOUN
ejde-681	9	7	q	q	NOUN
ejde-681	9	8	=	=	SYM
ejde-681	9	9	2	2	NUM
ejde-681	9	10	the	the	DET
ejde-681	9	11	cubic	cubic	ADJ
ejde-681	9	12	system	system	NOUN
ejde-681	9	13	(	(	PUNCT
ejde-681	9	14	1.1	1.1	NUM
ejde-681	9	15	)	)	PUNCT
ejde-681	9	16	arises	arise	VERB
ejde-681	9	17	in	in	ADP
ejde-681	9	18	mathematical	mathematical	ADJ
ejde-681	9	19	models	model	NOUN
ejde-681	9	20	for	for	ADP
ejde-681	9	21	various	various	ADJ
ejde-681	9	22	physics	physics	NOUN
ejde-681	9	23	problems	problem	NOUN
ejde-681	9	24	,	,	PUNCT
ejde-681	9	25	especially	especially	ADV
ejde-681	9	26	in	in	ADP
ejde-681	9	27	nonlinear	nonlinear	ADJ
ejde-681	9	28	optics	optic	NOUN
ejde-681	9	29	and	and	CCONJ
ejde-681	9	30	bose	bose	NOUN
ejde-681	9	31	-	-	PUNCT
ejde-681	9	32	einstein	einstein	NOUN
ejde-681	9	33	condensation	condensation	NOUN
ejde-681	9	34	,	,	PUNCT
ejde-681	9	35	see	see	VERB
ejde-681	9	36	[	[	X
ejde-681	9	37	14	14	NUM
ejde-681	9	38	,	,	PUNCT
ejde-681	9	39	17	17	NUM
ejde-681	9	40	]	]	PUNCT
ejde-681	9	41	.	.	PUNCT
ejde-681	10	1	in	in	ADP
ejde-681	10	2	those	those	DET
ejde-681	10	3	works	work	NOUN
ejde-681	10	4	present	present	ADJ
ejde-681	10	5	information	information	NOUN
ejde-681	10	6	on	on	ADP
ejde-681	10	7	the	the	DET
ejde-681	10	8	physical	physical	ADJ
ejde-681	10	9	significance	significance	NOUN
ejde-681	10	10	of	of	ADP
ejde-681	10	11	noncubic	noncubic	ADJ
ejde-681	10	12	nonlinearities	nonlinearitie	NOUN
ejde-681	10	13	and	and	CCONJ
ejde-681	10	14	on	on	ADP
ejde-681	10	15	the	the	DET
ejde-681	10	16	existence	existence	NOUN
ejde-681	10	17	and	and	CCONJ
ejde-681	10	18	multiplicity	multiplicity	NOUN
ejde-681	10	19	of	of	ADP
ejde-681	10	20	solutions	solution	NOUN
ejde-681	10	21	.	.	PUNCT
ejde-681	11	1	furthermore	furthermore	ADV
ejde-681	11	2	,	,	PUNCT
ejde-681	11	3	when	when	SCONJ
ejde-681	11	4	λi	λi	ADP
ejde-681	11	5	<	<	X
ejde-681	11	6	0	0	PROPN
ejde-681	11	7	,	,	PUNCT
ejde-681	11	8	system	system	NOUN
ejde-681	11	9	(	(	PUNCT
ejde-681	11	10	1.1	1.1	NUM
ejde-681	11	11	)	)	PUNCT
ejde-681	11	12	comes	come	VERB
ejde-681	11	13	from	from	ADP
ejde-681	11	14	the	the	DET
ejde-681	11	15	study	study	NOUN
ejde-681	11	16	of	of	ADP
ejde-681	11	17	solitary	solitary	ADJ
ejde-681	11	18	wave	wave	NOUN
ejde-681	11	19	solutions	solution	NOUN
ejde-681	11	20	of	of	ADP
ejde-681	11	21	the	the	DET
ejde-681	11	22	coupled	couple	VERB
ejde-681	11	23	gross	gross	ADJ
ejde-681	11	24	-	-	PUNCT
ejde-681	11	25	pitaevskii	pitaevskii	ADJ
ejde-681	11	26	equations	equation	NOUN
ejde-681	11	27	,	,	PUNCT
ejde-681	11	28	−i	−i	PROPN
ejde-681	11	29	∂	∂	NOUN
ejde-681	12	1	∂t	∂t	PROPN
ejde-681	12	2	φ1	φ1	PROPN
ejde-681	12	3	=	=	SYM
ejde-681	12	4	∆φ1	∆φ1	PROPN
ejde-681	13	1	+	+	CCONJ
ejde-681	14	1	µ1|φ1|2φ2	µ1|φ1|2φ2	PROPN
ejde-681	14	2	+	+	NUM
ejde-681	14	3	βφ2	βφ2	DET
ejde-681	14	4	2φ1	2φ1	NUM
ejde-681	14	5	,	,	PUNCT
ejde-681	14	6	x	x	PROPN
ejde-681	14	7	∈	∈	PROPN
ejde-681	14	8	ω	ω	PROPN
ejde-681	14	9	,	,	PUNCT
ejde-681	14	10	t	t	PROPN
ejde-681	14	11	>	>	X
ejde-681	14	12	0	0	PUNCT
ejde-681	15	1	−i	−i	ADJ
ejde-681	15	2	∂	∂	NOUN
ejde-681	16	1	∂t	∂t	PROPN
ejde-681	16	2	φ2	φ2	PROPN
ejde-681	16	3	=	=	PROPN
ejde-681	16	4	∆φ2	∆φ2	PROPN
ejde-681	16	5	+	+	CCONJ
ejde-681	16	6	µ2|φ2|2φ1	µ2|φ2|2φ1	NOUN
ejde-681	16	7	+	+	CCONJ
ejde-681	16	8	βφ2	βφ2	DET
ejde-681	16	9	1φ2	1φ2	NUM
ejde-681	16	10	,	,	PUNCT
ejde-681	16	11	x	x	X
ejde-681	16	12	∈	∈	PROPN
ejde-681	16	13	ω	ω	PROPN
ejde-681	16	14	,	,	PUNCT
ejde-681	16	15	t	t	PROPN
ejde-681	16	16	>	>	X
ejde-681	16	17	0	0	PUNCT
ejde-681	17	1	φj	φj	ADP
ejde-681	17	2	=	=	PUNCT
ejde-681	17	3	φj(x	φj(x	PROPN
ejde-681	17	4	,	,	PUNCT
ejde-681	17	5	t	t	PROPN
ejde-681	17	6	)	)	PUNCT
ejde-681	17	7	∈	∈	PROPN
ejde-681	18	1	c	c	X
ejde-681	18	2	,	,	PUNCT
ejde-681	18	3	j	j	PROPN
ejde-681	18	4	=	=	SYM
ejde-681	18	5	1	1	NUM
ejde-681	18	6	,	,	PUNCT
ejde-681	18	7	2	2	NUM
ejde-681	18	8	φj(x	φj(x	X
ejde-681	18	9	,	,	PUNCT
ejde-681	18	10	t	t	PROPN
ejde-681	18	11	)	)	PUNCT
ejde-681	18	12	=	=	SYM
ejde-681	18	13	0	0	NUM
ejde-681	18	14	,	,	PUNCT
ejde-681	18	15	x	x	X
ejde-681	18	16	∈	∈	PROPN
ejde-681	18	17	∂ω	∂ω	PROPN
ejde-681	18	18	,	,	PUNCT
ejde-681	18	19	t	t	PROPN
ejde-681	18	20	>	>	X
ejde-681	18	21	0	0	PROPN
ejde-681	18	22	,	,	PUNCT
ejde-681	18	23	j	j	PROPN
ejde-681	18	24	=	=	SYM
ejde-681	18	25	1	1	NUM
ejde-681	18	26	,	,	PUNCT
ejde-681	18	27	2	2	NUM
ejde-681	18	28	.	.	PUNCT
ejde-681	18	29	(	(	PUNCT
ejde-681	18	30	1.2	1.2	NUM
ejde-681	18	31	)	)	PUNCT
ejde-681	18	32	when	when	SCONJ
ejde-681	18	33	φ1(x	φ1(x	NOUN
ejde-681	18	34	,	,	PUNCT
ejde-681	18	35	t	t	PROPN
ejde-681	18	36	)	)	PUNCT
ejde-681	18	37	=	=	SYM
ejde-681	18	38	e−iλ1tu	e−iλ1tu	NOUN
ejde-681	18	39	and	and	CCONJ
ejde-681	18	40	φ2(x	φ2(x	PROPN
ejde-681	18	41	,	,	PUNCT
ejde-681	18	42	t	t	PROPN
ejde-681	18	43	)	)	PUNCT
ejde-681	18	44	=	=	SYM
ejde-681	18	45	e−iλ2tv	e−iλ2tv	NOUN
ejde-681	18	46	,	,	PUNCT
ejde-681	18	47	system	system	NOUN
ejde-681	18	48	(	(	PUNCT
ejde-681	18	49	1.2	1.2	NUM
ejde-681	18	50	)	)	PUNCT
ejde-681	18	51	reduces	reduce	VERB
ejde-681	18	52	to	to	ADP
ejde-681	18	53	(	(	PUNCT
ejde-681	18	54	1.1	1.1	NUM
ejde-681	18	55	)	)	PUNCT
ejde-681	18	56	.	.	PUNCT
ejde-681	19	1	in	in	ADP
ejde-681	19	2	the	the	DET
ejde-681	19	3	kerr	kerr	NOUN
ejde-681	19	4	-	-	PUNCT
ejde-681	19	5	like	like	ADJ
ejde-681	19	6	photorefractive	photorefractive	ADJ
ejde-681	19	7	media	medium	NOUN
ejde-681	19	8	,	,	PUNCT
ejde-681	19	9	the	the	DET
ejde-681	19	10	solution	solution	NOUN
ejde-681	19	11	φj	φj	ADP
ejde-681	19	12	represents	represent	VERB
ejde-681	19	13	the	the	DET
ejde-681	19	14	jth	jth	PROPN
ejde-681	19	15	element	element	NOUN
ejde-681	19	16	of	of	ADP
ejde-681	19	17	the	the	DET
ejde-681	19	18	beam	beam	NOUN
ejde-681	19	19	(	(	PUNCT
ejde-681	19	20	see	see	VERB
ejde-681	19	21	[	[	X
ejde-681	19	22	2	2	NUM
ejde-681	19	23	]	]	NUM
ejde-681	19	24	)	)	PUNCT
ejde-681	19	25	.	.	PUNCT
ejde-681	20	1	the	the	DET
ejde-681	20	2	self	self	NOUN
ejde-681	20	3	-	-	PUNCT
ejde-681	20	4	focusing	focus	VERB
ejde-681	20	5	in	in	ADP
ejde-681	20	6	the	the	DET
ejde-681	20	7	jth	jth	PROPN
ejde-681	20	8	component	component	NOUN
ejde-681	20	9	of	of	ADP
ejde-681	20	10	the	the	DET
ejde-681	20	11	beam	beam	NOUN
ejde-681	20	12	is	be	AUX
ejde-681	20	13	related	relate	VERB
ejde-681	20	14	to	to	ADP
ejde-681	20	15	the	the	DET
ejde-681	20	16	positive	positive	ADJ
ejde-681	20	17	constant	constant	ADJ
ejde-681	20	18	µj	µj	INTJ
ejde-681	20	19	,	,	PUNCT
ejde-681	20	20	whereas	whereas	SCONJ
ejde-681	20	21	the	the	DET
ejde-681	20	22	coupling	couple	VERB
ejde-681	20	23	constant	constant	ADJ
ejde-681	20	24	β	β	X
ejde-681	20	25	>	>	X
ejde-681	20	26	0	0	PUNCT
ejde-681	20	27	signifies	signify	VERB
ejde-681	20	28	the	the	DET
ejde-681	20	29	interaction	interaction	NOUN
ejde-681	20	30	between	between	ADP
ejde-681	20	31	the	the	DET
ejde-681	20	32	two	two	NUM
ejde-681	20	33	beam	beam	NOUN
ejde-681	20	34	components	component	NOUN
ejde-681	20	35	.	.	PUNCT
ejde-681	21	1	when	when	SCONJ
ejde-681	21	2	µj	µj	PROPN
ejde-681	21	3	=	=	SYM
ejde-681	21	4	0	0	PROPN
ejde-681	21	5	,	,	PUNCT
ejde-681	21	6	the	the	DET
ejde-681	21	7	self	self	NOUN
ejde-681	21	8	-	-	PUNCT
ejde-681	21	9	focusing	focus	VERB
ejde-681	21	10	2020	2020	NUM
ejde-681	21	11	mathematics	mathematic	NOUN
ejde-681	21	12	subject	subject	ADJ
ejde-681	21	13	classification	classification	NOUN
ejde-681	21	14	.	.	PUNCT
ejde-681	22	1	35j47	35j47	NUM
ejde-681	22	2	,	,	PUNCT
ejde-681	22	3	35j50	35j50	NUM
ejde-681	22	4	.	.	PUNCT
ejde-681	23	1	key	key	ADJ
ejde-681	23	2	words	word	NOUN
ejde-681	23	3	and	and	CCONJ
ejde-681	23	4	phrases	phrase	NOUN
ejde-681	23	5	.	.	PUNCT
ejde-681	24	1	elliptic	elliptic	ADJ
ejde-681	24	2	systems	system	NOUN
ejde-681	24	3	;	;	PUNCT
ejde-681	24	4	variational	variational	ADJ
ejde-681	24	5	methods	method	NOUN
ejde-681	24	6	;	;	PUNCT
ejde-681	24	7	semi	semi	ADJ
ejde-681	24	8	-	-	ADJ
ejde-681	24	9	nodal	nodal	ADJ
ejde-681	24	10	solutions	solution	NOUN
ejde-681	24	11	;	;	PUNCT
ejde-681	24	12	gross	gross	ADJ
ejde-681	24	13	-	-	PUNCT
ejde-681	24	14	pitaevskii	pitaevskii	ADJ
ejde-681	24	15	equation	equation	NOUN
ejde-681	24	16	.	.	PUNCT
ejde-681	25	1	©	©	PROPN
ejde-681	25	2	2024	2024	NUM
ejde-681	25	3	.	.	PUNCT
ejde-681	26	1	this	this	DET
ejde-681	26	2	work	work	NOUN
ejde-681	26	3	is	be	AUX
ejde-681	26	4	licensed	license	VERB
ejde-681	26	5	under	under	ADP
ejde-681	26	6	a	a	DET
ejde-681	26	7	cc	cc	NOUN
ejde-681	26	8	by	by	ADP
ejde-681	26	9	4.0	4.0	NUM
ejde-681	26	10	license	license	NOUN
ejde-681	26	11	.	.	PUNCT
ejde-681	27	1	submitted	submit	VERB
ejde-681	27	2	june	june	PROPN
ejde-681	27	3	10	10	NUM
ejde-681	27	4	,	,	PUNCT
ejde-681	27	5	2023	2023	NUM
ejde-681	27	6	.	.	PUNCT
ejde-681	28	1	published	publish	VERB
ejde-681	28	2	april	april	PROPN
ejde-681	28	3	25	25	NUM
ejde-681	28	4	,	,	PUNCT
ejde-681	28	5	2024	2024	NUM
ejde-681	28	6	.	.	PUNCT
ejde-681	28	7	1	1	NUM
ejde-681	28	8	2	2	NUM
ejde-681	29	1	j.	j.	PROPN
ejde-681	29	2	p.	p.	PROPN
ejde-681	29	3	p.	p.	PROPN
ejde-681	30	1	d.	d.	PROPN
ejde-681	30	2	silva	silva	PROPN
ejde-681	30	3	,	,	PUNCT
ejde-681	30	4	e.	e.	PROPN
ejde-681	30	5	d.	d.	PROPN
ejde-681	30	6	silva	silva	PROPN
ejde-681	30	7	ejde-2024/32	ejde-2024/32	PROPN
ejde-681	30	8	has	have	AUX
ejde-681	30	9	been	be	AUX
ejde-681	30	10	suppressed	suppress	VERB
ejde-681	30	11	,	,	PUNCT
ejde-681	30	12	and	and	CCONJ
ejde-681	30	13	this	this	DET
ejde-681	30	14	type	type	NOUN
ejde-681	30	15	of	of	ADP
ejde-681	30	16	situation	situation	NOUN
ejde-681	30	17	is	be	AUX
ejde-681	30	18	also	also	ADV
ejde-681	30	19	relevant	relevant	ADJ
ejde-681	30	20	in	in	ADP
ejde-681	30	21	optics	optic	NOUN
ejde-681	30	22	(	(	PUNCT
ejde-681	30	23	see	see	VERB
ejde-681	30	24	for	for	ADP
ejde-681	30	25	example	example	NOUN
ejde-681	31	1	[	[	X
ejde-681	31	2	15	15	NUM
ejde-681	31	3	,	,	PUNCT
ejde-681	31	4	16	16	NUM
ejde-681	31	5	,	,	PUNCT
ejde-681	31	6	20	20	NUM
ejde-681	31	7	]	]	PUNCT
ejde-681	31	8	)	)	PUNCT
ejde-681	31	9	.	.	PUNCT
ejde-681	32	1	the	the	DET
ejde-681	32	2	problem	problem	NOUN
ejde-681	32	3	denoted	denote	VERB
ejde-681	32	4	by	by	ADP
ejde-681	32	5	system	system	NOUN
ejde-681	32	6	(	(	PUNCT
ejde-681	32	7	1.2	1.2	NUM
ejde-681	32	8	)	)	PUNCT
ejde-681	32	9	is	be	AUX
ejde-681	32	10	also	also	ADV
ejde-681	32	11	encountered	encounter	VERB
ejde-681	32	12	in	in	ADP
ejde-681	32	13	the	the	DET
ejde-681	32	14	hartree	hartree	ADV
ejde-681	32	15	-	-	PUNCT
ejde-681	32	16	fock	fock	ADJ
ejde-681	32	17	theory	theory	NOUN
ejde-681	32	18	for	for	ADP
ejde-681	32	19	a	a	DET
ejde-681	32	20	binary	binary	ADJ
ejde-681	32	21	mixture	mixture	NOUN
ejde-681	32	22	of	of	ADP
ejde-681	32	23	bose	bose	NOUN
ejde-681	32	24	-	-	PUNCT
ejde-681	32	25	einstein	einstein	NOUN
ejde-681	32	26	condensates	condensate	NOUN
ejde-681	32	27	in	in	ADP
ejde-681	32	28	two	two	NUM
ejde-681	32	29	different	different	ADJ
ejde-681	32	30	hyperfine	hyperfine	ADJ
ejde-681	32	31	states	state	NOUN
ejde-681	32	32	|1⟩	|1⟩	ADJ
ejde-681	32	33	and	and	CCONJ
ejde-681	32	34	|2⟩	|2⟩	NOUN
ejde-681	32	35	(	(	PUNCT
ejde-681	32	36	see	see	VERB
ejde-681	32	37	for	for	ADP
ejde-681	32	38	example	example	NOUN
ejde-681	32	39	[	[	X
ejde-681	32	40	13	13	NUM
ejde-681	32	41	]	]	NUM
ejde-681	32	42	)	)	PUNCT
ejde-681	32	43	.	.	PUNCT
ejde-681	33	1	in	in	ADP
ejde-681	33	2	this	this	DET
ejde-681	33	3	context	context	NOUN
ejde-681	33	4	,	,	PUNCT
ejde-681	33	5	each	each	DET
ejde-681	33	6	φj	φj	NOUN
ejde-681	33	7	represents	represent	VERB
ejde-681	33	8	the	the	DET
ejde-681	33	9	corresponding	corresponding	ADJ
ejde-681	33	10	condensate	condensate	NOUN
ejde-681	33	11	amplitude	amplitude	NOUN
ejde-681	33	12	,	,	PUNCT
ejde-681	33	13	while	while	SCONJ
ejde-681	33	14	µj	µj	PROPN
ejde-681	33	15	and	and	CCONJ
ejde-681	33	16	β	β	PROPN
ejde-681	33	17	denote	denote	VERB
ejde-681	33	18	the	the	DET
ejde-681	33	19	intra	intra	ADJ
ejde-681	33	20	and	and	CCONJ
ejde-681	33	21	interspecies	interspecie	VERB
ejde-681	33	22	scattering	scatter	VERB
ejde-681	33	23	lengths	length	NOUN
ejde-681	33	24	.	.	PUNCT
ejde-681	34	1	the	the	DET
ejde-681	34	2	self	self	NOUN
ejde-681	34	3	-	-	PUNCT
ejde-681	34	4	interactions	interaction	NOUN
ejde-681	34	5	of	of	ADP
ejde-681	34	6	the	the	DET
ejde-681	34	7	single	single	ADJ
ejde-681	34	8	state	state	NOUN
ejde-681	34	9	|j⟩	|j⟩	PROPN
ejde-681	34	10	are	be	AUX
ejde-681	34	11	represented	represent	VERB
ejde-681	34	12	by	by	ADP
ejde-681	34	13	the	the	DET
ejde-681	34	14	sign	sign	NOUN
ejde-681	34	15	of	of	ADP
ejde-681	34	16	µj	µj	PROPN
ejde-681	34	17	,	,	PUNCT
ejde-681	34	18	with	with	ADP
ejde-681	34	19	µj	µj	PROPN
ejde-681	34	20	>	>	X
ejde-681	34	21	0	0	NUM
ejde-681	34	22	indicating	indicate	VERB
ejde-681	34	23	the	the	DET
ejde-681	34	24	focusing	focus	VERB
ejde-681	34	25	case	case	NOUN
ejde-681	34	26	and	and	CCONJ
ejde-681	34	27	µj	µj	X
ejde-681	34	28	<	<	X
ejde-681	34	29	0	0	NUM
ejde-681	34	30	corresponding	correspond	VERB
ejde-681	34	31	to	to	ADP
ejde-681	34	32	the	the	DET
ejde-681	34	33	defocusing	defocuse	VERB
ejde-681	34	34	case	case	NOUN
ejde-681	34	35	.	.	PUNCT
ejde-681	35	1	when	when	SCONJ
ejde-681	35	2	the	the	DET
ejde-681	35	3	intraspecies	intraspecie	NOUN
ejde-681	35	4	scattering	scatter	VERB
ejde-681	35	5	length	length	NOUN
ejde-681	35	6	µj	µj	PROPN
ejde-681	35	7	is	be	AUX
ejde-681	35	8	zero	zero	NUM
ejde-681	35	9	,	,	PUNCT
ejde-681	35	10	it	it	PRON
ejde-681	35	11	means	mean	VERB
ejde-681	35	12	that	that	SCONJ
ejde-681	35	13	the	the	DET
ejde-681	35	14	interaction	interaction	NOUN
ejde-681	35	15	between	between	ADP
ejde-681	35	16	particles	particle	NOUN
ejde-681	35	17	of	of	ADP
ejde-681	35	18	the	the	DET
ejde-681	35	19	same	same	ADJ
ejde-681	35	20	species	specie	NOUN
ejde-681	35	21	is	be	AUX
ejde-681	35	22	extremely	extremely	ADV
ejde-681	35	23	weak	weak	ADJ
ejde-681	35	24	or	or	CCONJ
ejde-681	35	25	nonexistent	nonexistent	ADJ
ejde-681	35	26	(	(	PUNCT
ejde-681	35	27	see	see	VERB
ejde-681	35	28	for	for	ADP
ejde-681	35	29	example	example	NOUN
ejde-681	35	30	[	[	X
ejde-681	35	31	22	22	NUM
ejde-681	35	32	]	]	PUNCT
ejde-681	35	33	)	)	PUNCT
ejde-681	35	34	.	.	PUNCT
ejde-681	36	1	in	in	ADP
ejde-681	36	2	addition	addition	NOUN
ejde-681	36	3	,	,	PUNCT
ejde-681	36	4	the	the	DET
ejde-681	36	5	sign	sign	NOUN
ejde-681	36	6	of	of	ADP
ejde-681	36	7	β	β	PROPN
ejde-681	36	8	plays	play	VERB
ejde-681	36	9	a	a	DET
ejde-681	36	10	crucial	crucial	ADJ
ejde-681	36	11	role	role	NOUN
ejde-681	36	12	in	in	ADP
ejde-681	36	13	determining	determine	VERB
ejde-681	36	14	whether	whether	SCONJ
ejde-681	36	15	the	the	DET
ejde-681	36	16	interactions	interaction	NOUN
ejde-681	36	17	between	between	ADP
ejde-681	36	18	states	state	NOUN
ejde-681	36	19	|1⟩	|1⟩	ADJ
ejde-681	36	20	and	and	CCONJ
ejde-681	36	21	|2⟩	|2⟩	NOUN
ejde-681	36	22	are	be	AUX
ejde-681	36	23	attractive	attractive	ADJ
ejde-681	36	24	or	or	CCONJ
ejde-681	36	25	repulsive	repulsive	ADJ
ejde-681	36	26	.	.	PUNCT
ejde-681	37	1	specifically	specifically	ADV
ejde-681	37	2	,	,	PUNCT
ejde-681	37	3	if	if	SCONJ
ejde-681	37	4	β	β	X
ejde-681	37	5	>	>	X
ejde-681	37	6	0	0	PROPN
ejde-681	37	7	,	,	PUNCT
ejde-681	37	8	the	the	DET
ejde-681	37	9	interactions	interaction	NOUN
ejde-681	37	10	are	be	AUX
ejde-681	37	11	attractive	attractive	ADJ
ejde-681	37	12	,	,	PUNCT
ejde-681	37	13	while	while	SCONJ
ejde-681	37	14	β	β	X
ejde-681	37	15	<	<	X
ejde-681	37	16	0	0	NUM
ejde-681	37	17	implies	imply	VERB
ejde-681	37	18	that	that	SCONJ
ejde-681	37	19	the	the	DET
ejde-681	37	20	interactions	interaction	NOUN
ejde-681	37	21	are	be	AUX
ejde-681	37	22	repulsive	repulsive	ADJ
ejde-681	37	23	.	.	PUNCT
ejde-681	38	1	this	this	DET
ejde-681	38	2	feature	feature	NOUN
ejde-681	38	3	is	be	AUX
ejde-681	38	4	important	important	ADJ
ejde-681	38	5	in	in	ADP
ejde-681	38	6	understanding	understand	VERB
ejde-681	38	7	the	the	DET
ejde-681	38	8	competition	competition	NOUN
ejde-681	38	9	between	between	ADP
ejde-681	38	10	different	different	ADJ
ejde-681	38	11	states	state	NOUN
ejde-681	38	12	and	and	CCONJ
ejde-681	38	13	can	can	AUX
ejde-681	38	14	have	have	VERB
ejde-681	38	15	a	a	DET
ejde-681	38	16	significant	significant	ADJ
ejde-681	38	17	impact	impact	NOUN
ejde-681	38	18	on	on	ADP
ejde-681	38	19	the	the	DET
ejde-681	38	20	behavior	behavior	NOUN
ejde-681	38	21	of	of	ADP
ejde-681	38	22	the	the	DET
ejde-681	38	23	system	system	NOUN
ejde-681	38	24	as	as	ADP
ejde-681	38	25	a	a	DET
ejde-681	38	26	whole	whole	NOUN
ejde-681	38	27	.	.	PUNCT
ejde-681	39	1	recently	recently	ADV
ejde-681	39	2	,	,	PUNCT
ejde-681	39	3	there	there	PRON
ejde-681	39	4	has	have	AUX
ejde-681	39	5	been	be	AUX
ejde-681	39	6	growing	grow	VERB
ejde-681	39	7	interest	interest	NOUN
ejde-681	39	8	in	in	ADP
ejde-681	39	9	studying	study	VERB
ejde-681	39	10	systems	system	NOUN
ejde-681	39	11	of	of	ADP
ejde-681	39	12	the	the	DET
ejde-681	39	13	form	form	NOUN
ejde-681	39	14	(	(	PUNCT
ejde-681	39	15	1.1	1.1	NUM
ejde-681	39	16	)	)	PUNCT
ejde-681	39	17	that	that	PRON
ejde-681	39	18	are	be	AUX
ejde-681	39	19	related	relate	VERB
ejde-681	39	20	to	to	ADP
ejde-681	39	21	the	the	DET
ejde-681	39	22	system	system	NOUN
ejde-681	39	23	(	(	PUNCT
ejde-681	39	24	1.2	1.2	NUM
ejde-681	39	25	)	)	PUNCT
ejde-681	39	26	in	in	ADP
ejde-681	39	27	the	the	DET
ejde-681	39	28	cubic	cubic	ADJ
ejde-681	39	29	case	case	NOUN
ejde-681	39	30	p	p	X
ejde-681	40	1	=	=	X
ejde-681	40	2	q	q	NOUN
ejde-681	40	3	=	=	NOUN
ejde-681	40	4	2	2	X
ejde-681	40	5	.	.	PUNCT
ejde-681	41	1	this	this	PRON
ejde-681	41	2	is	be	AUX
ejde-681	41	3	evidenced	evidence	VERB
ejde-681	41	4	by	by	ADP
ejde-681	41	5	the	the	DET
ejde-681	41	6	increasing	increase	VERB
ejde-681	41	7	number	number	NOUN
ejde-681	41	8	of	of	ADP
ejde-681	41	9	research	research	NOUN
ejde-681	41	10	papers	paper	NOUN
ejde-681	41	11	published	publish	VERB
ejde-681	41	12	on	on	ADP
ejde-681	41	13	the	the	DET
ejde-681	41	14	topic	topic	NOUN
ejde-681	41	15	,	,	PUNCT
ejde-681	41	16	among	among	ADP
ejde-681	41	17	which	which	PRON
ejde-681	41	18	we	we	PRON
ejde-681	41	19	highlight	highlight	VERB
ejde-681	41	20	[	[	X
ejde-681	41	21	1	1	NUM
ejde-681	41	22	,	,	PUNCT
ejde-681	41	23	3	3	NUM
ejde-681	41	24	,	,	PUNCT
ejde-681	41	25	8	8	NUM
ejde-681	41	26	,	,	PUNCT
ejde-681	41	27	9	9	NUM
ejde-681	41	28	,	,	PUNCT
ejde-681	41	29	10	10	NUM
ejde-681	41	30	,	,	PUNCT
ejde-681	41	31	18	18	NUM
ejde-681	41	32	,	,	PUNCT
ejde-681	41	33	19	19	NUM
ejde-681	41	34	,	,	PUNCT
ejde-681	41	35	21	21	NUM
ejde-681	41	36	,	,	PUNCT
ejde-681	41	37	25	25	NUM
ejde-681	41	38	]	]	PUNCT
ejde-681	41	39	and	and	CCONJ
ejde-681	41	40	references	reference	NOUN
ejde-681	41	41	therein	therein	ADV
ejde-681	41	42	.	.	PUNCT
ejde-681	42	1	on	on	ADP
ejde-681	42	2	this	this	DET
ejde-681	42	3	subject	subject	NOUN
ejde-681	42	4	,	,	PUNCT
ejde-681	42	5	we	we	PRON
ejde-681	42	6	also	also	ADV
ejde-681	42	7	refer	refer	VERB
ejde-681	42	8	the	the	DET
ejde-681	42	9	interested	interested	ADJ
ejde-681	42	10	reader	reader	NOUN
ejde-681	42	11	to	to	ADP
ejde-681	42	12	[	[	X
ejde-681	42	13	23	23	NUM
ejde-681	42	14	]	]	PUNCT
ejde-681	42	15	.	.	PUNCT
ejde-681	43	1	in	in	ADP
ejde-681	43	2	this	this	DET
ejde-681	43	3	work	work	NOUN
ejde-681	43	4	,	,	PUNCT
ejde-681	43	5	we	we	PRON
ejde-681	43	6	investigate	investigate	VERB
ejde-681	43	7	the	the	DET
ejde-681	43	8	existence	existence	NOUN
ejde-681	43	9	of	of	ADP
ejde-681	43	10	semi	semi	ADJ
ejde-681	43	11	-	-	ADJ
ejde-681	43	12	nodal	nodal	ADJ
ejde-681	43	13	solutions	solution	NOUN
ejde-681	43	14	for	for	ADP
ejde-681	43	15	system	system	NOUN
ejde-681	43	16	(	(	PUNCT
ejde-681	43	17	1.1	1.1	NUM
ejde-681	43	18	)	)	PUNCT
ejde-681	43	19	,	,	PUNCT
ejde-681	43	20	that	that	ADV
ejde-681	43	21	is	is	ADV
ejde-681	43	22	,	,	PUNCT
ejde-681	43	23	solutions	solution	NOUN
ejde-681	44	1	where	where	SCONJ
ejde-681	44	2	u	u	NOUN
ejde-681	44	3	>	>	X
ejde-681	44	4	0	0	PUNCT
ejde-681	44	5	in	in	ADP
ejde-681	44	6	ω	ω	PROPN
ejde-681	44	7	and	and	CCONJ
ejde-681	44	8	v±	v±	NUM
ejde-681	44	9	:	:	PUNCT
ejde-681	44	10	=	=	SYM
ejde-681	44	11	max{0,±v	max{0,±v	PROPN
ejde-681	44	12	}	}	PUNCT
ejde-681	44	13	̸≡	̸≡	NOUN
ejde-681	44	14	0	0	NUM
ejde-681	44	15	in	in	ADP
ejde-681	44	16	ω	ω	PROPN
ejde-681	44	17	,	,	PUNCT
ejde-681	44	18	which	which	PRON
ejde-681	44	19	has	have	AUX
ejde-681	44	20	also	also	ADV
ejde-681	44	21	received	receive	VERB
ejde-681	44	22	attention	attention	NOUN
ejde-681	44	23	in	in	ADP
ejde-681	44	24	recent	recent	ADJ
ejde-681	44	25	studies	study	NOUN
ejde-681	44	26	,	,	PUNCT
ejde-681	44	27	in	in	ADP
ejde-681	44	28	particular	particular	ADJ
ejde-681	44	29	,	,	PUNCT
ejde-681	44	30	we	we	PRON
ejde-681	44	31	are	be	AUX
ejde-681	44	32	interested	interested	ADJ
ejde-681	44	33	in	in	ADP
ejde-681	44	34	the	the	DET
ejde-681	44	35	case	case	NOUN
ejde-681	44	36	where	where	SCONJ
ejde-681	44	37	µ1	µ1	NOUN
ejde-681	44	38	=	=	SYM
ejde-681	44	39	µ2	µ2	PROPN
ejde-681	44	40	=	=	PUNCT
ejde-681	44	41	0	0	PROPN
ejde-681	44	42	and	and	CCONJ
ejde-681	44	43	p	p	X
ejde-681	45	1	+	+	NOUN
ejde-681	45	2	q	q	ADJ
ejde-681	45	3	<	<	X
ejde-681	45	4	2∗	2∗	PROPN
ejde-681	45	5	,	,	PUNCT
ejde-681	45	6	β	β	X
ejde-681	45	7	>	>	X
ejde-681	45	8	0	0	PUNCT
ejde-681	45	9	and	and	CCONJ
ejde-681	45	10	n	n	PRON
ejde-681	45	11	≤	≤	NUM
ejde-681	45	12	5	5	NUM
ejde-681	45	13	.	.	PUNCT
ejde-681	46	1	clapp	clapp	PROPN
ejde-681	46	2	and	and	CCONJ
ejde-681	46	3	soares	soar	VERB
ejde-681	46	4	[	[	X
ejde-681	46	5	11	11	NUM
ejde-681	46	6	]	]	PUNCT
ejde-681	46	7	dealt	deal	VERB
ejde-681	46	8	with	with	ADP
ejde-681	46	9	the	the	DET
ejde-681	46	10	case	case	NOUN
ejde-681	46	11	where	where	SCONJ
ejde-681	46	12	p	p	NOUN
ejde-681	46	13	=	=	X
ejde-681	46	14	q	q	X
ejde-681	46	15	<	<	X
ejde-681	46	16	2∗/2	2∗/2	NUM
ejde-681	46	17	=	=	NOUN
ejde-681	46	18	n/(n	n/(n	NOUN
ejde-681	46	19	−	−	NOUN
ejde-681	46	20	2	2	NUM
ejde-681	46	21	)	)	PUNCT
ejde-681	46	22	,	,	PUNCT
ejde-681	46	23	λj	λj	PROPN
ejde-681	46	24	=	=	SYM
ejde-681	46	25	−1	−1	NOUN
ejde-681	46	26	,	,	PUNCT
ejde-681	46	27	µj	µj	PROPN
ejde-681	47	1	=	=	SYM
ejde-681	47	2	0	0	NUM
ejde-681	47	3	and	and	CCONJ
ejde-681	47	4	ω	ω	NUM
ejde-681	47	5	=	=	SYM
ejde-681	47	6	rn	rn	PROPN
ejde-681	47	7	with	with	ADP
ejde-681	47	8	n	n	PRON
ejde-681	47	9	≥	≥	NUM
ejde-681	47	10	4	4	NUM
ejde-681	47	11	,	,	PUNCT
ejde-681	47	12	among	among	ADP
ejde-681	47	13	other	other	ADJ
ejde-681	47	14	results	result	NOUN
ejde-681	47	15	,	,	PUNCT
ejde-681	47	16	they	they	PRON
ejde-681	47	17	showed	show	VERB
ejde-681	47	18	the	the	DET
ejde-681	47	19	existence	existence	NOUN
ejde-681	47	20	of	of	ADP
ejde-681	47	21	semi	semi	ADJ
ejde-681	47	22	-	-	ADJ
ejde-681	47	23	nodal	nodal	ADJ
ejde-681	47	24	solutions	solution	NOUN
ejde-681	47	25	subject	subject	ADJ
ejde-681	47	26	to	to	ADP
ejde-681	47	27	the	the	DET
ejde-681	47	28	mentioned	mention	VERB
ejde-681	47	29	conditions	condition	NOUN
ejde-681	47	30	.	.	PUNCT
ejde-681	48	1	chen	chen	PROPN
ejde-681	48	2	,	,	PUNCT
ejde-681	48	3	lin	lin	PROPN
ejde-681	48	4	&	&	CCONJ
ejde-681	48	5	zou	zou	PROPN
ejde-681	49	1	[	[	X
ejde-681	49	2	5	5	NUM
ejde-681	49	3	,	,	PUNCT
ejde-681	49	4	6	6	NUM
ejde-681	49	5	]	]	PUNCT
ejde-681	49	6	dealt	deal	VERB
ejde-681	49	7	with	with	ADP
ejde-681	49	8	the	the	DET
ejde-681	49	9	case	case	NOUN
ejde-681	49	10	p	p	X
ejde-681	49	11	=	=	X
ejde-681	49	12	q	q	NOUN
ejde-681	49	13	=	=	SYM
ejde-681	49	14	2	2	NUM
ejde-681	49	15	,	,	PUNCT
ejde-681	49	16	λj	λj	X
ejde-681	49	17	<	<	X
ejde-681	49	18	0	0	PROPN
ejde-681	49	19	,	,	PUNCT
ejde-681	49	20	µj	µj	PROPN
ejde-681	49	21	>	>	X
ejde-681	49	22	0	0	PROPN
ejde-681	49	23	,	,	PUNCT
ejde-681	49	24	β	β	X
ejde-681	49	25	>	>	X
ejde-681	49	26	0	0	NUM
ejde-681	49	27	,	,	PUNCT
ejde-681	49	28	and	and	CCONJ
ejde-681	49	29	ω	ω	NUM
ejde-681	49	30	⊂	⊂	PROPN
ejde-681	49	31	rn	rn	PROPN
ejde-681	49	32	bounded	bound	VERB
ejde-681	49	33	with	with	ADP
ejde-681	49	34	n	n	PRON
ejde-681	49	35	∈	∈	PROPN
ejde-681	49	36	{	{	PUNCT
ejde-681	49	37	1	1	NUM
ejde-681	49	38	,	,	PUNCT
ejde-681	49	39	2	2	NUM
ejde-681	49	40	,	,	PUNCT
ejde-681	49	41	3	3	NUM
ejde-681	49	42	}	}	PUNCT
ejde-681	49	43	,	,	PUNCT
ejde-681	49	44	they	they	PRON
ejde-681	49	45	showed	show	VERB
ejde-681	49	46	existence	existence	NOUN
ejde-681	49	47	and	and	CCONJ
ejde-681	49	48	multiplicity	multiplicity	NOUN
ejde-681	49	49	results	result	NOUN
ejde-681	49	50	of	of	ADP
ejde-681	49	51	nodal	nodal	ADJ
ejde-681	49	52	solutions	solution	NOUN
ejde-681	49	53	for	for	ADP
ejde-681	49	54	(	(	PUNCT
ejde-681	49	55	1.1	1.1	NUM
ejde-681	49	56	)	)	PUNCT
ejde-681	49	57	.	.	PUNCT
ejde-681	50	1	in	in	ADP
ejde-681	50	2	[	[	X
ejde-681	50	3	7	7	NUM
ejde-681	50	4	]	]	PUNCT
ejde-681	50	5	,	,	PUNCT
ejde-681	50	6	the	the	DET
ejde-681	50	7	same	same	ADJ
ejde-681	50	8	authors	author	NOUN
ejde-681	50	9	provided	provide	VERB
ejde-681	50	10	the	the	DET
ejde-681	50	11	existence	existence	NOUN
ejde-681	50	12	of	of	ADP
ejde-681	50	13	semi	semi	ADJ
ejde-681	50	14	-	-	ADJ
ejde-681	50	15	nodal	nodal	ADJ
ejde-681	50	16	solutions	solution	NOUN
ejde-681	50	17	for	for	ADP
ejde-681	50	18	(	(	PUNCT
ejde-681	50	19	1.1	1.1	NUM
ejde-681	50	20	)	)	PUNCT
ejde-681	50	21	for	for	ADP
ejde-681	50	22	the	the	DET
ejde-681	50	23	critical	critical	ADJ
ejde-681	50	24	case	case	NOUN
ejde-681	50	25	p	p	X
ejde-681	50	26	=	=	X
ejde-681	50	27	q	q	NOUN
ejde-681	50	28	=	=	NOUN
ejde-681	50	29	2∗/2	2∗/2	NUM
ejde-681	50	30	with	with	ADP
ejde-681	50	31	ω	ω	PROPN
ejde-681	50	32	⊂	⊂	PROPN
ejde-681	50	33	rn	rn	PROPN
ejde-681	50	34	bounded	bound	VERB
ejde-681	50	35	,	,	PUNCT
ejde-681	50	36	n	n	X
ejde-681	50	37	≥	≥	NUM
ejde-681	50	38	6	6	NUM
ejde-681	50	39	,	,	PUNCT
ejde-681	50	40	µj	µj	PROPN
ejde-681	50	41	>	>	X
ejde-681	50	42	0	0	PROPN
ejde-681	50	43	,	,	PUNCT
ejde-681	50	44	λj	λj	PROPN
ejde-681	50	45	∈	∈	PROPN
ejde-681	50	46	(	(	PUNCT
ejde-681	50	47	0	0	NUM
ejde-681	50	48	,	,	PUNCT
ejde-681	50	49	λ1(ω	λ1(ω	NOUN
ejde-681	50	50	)	)	PUNCT
ejde-681	50	51	)	)	PUNCT
ejde-681	50	52	and	and	CCONJ
ejde-681	50	53	β	β	X
ejde-681	50	54	<	<	X
ejde-681	50	55	0	0	PROPN
ejde-681	50	56	,	,	PUNCT
ejde-681	50	57	here	here	ADV
ejde-681	50	58	λ1(ω	λ1(ω	PROPN
ejde-681	50	59	)	)	PUNCT
ejde-681	50	60	is	be	AUX
ejde-681	50	61	the	the	DET
ejde-681	50	62	first	first	ADJ
ejde-681	50	63	eigenvalue	eigenvalue	NOUN
ejde-681	50	64	of	of	ADP
ejde-681	50	65	(	(	PUNCT
ejde-681	50	66	−∆	−∆	PROPN
ejde-681	50	67	,	,	PUNCT
ejde-681	50	68	h1	h1	NOUN
ejde-681	50	69	0	0	NUM
ejde-681	50	70	(	(	PUNCT
ejde-681	50	71	ω	ω	NOUN
ejde-681	50	72	)	)	PUNCT
ejde-681	50	73	)	)	PUNCT
ejde-681	50	74	.	.	PUNCT
ejde-681	51	1	in	in	ADP
ejde-681	51	2	this	this	DET
ejde-681	51	3	work	work	NOUN
ejde-681	51	4	,	,	PUNCT
ejde-681	51	5	we	we	PRON
ejde-681	51	6	are	be	AUX
ejde-681	51	7	interested	interested	ADJ
ejde-681	51	8	in	in	ADP
ejde-681	51	9	the	the	DET
ejde-681	51	10	case	case	NOUN
ejde-681	51	11	where	where	SCONJ
ejde-681	51	12	µj	µj	PROPN
ejde-681	51	13	=	=	SYM
ejde-681	51	14	0	0	PROPN
ejde-681	51	15	,	,	PUNCT
ejde-681	51	16	λj	λj	X
ejde-681	51	17	<	<	X
ejde-681	51	18	λ1(ω	λ1(ω	PROPN
ejde-681	51	19	)	)	PUNCT
ejde-681	51	20	,	,	PUNCT
ejde-681	51	21	β	β	X
ejde-681	51	22	>	>	X
ejde-681	51	23	0	0	NUM
ejde-681	51	24	,	,	PUNCT
ejde-681	51	25	p	p	X
ejde-681	51	26	>	>	X
ejde-681	51	27	1	1	NUM
ejde-681	51	28	,	,	PUNCT
ejde-681	51	29	q	q	X
ejde-681	51	30	>	>	X
ejde-681	51	31	2	2	NUM
ejde-681	51	32	with	with	ADP
ejde-681	51	33	p	p	PROPN
ejde-681	52	1	+	+	NOUN
ejde-681	52	2	q	q	ADJ
ejde-681	52	3	<	<	X
ejde-681	52	4	2∗.	2∗.	NUM
ejde-681	52	5	in	in	ADP
ejde-681	52	6	particular	particular	ADJ
ejde-681	52	7	,	,	PUNCT
ejde-681	52	8	3	3	NUM
ejde-681	52	9	<	<	X
ejde-681	52	10	p	p	X
ejde-681	53	1	+	+	NOUN
ejde-681	53	2	q	q	X
ejde-681	53	3	<	<	X
ejde-681	53	4	2∗	2∗	NUM
ejde-681	53	5	which	which	PRON
ejde-681	53	6	implies	imply	VERB
ejde-681	53	7	that	that	SCONJ
ejde-681	53	8	3	3	NUM
ejde-681	53	9	<	<	X
ejde-681	53	10	2∗.	2∗.	NOUN
ejde-681	53	11	hence	hence	ADV
ejde-681	53	12	our	our	PRON
ejde-681	53	13	main	main	ADJ
ejde-681	53	14	result	result	NOUN
ejde-681	53	15	applies	apply	VERB
ejde-681	53	16	only	only	ADV
ejde-681	53	17	for	for	ADP
ejde-681	53	18	the	the	DET
ejde-681	53	19	cases	case	NOUN
ejde-681	53	20	n	n	PRON
ejde-681	53	21	∈	∈	NOUN
ejde-681	53	22	{	{	PUNCT
ejde-681	53	23	3	3	NUM
ejde-681	53	24	,	,	PUNCT
ejde-681	53	25	4	4	NUM
ejde-681	53	26	,	,	PUNCT
ejde-681	53	27	5	5	NUM
ejde-681	53	28	}	}	PUNCT
ejde-681	53	29	where	where	SCONJ
ejde-681	53	30	p+	p+	ADV
ejde-681	53	31	q	q	X
ejde-681	53	32	<	<	X
ejde-681	53	33	2∗.	2∗.	NUM
ejde-681	53	34	furthermore	furthermore	ADV
ejde-681	53	35	,	,	PUNCT
ejde-681	53	36	assuming	assume	VERB
ejde-681	53	37	that	that	SCONJ
ejde-681	53	38	n	n	PRON
ejde-681	53	39	∈	∈	NOUN
ejde-681	53	40	{	{	PUNCT
ejde-681	53	41	1	1	NUM
ejde-681	53	42	,	,	PUNCT
ejde-681	53	43	2	2	NUM
ejde-681	53	44	}	}	PUNCT
ejde-681	53	45	,	,	PUNCT
ejde-681	53	46	it	it	PRON
ejde-681	53	47	suffices	suffice	VERB
ejde-681	53	48	that	that	SCONJ
ejde-681	53	49	p	p	X
ejde-681	53	50	>	>	X
ejde-681	53	51	1	1	NUM
ejde-681	53	52	and	and	CCONJ
ejde-681	53	53	q	q	ADJ
ejde-681	54	1	>	>	X
ejde-681	54	2	2	2	NUM
ejde-681	54	3	because	because	SCONJ
ejde-681	54	4	2∗	2∗	NUM
ejde-681	54	5	=	=	PUNCT
ejde-681	55	1	+	+	NUM
ejde-681	55	2	∞.	∞.	PROPN
ejde-681	55	3	for	for	ADP
ejde-681	55	4	the	the	DET
ejde-681	55	5	sake	sake	NOUN
ejde-681	55	6	of	of	ADP
ejde-681	55	7	convenience	convenience	NOUN
ejde-681	55	8	,	,	PUNCT
ejde-681	55	9	we	we	PRON
ejde-681	55	10	will	will	AUX
ejde-681	55	11	change	change	VERB
ejde-681	55	12	the	the	DET
ejde-681	55	13	notation	notation	NOUN
ejde-681	55	14	of	of	ADP
ejde-681	55	15	system	system	NOUN
ejde-681	55	16	(	(	PUNCT
ejde-681	55	17	1.1	1.1	NUM
ejde-681	55	18	)	)	PUNCT
ejde-681	55	19	to	to	ADP
ejde-681	55	20	this	this	DET
ejde-681	55	21	case	case	NOUN
ejde-681	55	22	,	,	PUNCT
ejde-681	55	23	more	more	ADV
ejde-681	55	24	specifically	specifically	ADV
ejde-681	55	25	,	,	PUNCT
ejde-681	55	26	we	we	PRON
ejde-681	55	27	will	will	AUX
ejde-681	55	28	consider	consider	VERB
ejde-681	55	29	the	the	DET
ejde-681	55	30	system	system	NOUN
ejde-681	55	31	−∆u	−∆u	X
ejde-681	56	1	=	=	PUNCT
ejde-681	57	1	λu+	λu+	PROPN
ejde-681	57	2	ξup−1|v|q	ξup−1|v|q	PROPN
ejde-681	57	3	,	,	PUNCT
ejde-681	57	4	in	in	ADP
ejde-681	57	5	ω	ω	NUM
ejde-681	57	6	−∆v	−∆v	PUNCT
ejde-681	58	1	=	=	PUNCT
ejde-681	58	2	µv	µv	NOUN
ejde-681	58	3	+	+	CCONJ
ejde-681	59	1	τup|v|q−2v	τup|v|q−2v	ADJ
ejde-681	59	2	,	,	PUNCT
ejde-681	59	3	in	in	ADP
ejde-681	59	4	ω	ω	NUM
ejde-681	59	5	u	u	NOUN
ejde-681	59	6	=	=	X
ejde-681	59	7	v	v	NOUN
ejde-681	59	8	=	=	SYM
ejde-681	59	9	0	0	NUM
ejde-681	59	10	,	,	PUNCT
ejde-681	59	11	on	on	ADP
ejde-681	59	12	∂ω	∂ω	ADJ
ejde-681	59	13	u	u	NOUN
ejde-681	59	14	>	>	X
ejde-681	59	15	0	0	PROPN
ejde-681	59	16	,	,	PUNCT
ejde-681	59	17	v±	v±	PROPN
ejde-681	59	18	̸≡	̸≡	NOUN
ejde-681	59	19	0	0	NUM
ejde-681	59	20	in	in	ADP
ejde-681	59	21	ω	ω	PROPN
ejde-681	59	22	.	.	PUNCT
ejde-681	60	1	(	(	PUNCT
ejde-681	60	2	1.3	1.3	NUM
ejde-681	60	3	)	)	PUNCT
ejde-681	60	4	our	our	PRON
ejde-681	60	5	main	main	ADJ
ejde-681	60	6	result	result	NOUN
ejde-681	60	7	reads	read	VERB
ejde-681	60	8	as	as	SCONJ
ejde-681	60	9	follows	follow	VERB
ejde-681	60	10	.	.	PUNCT
ejde-681	61	1	theorem	theorem	VERB
ejde-681	61	2	1.1	1.1	NUM
ejde-681	61	3	.	.	PUNCT
ejde-681	62	1	assume	assume	VERB
ejde-681	62	2	that	that	SCONJ
ejde-681	62	3	ω	ω	PROPN
ejde-681	62	4	⊂	⊂	PROPN
ejde-681	62	5	rn	rn	PROPN
ejde-681	62	6	is	be	AUX
ejde-681	62	7	a	a	DET
ejde-681	62	8	smooth	smooth	ADJ
ejde-681	62	9	bounded	bounded	ADJ
ejde-681	62	10	domain	domain	NOUN
ejde-681	62	11	,	,	PUNCT
ejde-681	62	12	p	p	X
ejde-681	62	13	>	>	X
ejde-681	62	14	1	1	NUM
ejde-681	62	15	,	,	PUNCT
ejde-681	62	16	q	q	X
ejde-681	62	17	>	>	X
ejde-681	62	18	2	2	NUM
ejde-681	62	19	with	with	ADP
ejde-681	62	20	p	p	PROPN
ejde-681	63	1	+	+	NOUN
ejde-681	63	2	q	q	ADJ
ejde-681	63	3	<	<	X
ejde-681	63	4	2∗	2∗	NUM
ejde-681	63	5	=	=	SYM
ejde-681	63	6	2n/(n	2n/(n	NUM
ejde-681	63	7	−	−	NUM
ejde-681	63	8	2	2	NUM
ejde-681	63	9	)	)	PUNCT
ejde-681	63	10	for	for	ADP
ejde-681	63	11	n	n	PRON
ejde-681	63	12	∈	∈	PROPN
ejde-681	63	13	{	{	PUNCT
ejde-681	63	14	3	3	NUM
ejde-681	63	15	,	,	PUNCT
ejde-681	63	16	4	4	NUM
ejde-681	63	17	,	,	PUNCT
ejde-681	63	18	5	5	NUM
ejde-681	63	19	}	}	PUNCT
ejde-681	63	20	,	,	PUNCT
ejde-681	63	21	and	and	CCONJ
ejde-681	63	22	p	p	X
ejde-681	64	1	+	+	NOUN
ejde-681	64	2	q	q	ADJ
ejde-681	64	3	<	<	X
ejde-681	64	4	+	+	NOUN
ejde-681	64	5	∞	∞	NUM
ejde-681	64	6	for	for	ADP
ejde-681	64	7	n	n	PRON
ejde-681	64	8	∈	∈	PROPN
ejde-681	64	9	{	{	PUNCT
ejde-681	64	10	1	1	NUM
ejde-681	64	11	,	,	PUNCT
ejde-681	64	12	2	2	NUM
ejde-681	64	13	}	}	PUNCT
ejde-681	64	14	,	,	PUNCT
ejde-681	64	15	ejde-2024/32	ejde-2024/32	VERB
ejde-681	64	16	solutions	solution	NOUN
ejde-681	64	17	to	to	ADP
ejde-681	64	18	semi	semi	ADJ
ejde-681	64	19	-	-	ADJ
ejde-681	64	20	nodal	nodal	ADJ
ejde-681	64	21	solutions	solution	NOUN
ejde-681	64	22	3	3	NUM
ejde-681	64	23	λ	λ	NOUN
ejde-681	64	24	,	,	PUNCT
ejde-681	64	25	µ	µ	X
ejde-681	64	26	<	<	X
ejde-681	64	27	λ1(ω	λ1(ω	PROPN
ejde-681	64	28	)	)	PUNCT
ejde-681	64	29	,	,	PUNCT
ejde-681	64	30	where	where	SCONJ
ejde-681	64	31	λ1(ω	λ1(ω	X
ejde-681	64	32	)	)	PUNCT
ejde-681	64	33	is	be	AUX
ejde-681	64	34	the	the	DET
ejde-681	64	35	first	first	ADJ
ejde-681	64	36	eigenvalue	eigenvalue	NOUN
ejde-681	64	37	of	of	ADP
ejde-681	64	38	(	(	PUNCT
ejde-681	64	39	−∆	−∆	PROPN
ejde-681	64	40	,	,	PUNCT
ejde-681	64	41	h1	h1	NOUN
ejde-681	64	42	0	0	NUM
ejde-681	64	43	(	(	PUNCT
ejde-681	64	44	ω	ω	NOUN
ejde-681	64	45	)	)	PUNCT
ejde-681	64	46	)	)	PUNCT
ejde-681	64	47	.	.	PUNCT
ejde-681	65	1	then	then	ADV
ejde-681	65	2	there	there	PRON
ejde-681	65	3	exists	exist	VERB
ejde-681	65	4	a	a	DET
ejde-681	65	5	pair	pair	NOUN
ejde-681	65	6	of	of	ADP
ejde-681	65	7	solution	solution	NOUN
ejde-681	65	8	u	u	NOUN
ejde-681	65	9	,	,	PUNCT
ejde-681	65	10	v	v	NOUN
ejde-681	65	11	∈	∈	PROPN
ejde-681	65	12	c2(ω	c2(ω	PRON
ejde-681	65	13	)	)	PUNCT
ejde-681	65	14	to	to	ADP
ejde-681	65	15	(	(	PUNCT
ejde-681	65	16	1.3	1.3	NUM
ejde-681	65	17	)	)	PUNCT
ejde-681	65	18	.	.	PUNCT
ejde-681	66	1	our	our	PRON
ejde-681	66	2	approach	approach	NOUN
ejde-681	66	3	is	be	AUX
ejde-681	66	4	based	base	VERB
ejde-681	66	5	on	on	ADP
ejde-681	66	6	minimization	minimization	NOUN
ejde-681	66	7	arguments	argument	NOUN
ejde-681	66	8	presented	present	VERB
ejde-681	66	9	in	in	ADP
ejde-681	66	10	[	[	X
ejde-681	66	11	4	4	NUM
ejde-681	66	12	,	,	PUNCT
ejde-681	66	13	24	24	NUM
ejde-681	66	14	]	]	PUNCT
ejde-681	66	15	with	with	ADP
ejde-681	66	16	the	the	DET
ejde-681	66	17	necessary	necessary	ADJ
ejde-681	66	18	technical	technical	ADJ
ejde-681	66	19	modifications	modification	NOUN
ejde-681	66	20	.	.	PUNCT
ejde-681	67	1	the	the	DET
ejde-681	67	2	main	main	ADJ
ejde-681	67	3	difficulties	difficulty	NOUN
ejde-681	67	4	in	in	ADP
ejde-681	67	5	our	our	PRON
ejde-681	67	6	approach	approach	NOUN
ejde-681	67	7	are	be	AUX
ejde-681	67	8	to	to	PART
ejde-681	67	9	avoid	avoid	VERB
ejde-681	67	10	semi	semi	ADJ
ejde-681	67	11	-	-	ADJ
ejde-681	67	12	trivial	trivial	ADJ
ejde-681	67	13	solutions	solution	NOUN
ejde-681	67	14	(	(	PUNCT
ejde-681	67	15	i.e.	i.e.	X
ejde-681	67	16	solution	solution	NOUN
ejde-681	67	17	of	of	ADP
ejde-681	67	18	the	the	DET
ejde-681	67	19	form	form	NOUN
ejde-681	67	20	(	(	PUNCT
ejde-681	67	21	u	u	NOUN
ejde-681	67	22	,	,	PUNCT
ejde-681	67	23	0	0	NUM
ejde-681	67	24	)	)	PUNCT
ejde-681	67	25	or	or	CCONJ
ejde-681	67	26	(	(	PUNCT
ejde-681	67	27	0	0	NUM
ejde-681	67	28	,	,	PUNCT
ejde-681	67	29	v	v	NOUN
ejde-681	67	30	)	)	PUNCT
ejde-681	67	31	)	)	PUNCT
ejde-681	67	32	and	and	CCONJ
ejde-681	67	33	to	to	PART
ejde-681	67	34	construct	construct	VERB
ejde-681	67	35	palais	palais	PROPN
ejde-681	67	36	-	-	PUNCT
ejde-681	67	37	smale	smale	ADJ
ejde-681	67	38	sequence	sequence	NOUN
ejde-681	67	39	that	that	PRON
ejde-681	67	40	converges	converge	VERB
ejde-681	67	41	to	to	ADP
ejde-681	67	42	the	the	DET
ejde-681	67	43	infimum	infimum	NOUN
ejde-681	67	44	of	of	ADP
ejde-681	67	45	the	the	DET
ejde-681	67	46	functional	functional	ADJ
ejde-681	67	47	associated	associate	VERB
ejde-681	67	48	with	with	ADP
ejde-681	67	49	system	system	NOUN
ejde-681	67	50	(	(	PUNCT
ejde-681	67	51	2.21	2.21	NUM
ejde-681	67	52	)	)	PUNCT
ejde-681	67	53	restricted	restrict	VERB
ejde-681	67	54	to	to	ADP
ejde-681	67	55	a	a	DET
ejde-681	67	56	certain	certain	ADJ
ejde-681	67	57	subset	subset	NOUN
ejde-681	67	58	of	of	ADP
ejde-681	67	59	the	the	DET
ejde-681	67	60	nehari	nehari	NOUN
ejde-681	67	61	manifold	manifold	ADJ
ejde-681	67	62	.	.	PUNCT
ejde-681	68	1	2	2	X
ejde-681	68	2	.	.	X
ejde-681	68	3	main	main	ADJ
ejde-681	68	4	result	result	NOUN
ejde-681	68	5	to	to	PART
ejde-681	68	6	present	present	VERB
ejde-681	68	7	our	our	PRON
ejde-681	68	8	main	main	ADJ
ejde-681	68	9	result	result	NOUN
ejde-681	68	10	,	,	PUNCT
ejde-681	68	11	we	we	PRON
ejde-681	68	12	use	use	VERB
ejde-681	68	13	the	the	DET
ejde-681	68	14	following	following	ADJ
ejde-681	68	15	notation	notation	NOUN
ejde-681	68	16	:	:	PUNCT
ejde-681	68	17	h	h	NOUN
ejde-681	68	18	:	:	PUNCT
ejde-681	68	19	=	=	PUNCT
ejde-681	68	20	h1	h1	NOUN
ejde-681	68	21	0	0	NUM
ejde-681	68	22	(	(	PUNCT
ejde-681	68	23	ω)×h1	ω)×h1	NUM
ejde-681	68	24	0	0	NUM
ejde-681	68	25	(	(	PUNCT
ejde-681	68	26	ω	ω	NOUN
ejde-681	68	27	)	)	PUNCT
ejde-681	68	28	,	,	PUNCT
ejde-681	68	29	∥u∥2λ	∥u∥2λ	PROPN
ejde-681	68	30	:	:	PUNCT
ejde-681	68	31	=	=	NUM
ejde-681	68	32	∥u∥2	∥u∥2	NOUN
ejde-681	68	33	−	−	NOUN
ejde-681	68	34	λ|u|22	λ|u|22	NOUN
ejde-681	68	35	,	,	PUNCT
ejde-681	68	36	and	and	CCONJ
ejde-681	68	37	∥v∥2µ	∥v∥2µ	ADV
ejde-681	68	38	:	:	PUNCT
ejde-681	68	39	=	=	NOUN
ejde-681	68	40	∥v∥2	∥v∥2	ADJ
ejde-681	69	1	−	−	X
ejde-681	69	2	µ|v|22	µ|v|22	NOUN
ejde-681	69	3	,	,	PUNCT
ejde-681	69	4	where	where	SCONJ
ejde-681	69	5	∥f∥	∥f∥	ADJ
ejde-681	69	6	:	:	PUNCT
ejde-681	69	7	=	=	SYM
ejde-681	69	8	(	(	PUNCT
ejde-681	69	9	∫	∫	PROPN
ejde-681	69	10	ω	ω	PROPN
ejde-681	69	11	|∇f	|∇f	PROPN
ejde-681	69	12	|2dx	|2dx	PROPN
ejde-681	69	13	)	)	PUNCT
ejde-681	69	14	1/2	1/2	NUM
ejde-681	69	15	is	be	AUX
ejde-681	69	16	the	the	DET
ejde-681	69	17	norm	norm	NOUN
ejde-681	69	18	of	of	ADP
ejde-681	69	19	h1	h1	PROPN
ejde-681	69	20	0	0	NUM
ejde-681	69	21	(	(	PUNCT
ejde-681	69	22	ω	ω	NOUN
ejde-681	69	23	)	)	PUNCT
ejde-681	69	24	,	,	PUNCT
ejde-681	69	25	we	we	PRON
ejde-681	69	26	will	will	AUX
ejde-681	69	27	write	write	VERB
ejde-681	69	28	|f	|f	PROPN
ejde-681	69	29	|s	|s	PROPN
ejde-681	69	30	as	as	ADP
ejde-681	69	31	the	the	DET
ejde-681	69	32	norm	norm	NOUN
ejde-681	69	33	of	of	ADP
ejde-681	69	34	ls(ω	ls(ω	NOUN
ejde-681	69	35	)	)	PUNCT
ejde-681	69	36	and	and	CCONJ
ejde-681	69	37	f±(x	f±(x	PROPN
ejde-681	69	38	)	)	PUNCT
ejde-681	69	39	:	:	PUNCT
ejde-681	69	40	=	=	X
ejde-681	69	41	max{0,±f(x	max{0,±f(x	PROPN
ejde-681	69	42	)	)	PUNCT
ejde-681	69	43	}	}	PUNCT
ejde-681	69	44	.	.	PUNCT
ejde-681	70	1	given	give	VERB
ejde-681	70	2	the	the	DET
ejde-681	70	3	condition	condition	NOUN
ejde-681	70	4	λ	λ	PROPN
ejde-681	70	5	,	,	PUNCT
ejde-681	70	6	µ	µ	AUX
ejde-681	70	7	<	<	X
ejde-681	70	8	λ1(ω	λ1(ω	PROPN
ejde-681	70	9	)	)	PUNCT
ejde-681	70	10	,	,	PUNCT
ejde-681	70	11	we	we	PRON
ejde-681	70	12	see	see	VERB
ejde-681	70	13	that	that	SCONJ
ejde-681	70	14	there	there	PRON
ejde-681	70	15	exists	exist	VERB
ejde-681	70	16	cλµ	cλµ	VERB
ejde-681	70	17	:	:	PUNCT
ejde-681	70	18	=	=	SYM
ejde-681	70	19	cλµ(λ1(ω	cλµ(λ1(ω	NUM
ejde-681	70	20	)	)	PUNCT
ejde-681	70	21	)	)	PUNCT
ejde-681	70	22	such	such	ADJ
ejde-681	70	23	that	that	SCONJ
ejde-681	70	24	cλµ∥u∥	cλµ∥u∥	NUM
ejde-681	70	25	≤	≤	NUM
ejde-681	70	26	∥u∥λ	∥u∥λ	CCONJ
ejde-681	70	27	≤	≤	VERB
ejde-681	70	28	c−1	c−1	PROPN
ejde-681	70	29	λµ	λµ	NOUN
ejde-681	70	30	∥u∥	∥u∥	NOUN
ejde-681	70	31	and	and	CCONJ
ejde-681	70	32	cλµ∥v∥	cλµ∥v∥	X
ejde-681	70	33	≤	≤	NUM
ejde-681	70	34	∥v∥µ	∥v∥µ	NOUN
ejde-681	70	35	≤	≤	ADJ
ejde-681	70	36	c−1	c−1	PROPN
ejde-681	70	37	λµ	λµ	PRON
ejde-681	70	38	∥v∥	∥v∥	PROPN
ejde-681	70	39	for	for	ADP
ejde-681	70	40	all	all	DET
ejde-681	70	41	u	u	NOUN
ejde-681	70	42	,	,	PUNCT
ejde-681	70	43	v	v	PROPN
ejde-681	70	44	∈	∈	PROPN
ejde-681	70	45	h1	h1	NOUN
ejde-681	70	46	0	0	NUM
ejde-681	70	47	(	(	PUNCT
ejde-681	70	48	ω	ω	NOUN
ejde-681	70	49	)	)	PUNCT
ejde-681	70	50	(	(	PUNCT
ejde-681	70	51	2.1	2.1	NUM
ejde-681	70	52	)	)	PUNCT
ejde-681	70	53	to	to	PART
ejde-681	70	54	obtain	obtain	VERB
ejde-681	70	55	solutions	solution	NOUN
ejde-681	70	56	for	for	ADP
ejde-681	70	57	system	system	NOUN
ejde-681	70	58	(	(	PUNCT
ejde-681	70	59	1.3	1.3	NUM
ejde-681	70	60	)	)	PUNCT
ejde-681	70	61	,	,	PUNCT
ejde-681	70	62	we	we	PRON
ejde-681	70	63	define	define	VERB
ejde-681	70	64	the	the	DET
ejde-681	70	65	functional	functional	ADJ
ejde-681	70	66	iλµ	iλµ	NOUN
ejde-681	70	67	∈	∈	PROPN
ejde-681	70	68	c1(h	c1(h	PROPN
ejde-681	70	69	,	,	PUNCT
ejde-681	70	70	r	r	NOUN
ejde-681	70	71	)	)	PUNCT
ejde-681	70	72	given	give	VERB
ejde-681	70	73	by	by	ADP
ejde-681	70	74	iλµ(u	iλµ(u	NOUN
ejde-681	70	75	,	,	PUNCT
ejde-681	70	76	v	v	NOUN
ejde-681	70	77	)	)	PUNCT
ejde-681	70	78	=	=	SYM
ejde-681	70	79	1	1	NUM
ejde-681	70	80	2	2	NUM
ejde-681	70	81	∥u∥2λ	∥u∥2λ	NUM
ejde-681	70	82	+	+	CCONJ
ejde-681	70	83	1	1	NUM
ejde-681	70	84	2	2	NUM
ejde-681	70	85	∥v∥2µ	∥v∥2µ	ADV
ejde-681	70	86	−	−	NUM
ejde-681	70	87	1	1	NUM
ejde-681	70	88	p+	p+	NOUN
ejde-681	70	89	q	q	PROPN
ejde-681	70	90	∫	∫	PROPN
ejde-681	70	91	ω	ω	PROPN
ejde-681	70	92	|u|p|v|q	|u|p|v|q	PROPN
ejde-681	70	93	dx	dx	PROPN
ejde-681	70	94	here	here	ADV
ejde-681	70	95	we	we	PRON
ejde-681	70	96	shall	shall	AUX
ejde-681	70	97	follow	follow	VERB
ejde-681	70	98	same	same	ADJ
ejde-681	70	99	ideas	idea	NOUN
ejde-681	70	100	from	from	ADP
ejde-681	70	101	[	[	X
ejde-681	70	102	4	4	NUM
ejde-681	70	103	]	]	PUNCT
ejde-681	70	104	which	which	PRON
ejde-681	70	105	allows	allow	VERB
ejde-681	70	106	us	we	PRON
ejde-681	70	107	to	to	PART
ejde-681	70	108	minimize	minimize	VERB
ejde-681	70	109	the	the	DET
ejde-681	70	110	functional	functional	ADJ
ejde-681	70	111	iλµ	iλµ	NOUN
ejde-681	70	112	over	over	ADP
ejde-681	70	113	the	the	DET
ejde-681	70	114	following	follow	VERB
ejde-681	70	115	subsets	subset	NOUN
ejde-681	70	116	of	of	ADP
ejde-681	70	117	the	the	DET
ejde-681	70	118	nehari	nehari	NOUN
ejde-681	70	119	manifold	manifold	ADJ
ejde-681	70	120	nλ	nλ	NOUN
ejde-681	70	121	:	:	PUNCT
ejde-681	70	122	=	=	SYM
ejde-681	70	123	{	{	PUNCT
ejde-681	70	124	(	(	PUNCT
ejde-681	70	125	u	u	NOUN
ejde-681	70	126	,	,	PUNCT
ejde-681	70	127	v	v	NOUN
ejde-681	70	128	)	)	PUNCT
ejde-681	70	129	∈	∈	PROPN
ejde-681	70	130	h	h	NOUN
ejde-681	70	131	:	:	PUNCT
ejde-681	70	132	i	i	PROPN
ejde-681	70	133	′λµ(u	′λµ(u	PROPN
ejde-681	70	134	,	,	PUNCT
ejde-681	70	135	v)(u	v)(u	ADJ
ejde-681	70	136	,	,	PUNCT
ejde-681	70	137	0	0	NUM
ejde-681	70	138	)	)	PUNCT
ejde-681	70	139	=	=	SYM
ejde-681	70	140	0	0	NUM
ejde-681	70	141	,	,	PUNCT
ejde-681	70	142	u	u	NOUN
ejde-681	70	143	̸≡	̸≡	PROPN
ejde-681	70	144	0	0	NUM
ejde-681	70	145	,	,	PUNCT
ejde-681	70	146	v	v	ADP
ejde-681	70	147	̸≡	̸≡	NOUN
ejde-681	70	148	0	0	NUM
ejde-681	70	149	}	}	PUNCT
ejde-681	70	150	,	,	PUNCT
ejde-681	70	151	n±	n±	PROPN
ejde-681	70	152	µ	µ	X
ejde-681	70	153	:	:	PUNCT
ejde-681	70	154	=	=	SYM
ejde-681	70	155	{	{	PUNCT
ejde-681	70	156	(	(	PUNCT
ejde-681	70	157	u	u	NOUN
ejde-681	70	158	,	,	PUNCT
ejde-681	70	159	v	v	NOUN
ejde-681	70	160	)	)	PUNCT
ejde-681	71	1	∈	∈	PROPN
ejde-681	71	2	h	h	NOUN
ejde-681	71	3	:	:	PUNCT
ejde-681	71	4	i	i	PROPN
ejde-681	71	5	′λµ(u	′λµ(u	PROPN
ejde-681	71	6	,	,	PUNCT
ejde-681	71	7	v)(0	v)(0	NUM
ejde-681	71	8	,	,	PUNCT
ejde-681	71	9	v	v	NOUN
ejde-681	71	10	±	±	NUM
ejde-681	71	11	)	)	PUNCT
ejde-681	71	12	=	=	SYM
ejde-681	71	13	0	0	NUM
ejde-681	71	14	,	,	PUNCT
ejde-681	71	15	u	u	NOUN
ejde-681	71	16	̸≡	̸≡	PROPN
ejde-681	71	17	0	0	NUM
ejde-681	71	18	,	,	PUNCT
ejde-681	71	19	v±	v±	PROPN
ejde-681	71	20	̸≡	̸≡	NOUN
ejde-681	71	21	0	0	NUM
ejde-681	71	22	}	}	PUNCT
ejde-681	71	23	,	,	PUNCT
ejde-681	71	24	mλµ	mλµ	NOUN
ejde-681	71	25	:	:	PUNCT
ejde-681	71	26	=	=	SYM
ejde-681	71	27	nλ	nλ	NUM
ejde-681	71	28	∩n+	∩n+	PROPN
ejde-681	71	29	µ	µ	X
ejde-681	71	30	∩n−	∩n−	X
ejde-681	71	31	µ	µ	NOUN
ejde-681	71	32	the	the	DET
ejde-681	71	33	following	following	ADJ
ejde-681	71	34	result	result	NOUN
ejde-681	71	35	is	be	AUX
ejde-681	71	36	of	of	ADP
ejde-681	71	37	fundamental	fundamental	ADJ
ejde-681	71	38	importance	importance	NOUN
ejde-681	71	39	for	for	ADP
ejde-681	71	40	constructing	construct	VERB
ejde-681	71	41	a	a	DET
ejde-681	71	42	palais	palais	ADJ
ejde-681	71	43	-	-	PUNCT
ejde-681	71	44	smale	smale	ADJ
ejde-681	71	45	sequence	sequence	NOUN
ejde-681	71	46	at	at	ADP
ejde-681	71	47	the	the	DET
ejde-681	71	48	level	level	NOUN
ejde-681	71	49	where	where	SCONJ
ejde-681	71	50	we	we	PRON
ejde-681	71	51	obtain	obtain	VERB
ejde-681	71	52	solutions	solution	NOUN
ejde-681	71	53	to	to	ADP
ejde-681	71	54	our	our	PRON
ejde-681	71	55	problem	problem	NOUN
ejde-681	71	56	.	.	PUNCT
ejde-681	72	1	this	this	DET
ejde-681	72	2	approach	approach	NOUN
ejde-681	72	3	is	be	AUX
ejde-681	72	4	based	base	VERB
ejde-681	72	5	on	on	ADP
ejde-681	72	6	an	an	DET
ejde-681	72	7	idea	idea	NOUN
ejde-681	72	8	presented	present	VERB
ejde-681	72	9	in	in	ADP
ejde-681	72	10	the	the	DET
ejde-681	72	11	work	work	NOUN
ejde-681	72	12	[	[	X
ejde-681	72	13	24	24	NUM
ejde-681	72	14	]	]	PUNCT
ejde-681	72	15	.	.	PUNCT
ejde-681	73	1	lemma	lemma	PROPN
ejde-681	73	2	2.1	2.1	NUM
ejde-681	73	3	.	.	PUNCT
ejde-681	74	1	let	let	VERB
ejde-681	74	2	(	(	PUNCT
ejde-681	74	3	u	u	NOUN
ejde-681	74	4	,	,	PUNCT
ejde-681	74	5	v	v	NOUN
ejde-681	74	6	)	)	PUNCT
ejde-681	74	7	∈	∈	NOUN
ejde-681	74	8	mλµ	mλµ	NOUN
ejde-681	74	9	and	and	CCONJ
ejde-681	74	10	z	z	NOUN
ejde-681	74	11	,	,	PUNCT
ejde-681	74	12	w	w	PROPN
ejde-681	74	13	∈	∈	PROPN
ejde-681	74	14	h1	h1	NOUN
ejde-681	74	15	0	0	NUM
ejde-681	74	16	(	(	PUNCT
ejde-681	74	17	ω	ω	NOUN
ejde-681	74	18	)	)	PUNCT
ejde-681	74	19	\	\	NOUN
ejde-681	74	20	{	{	PUNCT
ejde-681	74	21	0	0	NUM
ejde-681	74	22	}	}	PUNCT
ejde-681	74	23	then	then	ADV
ejde-681	74	24	for	for	ADP
ejde-681	74	25	all	all	DET
ejde-681	74	26	δ	δ	PROPN
ejde-681	74	27	>	>	X
ejde-681	74	28	0	0	PUNCT
ejde-681	75	1	there	there	PRON
ejde-681	75	2	are	be	VERB
ejde-681	75	3	unique	unique	ADJ
ejde-681	75	4	positive	positive	ADJ
ejde-681	75	5	numbers	number	NOUN
ejde-681	75	6	t	t	NOUN
ejde-681	75	7	=	=	SYM
ejde-681	75	8	t(δ	t(δ	PROPN
ejde-681	75	9	)	)	PUNCT
ejde-681	75	10	,	,	PUNCT
ejde-681	75	11	r	r	NOUN
ejde-681	75	12	=	=	SYM
ejde-681	75	13	r(δ	r(δ	NOUN
ejde-681	75	14	)	)	PUNCT
ejde-681	75	15	,	,	PUNCT
ejde-681	75	16	and	and	CCONJ
ejde-681	75	17	s	s	NOUN
ejde-681	75	18	=	=	SYM
ejde-681	75	19	s(δ	s(δ	NOUN
ejde-681	75	20	)	)	PUNCT
ejde-681	75	21	such	such	ADJ
ejde-681	75	22	that	that	SCONJ
ejde-681	75	23	(	(	PUNCT
ejde-681	75	24	t(u−	t(u−	X
ejde-681	75	25	δz	δz	NOUN
ejde-681	75	26	)	)	PUNCT
ejde-681	75	27	,	,	PUNCT
ejde-681	75	28	r(v	r(v	PROPN
ejde-681	75	29	−	−	PROPN
ejde-681	75	30	δw)+	δw)+	NOUN
ejde-681	75	31	−	−	PROPN
ejde-681	75	32	s(v	s(v	PROPN
ejde-681	75	33	−	−	PROPN
ejde-681	75	34	δw)−	δw)−	PRON
ejde-681	75	35	)	)	PUNCT
ejde-681	75	36	∈	∈	PROPN
ejde-681	75	37	mλµ.	mλµ.	NOUN
ejde-681	75	38	moreover	moreover	ADV
ejde-681	75	39	if	if	SCONJ
ejde-681	75	40	∥z∥	∥z∥	NOUN
ejde-681	75	41	,	,	PUNCT
ejde-681	75	42	∥w∥	∥w∥	VERB
ejde-681	75	43	≤	≤	NUM
ejde-681	75	44	1	1	NUM
ejde-681	75	45	and	and	CCONJ
ejde-681	75	46	∥u∥	∥u∥	NOUN
ejde-681	75	47	,	,	PUNCT
ejde-681	75	48	∥v∥	∥v∥	ADJ
ejde-681	75	49	≤	≤	ADJ
ejde-681	75	50	m1	m1	NOUN
ejde-681	75	51	,	,	PUNCT
ejde-681	75	52	then	then	ADV
ejde-681	75	53	there	there	PRON
ejde-681	75	54	are	be	VERB
ejde-681	75	55	constants	constant	NOUN
ejde-681	75	56	m0	m0	NOUN
ejde-681	75	57	=	=	PUNCT
ejde-681	75	58	m0(p	m0(p	PROPN
ejde-681	75	59	,	,	PUNCT
ejde-681	75	60	q	q	ADJ
ejde-681	75	61	,	,	PUNCT
ejde-681	75	62	λ	λ	PROPN
ejde-681	75	63	,	,	PUNCT
ejde-681	75	64	µ	µ	NOUN
ejde-681	75	65	,	,	PUNCT
ejde-681	75	66	λ1(ω),ω	λ1(ω),ω	NOUN
ejde-681	75	67	,	,	PUNCT
ejde-681	75	68	m1	m1	NOUN
ejde-681	75	69	,	,	PUNCT
ejde-681	75	70	n	n	CCONJ
ejde-681	75	71	)	)	PUNCT
ejde-681	75	72	>	>	X
ejde-681	75	73	0	0	NUM
ejde-681	75	74	,	,	PUNCT
ejde-681	75	75	and	and	CCONJ
ejde-681	75	76	ci	ci	NOUN
ejde-681	75	77	=	=	PUNCT
ejde-681	75	78	ci(p	ci(p	X
ejde-681	75	79	,	,	PUNCT
ejde-681	75	80	q	q	X
ejde-681	75	81	,	,	PUNCT
ejde-681	75	82	λ	λ	PROPN
ejde-681	75	83	,	,	PUNCT
ejde-681	75	84	µ	µ	NOUN
ejde-681	75	85	,	,	PUNCT
ejde-681	75	86	λ1(ω),ω	λ1(ω),ω	NOUN
ejde-681	75	87	,	,	PUNCT
ejde-681	75	88	m1	m1	NOUN
ejde-681	75	89	,	,	PUNCT
ejde-681	75	90	n	n	CCONJ
ejde-681	75	91	)	)	PUNCT
ejde-681	75	92	>	>	X
ejde-681	75	93	0	0	PUNCT
ejde-681	75	94	such	such	ADJ
ejde-681	75	95	that	that	DET
ejde-681	75	96	|t′(0)|	|t′(0)|	NOUN
ejde-681	75	97	,	,	PUNCT
ejde-681	75	98	|r′(0)|	|r′(0)|	NOUN
ejde-681	75	99	,	,	PUNCT
ejde-681	75	100	|s′(0)|	|s′(0)|	NOUN
ejde-681	75	101	∈	∈	PROPN
ejde-681	76	1	[	[	X
ejde-681	76	2	0	0	NUM
ejde-681	76	3	,	,	PUNCT
ejde-681	76	4	c2	c2	PROPN
ejde-681	76	5	]	]	PUNCT
ejde-681	76	6	and	and	CCONJ
ejde-681	76	7	|t(0)|	|t(0)|	NOUN
ejde-681	76	8	,	,	PUNCT
ejde-681	76	9	|r(0)|	|r(0)|	NOUN
ejde-681	76	10	,	,	PUNCT
ejde-681	76	11	|s(0)|	|s(0)|	NOUN
ejde-681	76	12	∈	∈	PROPN
ejde-681	77	1	[	[	X
ejde-681	77	2	c1	c1	PROPN
ejde-681	77	3	,	,	PUNCT
ejde-681	77	4	c2	c2	PROPN
ejde-681	77	5	]	]	PUNCT
ejde-681	77	6	,	,	PUNCT
ejde-681	77	7	(	(	PUNCT
ejde-681	77	8	2.2	2.2	NUM
ejde-681	77	9	)	)	PUNCT
ejde-681	77	10	∥u∥	∥u∥	NOUN
ejde-681	77	11	,	,	PUNCT
ejde-681	77	12	∥v±∥	∥v±∥	PROPN
ejde-681	77	13	≥	≥	NOUN
ejde-681	77	14	m0	m0	NOUN
ejde-681	77	15	(	(	PUNCT
ejde-681	77	16	2.3	2.3	NUM
ejde-681	77	17	)	)	PUNCT
ejde-681	77	18	proof	proof	NOUN
ejde-681	77	19	.	.	PUNCT
ejde-681	78	1	firstly	firstly	ADV
ejde-681	78	2	,	,	PUNCT
ejde-681	78	3	we	we	PRON
ejde-681	78	4	mention	mention	VERB
ejde-681	78	5	that	that	SCONJ
ejde-681	78	6	(	(	PUNCT
ejde-681	78	7	ϕ	ϕ	NOUN
ejde-681	78	8	,	,	PUNCT
ejde-681	78	9	φ	φ	NUM
ejde-681	78	10	)	)	PUNCT
ejde-681	78	11	∈	∈	NOUN
ejde-681	78	12	mλµ	mλµ	NOUN
ejde-681	78	13	if	if	SCONJ
ejde-681	78	14	and	and	CCONJ
ejde-681	78	15	only	only	ADV
ejde-681	78	16	if	if	SCONJ
ejde-681	78	17	∥ϕ∥2λ	∥ϕ∥2λ	PROPN
ejde-681	78	18	=	=	PUNCT
ejde-681	79	1	p	p	PROPN
ejde-681	79	2	p+	p+	ADJ
ejde-681	79	3	q	q	PROPN
ejde-681	79	4	∫	∫	PROPN
ejde-681	79	5	|ϕ|p|φ|qdx	|ϕ|p|φ|qdx	PROPN
ejde-681	79	6	and	and	CCONJ
ejde-681	79	7	∥φ±∥2µ	∥φ±∥2µ	PROPN
ejde-681	79	8	=	=	SYM
ejde-681	79	9	q	q	X
ejde-681	79	10	p+	p+	ADJ
ejde-681	79	11	q	q	PROPN
ejde-681	79	12	∫	∫	PROPN
ejde-681	79	13	|ϕ|p|φ±|dx	|ϕ|p|φ±|dx	PROPN
ejde-681	79	14	.	.	PUNCT
ejde-681	80	1	4	4	NUM
ejde-681	81	1	j.	j.	PROPN
ejde-681	81	2	p.	p.	PROPN
ejde-681	81	3	p.	p.	PROPN
ejde-681	82	1	d.	d.	PROPN
ejde-681	82	2	silva	silva	PROPN
ejde-681	82	3	,	,	PUNCT
ejde-681	82	4	e.	e.	PROPN
ejde-681	82	5	d.	d.	PROPN
ejde-681	82	6	silva	silva	PROPN
ejde-681	82	7	ejde-2024/32	ejde-2024/32	PROPN
ejde-681	82	8	therefore	therefore	ADV
ejde-681	82	9	,	,	PUNCT
ejde-681	82	10	for	for	ADP
ejde-681	82	11	each	each	DET
ejde-681	82	12	(	(	PUNCT
ejde-681	82	13	t(u−	t(u−	X
ejde-681	82	14	δz	δz	NOUN
ejde-681	82	15	)	)	PUNCT
ejde-681	82	16	,	,	PUNCT
ejde-681	82	17	r(v	r(v	PROPN
ejde-681	82	18	−	−	PROPN
ejde-681	82	19	δw)+	δw)+	NOUN
ejde-681	82	20	−	−	PROPN
ejde-681	82	21	s(v	s(v	PROPN
ejde-681	82	22	−	−	PROPN
ejde-681	82	23	δw)−	δw)−	X
ejde-681	82	24	)	)	PUNCT
ejde-681	82	25	∈	∈	NOUN
ejde-681	82	26	mλµ	mλµ	NOUN
ejde-681	83	1	,	,	PUNCT
ejde-681	83	2	we	we	PRON
ejde-681	83	3	obtain	obtain	VERB
ejde-681	83	4	that	that	SCONJ
ejde-681	83	5	∥t(u−	∥t(u−	PRON
ejde-681	83	6	δz)∥2λ	δz)∥2λ	VERB
ejde-681	84	1	=	=	SYM
ejde-681	84	2	p	p	PROPN
ejde-681	84	3	p+	p+	ADJ
ejde-681	84	4	q	q	X
ejde-681	84	5	∫	∫	PROPN
ejde-681	84	6	|t(u−	|t(u−	PROPN
ejde-681	84	7	δz)|p|r(v	δz)|p|r(v	PROPN
ejde-681	84	8	−	−	PROPN
ejde-681	84	9	δw)+	δw)+	NOUN
ejde-681	84	10	−	−	PROPN
ejde-681	84	11	s(v	s(v	PROPN
ejde-681	84	12	−	−	PROPN
ejde-681	84	13	δw)−|q	δw)−|q	PROPN
ejde-681	84	14	dx	dx	PROPN
ejde-681	85	1	∥r(v	∥r(v	NOUN
ejde-681	85	2	−	−	PROPN
ejde-681	85	3	δw)+∥2µ	δw)+∥2µ	PROPN
ejde-681	85	4	=	=	SYM
ejde-681	85	5	q	q	PROPN
ejde-681	85	6	p+	p+	ADJ
ejde-681	85	7	q	q	X
ejde-681	85	8	∫	∫	PROPN
ejde-681	85	9	|t(u−	|t(u−	PROPN
ejde-681	85	10	δz)|p|r(v	δz)|p|r(v	PROPN
ejde-681	85	11	−	−	PROPN
ejde-681	85	12	δw)+|	δw)+|	PROPN
ejde-681	85	13	dx	dx	PROPN
ejde-681	85	14	∥s(v	∥s(v	PROPN
ejde-681	85	15	−	−	PROPN
ejde-681	85	16	δw)−∥2µ	δw)−∥2µ	PROPN
ejde-681	85	17	=	=	SYM
ejde-681	85	18	q	q	PROPN
ejde-681	85	19	p+	p+	ADJ
ejde-681	85	20	q	q	X
ejde-681	85	21	∫	∫	PROPN
ejde-681	85	22	|t(u−	|t(u−	PROPN
ejde-681	85	23	δz)|p|s(v	δz)|p|s(v	PROPN
ejde-681	85	24	−	−	PROPN
ejde-681	85	25	δw)−|	δw)−|	PROPN
ejde-681	85	26	dx	dx	PROPN
ejde-681	85	27	(	(	PUNCT
ejde-681	85	28	2.4	2.4	NUM
ejde-681	85	29	)	)	PUNCT
ejde-681	85	30	to	to	PART
ejde-681	85	31	make	make	VERB
ejde-681	85	32	the	the	DET
ejde-681	85	33	presentation	presentation	NOUN
ejde-681	85	34	clear	clear	ADJ
ejde-681	85	35	,	,	PUNCT
ejde-681	85	36	we	we	PRON
ejde-681	85	37	define	define	VERB
ejde-681	85	38	the	the	DET
ejde-681	85	39	following	follow	VERB
ejde-681	85	40	functions	function	NOUN
ejde-681	85	41	:	:	PUNCT
ejde-681	85	42	f1(δ	f1(δ	X
ejde-681	85	43	)	)	PUNCT
ejde-681	85	44	=	=	SYM
ejde-681	85	45	∥u−	∥u−	NUM
ejde-681	85	46	δz∥2λ	δz∥2λ	PROPN
ejde-681	85	47	,	,	PUNCT
ejde-681	85	48	f2(δ	f2(δ	NUM
ejde-681	85	49	)	)	PUNCT
ejde-681	85	50	=	=	SYM
ejde-681	85	51	∫	∫	PROPN
ejde-681	85	52	ω	ω	PROPN
ejde-681	85	53	|u−	|u−	ADJ
ejde-681	85	54	δz|p[(v	δz|p[(v	NOUN
ejde-681	85	55	−	−	PROPN
ejde-681	85	56	δw)+]q	δw)+]q	PROPN
ejde-681	85	57	,	,	PUNCT
ejde-681	85	58	f3(δ	f3(δ	NOUN
ejde-681	85	59	)	)	PUNCT
ejde-681	85	60	=	=	SYM
ejde-681	85	61	∫	∫	PROPN
ejde-681	85	62	ω	ω	PROPN
ejde-681	85	63	|u−	|u−	ADJ
ejde-681	85	64	δz|p[(v	δz|p[(v	NOUN
ejde-681	85	65	−	−	PROPN
ejde-681	85	66	δw)−]q	δw)−]q	NOUN
ejde-681	85	67	,	,	PUNCT
ejde-681	85	68	f4(δ	f4(δ	PROPN
ejde-681	85	69	)	)	PUNCT
ejde-681	85	70	=	=	SYM
ejde-681	85	71	∥(v	∥(v	ADJ
ejde-681	85	72	−	−	ADP
ejde-681	85	73	δw)+∥2µ	δw)+∥2µ	PROPN
ejde-681	85	74	,	,	PUNCT
ejde-681	85	75	f5(δ	f5(δ	X
ejde-681	85	76	)	)	PUNCT
ejde-681	86	1	=	=	SYM
ejde-681	86	2	∥(v	∥(v	ADJ
ejde-681	86	3	−	−	ADP
ejde-681	86	4	δw)−∥2µ.	δw)−∥2µ.	PROPN
ejde-681	86	5	it	it	PRON
ejde-681	86	6	follows	follow	VERB
ejde-681	86	7	from	from	ADP
ejde-681	86	8	(	(	PUNCT
ejde-681	86	9	2.4	2.4	NUM
ejde-681	86	10	)	)	PUNCT
ejde-681	86	11	that	that	SCONJ
ejde-681	86	12	t(δ	t(δ	PROPN
ejde-681	86	13	)	)	PUNCT
ejde-681	86	14	,	,	PUNCT
ejde-681	86	15	r(δ	r(δ	PROPN
ejde-681	86	16	)	)	PUNCT
ejde-681	86	17	,	,	PUNCT
ejde-681	86	18	and	and	CCONJ
ejde-681	86	19	s(δ	s(δ	NOUN
ejde-681	86	20	)	)	PUNCT
ejde-681	86	21	are	be	AUX
ejde-681	86	22	precisely	precisely	ADV
ejde-681	86	23	the	the	DET
ejde-681	86	24	solutions	solution	NOUN
ejde-681	86	25	for	for	ADP
ejde-681	86	26	the	the	DET
ejde-681	86	27	system	system	NOUN
ejde-681	86	28	t2f1(δ	t2f1(δ	NOUN
ejde-681	86	29	)	)	PUNCT
ejde-681	86	30	=	=	SYM
ejde-681	87	1	p	p	X
ejde-681	87	2	p+	p+	ADJ
ejde-681	87	3	q	q	NOUN
ejde-681	87	4	tprqf2(δ	tprqf2(δ	NOUN
ejde-681	87	5	)	)	PUNCT
ejde-681	88	1	+	+	CCONJ
ejde-681	89	1	p	p	X
ejde-681	89	2	p+	p+	NOUN
ejde-681	89	3	q	q	NOUN
ejde-681	89	4	tpsqf3(δ	tpsqf3(δ	NOUN
ejde-681	89	5	)	)	PUNCT
ejde-681	89	6	,	,	PUNCT
ejde-681	89	7	(	(	PUNCT
ejde-681	89	8	2.5	2.5	NUM
ejde-681	89	9	)	)	PUNCT
ejde-681	89	10	r2f4(δ	r2f4(δ	NOUN
ejde-681	89	11	)	)	PUNCT
ejde-681	89	12	=	=	SYM
ejde-681	89	13	q	q	PROPN
ejde-681	89	14	p+	p+	ADJ
ejde-681	89	15	q	q	PROPN
ejde-681	89	16	tprqf2(δ	tprqf2(δ	NOUN
ejde-681	89	17	)	)	PUNCT
ejde-681	89	18	,	,	PUNCT
ejde-681	89	19	(	(	PUNCT
ejde-681	89	20	2.6	2.6	NUM
ejde-681	89	21	)	)	PUNCT
ejde-681	89	22	s2f5(δ	s2f5(δ	NOUN
ejde-681	89	23	)	)	PUNCT
ejde-681	89	24	=	=	SYM
ejde-681	90	1	q	q	PROPN
ejde-681	90	2	p+	p+	ADJ
ejde-681	90	3	q	q	NOUN
ejde-681	90	4	tpsqf3(δ	tpsqf3(δ	NOUN
ejde-681	90	5	)	)	PUNCT
ejde-681	90	6	,	,	PUNCT
ejde-681	90	7	(	(	PUNCT
ejde-681	90	8	2.7	2.7	NUM
ejde-681	90	9	)	)	PUNCT
ejde-681	90	10	here	here	ADV
ejde-681	90	11	we	we	PRON
ejde-681	90	12	observe	observe	VERB
ejde-681	90	13	that	that	SCONJ
ejde-681	90	14	the	the	DET
ejde-681	90	15	solution	solution	NOUN
ejde-681	90	16	t(δ	t(δ	PROPN
ejde-681	90	17	)	)	PUNCT
ejde-681	90	18	is	be	AUX
ejde-681	90	19	given	give	VERB
ejde-681	90	20	explicitly	explicitly	ADV
ejde-681	90	21	by	by	ADP
ejde-681	90	22	t(δ	t(δ	PROPN
ejde-681	90	23	)	)	PUNCT
ejde-681	90	24	=	=	PUNCT
ejde-681	91	1	(	(	PUNCT
ejde-681	91	2	1	1	NUM
ejde-681	91	3	+	+	CCONJ
ejde-681	91	4	p	p	X
ejde-681	91	5	q	q	NOUN
ejde-681	91	6	)	)	PUNCT
ejde-681	91	7	1	1	NUM
ejde-681	91	8	p+q−2	p+q−2	PROPN
ejde-681	91	9	[	[	X
ejde-681	91	10	f1(δ	f1(δ	X
ejde-681	91	11	)	)	PUNCT
ejde-681	91	12	]	]	PUNCT
ejde-681	92	1	−	−	PROPN
ejde-681	92	2	q−2	q−2	PROPN
ejde-681	92	3	2(p+q−2	2(p+q−2	NUM
ejde-681	92	4	)	)	PUNCT
ejde-681	92	5	{	{	PUNCT
ejde-681	93	1	[	[	X
ejde-681	93	2	f4(δ	f4(δ	NOUN
ejde-681	93	3	)	)	PUNCT
ejde-681	93	4	]	]	PUNCT
ejde-681	94	1	q	q	X
ejde-681	95	1	q−2	q−2	PROPN
ejde-681	95	2	[	[	X
ejde-681	95	3	f2(δ	f2(δ	PROPN
ejde-681	95	4	)	)	PUNCT
ejde-681	95	5	]	]	PUNCT
ejde-681	96	1	2	2	NUM
ejde-681	96	2	q−2	q−2	PROPN
ejde-681	96	3	+	+	PROPN
ejde-681	96	4	[	[	X
ejde-681	96	5	f5(δ	f5(δ	X
ejde-681	96	6	)	)	PUNCT
ejde-681	96	7	]	]	PUNCT
ejde-681	96	8	q	q	X
ejde-681	96	9	q−2	q−2	PROPN
ejde-681	96	10	[	[	X
ejde-681	96	11	f3(δ	f3(δ	NOUN
ejde-681	96	12	)	)	PUNCT
ejde-681	96	13	]	]	PUNCT
ejde-681	96	14	2	2	NUM
ejde-681	96	15	q−2	q−2	PROPN
ejde-681	96	16	}	}	PUNCT
ejde-681	96	17	q−2	q−2	PROPN
ejde-681	96	18	2(p+q−2	2(p+q−2	NUM
ejde-681	96	19	)	)	PUNCT
ejde-681	96	20	.	.	PUNCT
ejde-681	97	1	(	(	PUNCT
ejde-681	97	2	2.8	2.8	NUM
ejde-681	97	3	)	)	PUNCT
ejde-681	97	4	recall	recall	VERB
ejde-681	97	5	that	that	DET
ejde-681	97	6	f1(0	f1(0	PROPN
ejde-681	97	7	)	)	PUNCT
ejde-681	97	8	=	=	SYM
ejde-681	98	1	∥u∥2λ	∥u∥2λ	PROPN
ejde-681	98	2	,	,	PUNCT
ejde-681	98	3	f2(0	f2(0	NOUN
ejde-681	98	4	)	)	PUNCT
ejde-681	98	5	=	=	SYM
ejde-681	99	1	∫	∫	PROPN
ejde-681	99	2	ω	ω	NUM
ejde-681	99	3	|u|p|v+|q	|u|p|v+|q	PROPN
ejde-681	100	1	=	=	PRON
ejde-681	100	2	p+	p+	VERB
ejde-681	100	3	q	q	X
ejde-681	100	4	q	q	PROPN
ejde-681	100	5	∥v+∥2µ	∥v+∥2µ	PROPN
ejde-681	100	6	,	,	PUNCT
ejde-681	100	7	f3(0	f3(0	PROPN
ejde-681	100	8	)	)	PUNCT
ejde-681	101	1	=	=	SYM
ejde-681	101	2	∫	∫	PROPN
ejde-681	101	3	ω	ω	NUM
ejde-681	101	4	|u|p|v−|q	|u|p|v−|q	PROPN
ejde-681	102	1	=	=	PRON
ejde-681	102	2	p+	p+	VERB
ejde-681	102	3	q	q	X
ejde-681	102	4	q	q	ADJ
ejde-681	102	5	∥v−∥2µ	∥v−∥2µ	NOUN
ejde-681	102	6	,	,	PUNCT
ejde-681	102	7	f4(0	f4(0	NOUN
ejde-681	102	8	)	)	PUNCT
ejde-681	102	9	=	=	PUNCT
ejde-681	103	1	∥v+∥2µ	∥v+∥2µ	PROPN
ejde-681	103	2	,	,	PUNCT
ejde-681	103	3	f5(0	f5(0	ADJ
ejde-681	103	4	)	)	PUNCT
ejde-681	103	5	=	=	PUNCT
ejde-681	103	6	∥v−∥2µ	∥v−∥2µ	NOUN
ejde-681	103	7	here	here	ADV
ejde-681	103	8	we	we	PRON
ejde-681	103	9	used	use	VERB
ejde-681	103	10	that	that	SCONJ
ejde-681	103	11	(	(	PUNCT
ejde-681	103	12	u	u	NOUN
ejde-681	103	13	,	,	PUNCT
ejde-681	103	14	v	v	NOUN
ejde-681	103	15	)	)	PUNCT
ejde-681	103	16	∈	∈	NOUN
ejde-681	103	17	mλµ	mλµ	NOUN
ejde-681	103	18	to	to	PART
ejde-681	103	19	determine	determine	VERB
ejde-681	103	20	the	the	DET
ejde-681	103	21	values	value	NOUN
ejde-681	103	22	of	of	ADP
ejde-681	103	23	f2(0	f2(0	NOUN
ejde-681	103	24	)	)	PUNCT
ejde-681	103	25	and	and	CCONJ
ejde-681	103	26	f3(0	f3(0	PROPN
ejde-681	103	27	)	)	PUNCT
ejde-681	103	28	.	.	PUNCT
ejde-681	104	1	since	since	SCONJ
ejde-681	104	2	0	0	NUM
ejde-681	104	3	<	<	X
ejde-681	104	4	µ	µ	X
ejde-681	104	5	<	<	X
ejde-681	104	6	λ1(ω	λ1(ω	PROPN
ejde-681	104	7	)	)	PUNCT
ejde-681	104	8	,	,	PUNCT
ejde-681	104	9	h	h	NOUN
ejde-681	104	10	1	1	NUM
ejde-681	104	11	0	0	NUM
ejde-681	104	12	(	(	PUNCT
ejde-681	104	13	ω	ω	NOUN
ejde-681	104	14	)	)	PUNCT
ejde-681	104	15	↪	↪	PROPN
ejde-681	104	16	→	→	SYM
ejde-681	104	17	lp(ω	lp(ω	NUM
ejde-681	104	18	)	)	PUNCT
ejde-681	104	19	,	,	PUNCT
ejde-681	104	20	and	and	CCONJ
ejde-681	104	21	h1	h1	VERB
ejde-681	104	22	0	0	NUM
ejde-681	105	1	(	(	PUNCT
ejde-681	105	2	ω	ω	NOUN
ejde-681	105	3	)	)	PUNCT
ejde-681	105	4	↪	↪	PROPN
ejde-681	105	5	→	→	SYM
ejde-681	105	6	lq(ω	lq(ω	NOUN
ejde-681	105	7	)	)	PUNCT
ejde-681	105	8	by	by	ADP
ejde-681	105	9	hölder	hölder	NOUN
ejde-681	105	10	inequality	inequality	NOUN
ejde-681	105	11	’s	’	VERB
ejde-681	105	12	there	there	PRON
ejde-681	105	13	exists	exist	VERB
ejde-681	105	14	cpq	cpq	PROPN
ejde-681	105	15	=	=	SYM
ejde-681	105	16	cpq(ω	cpq(ω	PROPN
ejde-681	105	17	)	)	PUNCT
ejde-681	105	18	>	>	X
ejde-681	105	19	0	0	NUM
ejde-681	106	1	such	such	ADJ
ejde-681	106	2	that	that	SCONJ
ejde-681	106	3	(	(	PUNCT
ejde-681	106	4	1−	1−	NUM
ejde-681	106	5	µ	µ	X
ejde-681	106	6	λ1(ω	λ1(ω	NOUN
ejde-681	106	7	)	)	PUNCT
ejde-681	106	8	)	)	PUNCT
ejde-681	106	9	∥v±∥2	∥v±∥2	ADJ
ejde-681	106	10	≤	≤	NUM
ejde-681	106	11	∥v±∥2µ	∥v±∥2µ	NOUN
ejde-681	106	12	=	=	SYM
ejde-681	106	13	q	q	PROPN
ejde-681	106	14	p+	p+	ADJ
ejde-681	106	15	q	q	PROPN
ejde-681	106	16	∫	∫	PROPN
ejde-681	106	17	ω	ω	PROPN
ejde-681	106	18	|u|p|v±|q	|u|p|v±|q	PROPN
ejde-681	106	19	≤	≤	PROPN
ejde-681	106	20	cpq∥u∥p∥v±∥q	cpq∥u∥p∥v±∥q	NOUN
ejde-681	106	21	.	.	PUNCT
ejde-681	107	1	(	(	PUNCT
ejde-681	107	2	2.9	2.9	NUM
ejde-681	107	3	)	)	PUNCT
ejde-681	107	4	since	since	SCONJ
ejde-681	107	5	q	q	PROPN
ejde-681	107	6	>	>	X
ejde-681	107	7	2	2	NUM
ejde-681	107	8	and	and	CCONJ
ejde-681	107	9	∥u∥	∥u∥	NOUN
ejde-681	107	10	,	,	PUNCT
ejde-681	107	11	∥v∥	∥v∥	ADJ
ejde-681	107	12	≤	≤	ADJ
ejde-681	107	13	m1	m1	NOUN
ejde-681	107	14	,	,	PUNCT
ejde-681	107	15	expression	expression	NOUN
ejde-681	107	16	(	(	PUNCT
ejde-681	107	17	2.9	2.9	NUM
ejde-681	107	18	)	)	PUNCT
ejde-681	107	19	yields	yield	VERB
ejde-681	107	20	a	a	DET
ejde-681	107	21	constant	constant	ADJ
ejde-681	107	22	m0	m0	NOUN
ejde-681	107	23	>	>	X
ejde-681	107	24	0	0	NUM
ejde-681	107	25	such	such	ADJ
ejde-681	107	26	that	that	SCONJ
ejde-681	107	27	∥u∥	∥u∥	NOUN
ejde-681	107	28	,	,	PUNCT
ejde-681	107	29	∥v±∥2	∥v±∥2	PROPN
ejde-681	107	30	≥	≥	NUM
ejde-681	107	31	m0	m0	NOUN
ejde-681	107	32	,	,	PUNCT
ejde-681	107	33	hence	hence	ADV
ejde-681	107	34	(	(	PUNCT
ejde-681	107	35	2.3	2.3	NUM
ejde-681	107	36	)	)	PUNCT
ejde-681	107	37	is	be	AUX
ejde-681	107	38	proved	prove	VERB
ejde-681	107	39	.	.	PUNCT
ejde-681	108	1	as	as	ADP
ejde-681	108	2	∥u∥	∥u∥	NOUN
ejde-681	108	3	,	,	PUNCT
ejde-681	108	4	∥v±∥	∥v±∥	PROPN
ejde-681	108	5	∈	∈	PROPN
ejde-681	108	6	[	[	X
ejde-681	108	7	m0,m1	m0,m1	PROPN
ejde-681	108	8	]	]	X
ejde-681	108	9	,	,	PUNCT
ejde-681	108	10	we	we	PRON
ejde-681	108	11	easily	easily	ADV
ejde-681	108	12	see	see	VERB
ejde-681	108	13	from	from	ADP
ejde-681	108	14	the	the	DET
ejde-681	108	15	expressions	expression	NOUN
ejde-681	108	16	of	of	ADP
ejde-681	108	17	fi(0	fi(0	PROPN
ejde-681	108	18	)	)	PUNCT
ejde-681	108	19	that	that	SCONJ
ejde-681	108	20	there	there	ADV
ejde-681	108	21	existk1	existk1	PROPN
ejde-681	108	22	=	=	PUNCT
ejde-681	108	23	k1(a	k1(a	PROPN
ejde-681	108	24	,	,	PUNCT
ejde-681	108	25	b	b	PROPN
ejde-681	108	26	,	,	PUNCT
ejde-681	108	27	p	p	X
ejde-681	108	28	,	,	PUNCT
ejde-681	108	29	q	q	ADJ
ejde-681	108	30	,	,	PUNCT
ejde-681	108	31	λ	λ	PROPN
ejde-681	108	32	,	,	PUNCT
ejde-681	108	33	µ	µ	NUM
ejde-681	108	34	,	,	PUNCT
ejde-681	108	35	λ1(ω),m1	λ1(ω),m1	PROPN
ejde-681	108	36	,	,	PUNCT
ejde-681	108	37	n	n	CCONJ
ejde-681	108	38	)	)	PUNCT
ejde-681	108	39	>	>	PUNCT
ejde-681	108	40	0	0	PUNCT
ejde-681	109	1	and	and	CCONJ
ejde-681	109	2	k2	k2	PROPN
ejde-681	109	3	=	=	SYM
ejde-681	109	4	k2(a	k2(a	PROPN
ejde-681	109	5	,	,	PUNCT
ejde-681	109	6	b	b	NOUN
ejde-681	109	7	,	,	PUNCT
ejde-681	109	8	p	p	X
ejde-681	109	9	,	,	PUNCT
ejde-681	109	10	q	q	ADJ
ejde-681	109	11	,	,	PUNCT
ejde-681	109	12	λ	λ	PROPN
ejde-681	109	13	,	,	PUNCT
ejde-681	109	14	µ	µ	NUM
ejde-681	109	15	,	,	PUNCT
ejde-681	109	16	λ1(ω),m1	λ1(ω),m1	PROPN
ejde-681	109	17	,	,	PUNCT
ejde-681	109	18	n	n	CCONJ
ejde-681	109	19	)	)	PUNCT
ejde-681	109	20	>	>	X
ejde-681	109	21	0	0	PUNCT
ejde-681	110	1	such	such	ADJ
ejde-681	110	2	that	that	SCONJ
ejde-681	110	3	k1	k1	PROPN
ejde-681	110	4	≤	≤	PUNCT
ejde-681	110	5	fi(0	fi(0	PROPN
ejde-681	110	6	)	)	PUNCT
ejde-681	110	7	≤	≤	NOUN
ejde-681	110	8	k2	k2	NOUN
ejde-681	110	9	,	,	PUNCT
ejde-681	110	10	1	1	NUM
ejde-681	110	11	≤	≤	NUM
ejde-681	110	12	i	i	X
ejde-681	110	13	≤	≤	NOUN
ejde-681	110	14	5	5	NUM
ejde-681	110	15	.	.	PUNCT
ejde-681	110	16	(	(	PUNCT
ejde-681	110	17	2.10	2.10	NUM
ejde-681	110	18	)	)	PUNCT
ejde-681	110	19	a	a	DET
ejde-681	110	20	standard	standard	ADJ
ejde-681	110	21	calculation	calculation	NOUN
ejde-681	110	22	shows	show	VERB
ejde-681	110	23	that	that	SCONJ
ejde-681	110	24	f	f	PROPN
ejde-681	110	25	′	′	NUM
ejde-681	110	26	1(0	1(0	NUM
ejde-681	110	27	)	)	PUNCT
ejde-681	111	1	=	=	SYM
ejde-681	112	1	−	−	PROPN
ejde-681	113	1	(	(	PUNCT
ejde-681	113	2	∫	∫	PROPN
ejde-681	113	3	ω	ω	NUM
ejde-681	114	1	∇u∇z	∇u∇z	NOUN
ejde-681	114	2	−	−	PROPN
ejde-681	114	3	λuz	λuz	NOUN
ejde-681	114	4	)	)	PUNCT
ejde-681	114	5	,	,	PUNCT
ejde-681	114	6	f	f	PROPN
ejde-681	114	7	′	′	NUM
ejde-681	114	8	2(0	2(0	NUM
ejde-681	114	9	)	)	PUNCT
ejde-681	115	1	=	=	PUNCT
ejde-681	115	2	−p	−p	ADJ
ejde-681	115	3	∫	∫	PROPN
ejde-681	115	4	ω	ω	PROPN
ejde-681	115	5	|u|p−2uz|v+|q	|u|p−2uz|v+|q	PROPN
ejde-681	115	6	−	−	PROPN
ejde-681	115	7	q	q	PROPN
ejde-681	115	8	∫	∫	PROPN
ejde-681	115	9	|u|p|v+|q−1w	|u|p|v+|q−1w	NOUN
ejde-681	115	10	,	,	PUNCT
ejde-681	115	11	ejde-2024/32	ejde-2024/32	VERB
ejde-681	115	12	solutions	solution	NOUN
ejde-681	115	13	to	to	ADP
ejde-681	115	14	semi	semi	ADJ
ejde-681	115	15	-	-	ADJ
ejde-681	115	16	nodal	nodal	ADJ
ejde-681	115	17	solutions	solution	NOUN
ejde-681	115	18	5	5	NUM
ejde-681	115	19	f	f	NOUN
ejde-681	115	20	′	′	NOUN
ejde-681	115	21	3(0	3(0	NUM
ejde-681	115	22	)	)	PUNCT
ejde-681	116	1	=	=	PUNCT
ejde-681	116	2	−p	−p	ADJ
ejde-681	116	3	∫	∫	PROPN
ejde-681	116	4	ω	ω	PROPN
ejde-681	116	5	|u|p−2uz|v−|q	|u|p−2uz|v−|q	PROPN
ejde-681	116	6	−	−	PROPN
ejde-681	116	7	q	q	SYM
ejde-681	116	8	∫	∫	PROPN
ejde-681	116	9	|u|p|v−|q−1w	|u|p|v−|q−1w	PROPN
ejde-681	116	10	,	,	PUNCT
ejde-681	116	11	f	f	PROPN
ejde-681	116	12	′	′	NUM
ejde-681	116	13	4(0	4(0	NUM
ejde-681	116	14	)	)	PUNCT
ejde-681	116	15	=	=	PUNCT
ejde-681	117	1	−	−	PROPN
ejde-681	117	2	∫	∫	PROPN
ejde-681	117	3	ω	ω	PROPN
ejde-681	117	4	∇v+∇w	∇v+∇w	NOUN
ejde-681	117	5	−	−	PROPN
ejde-681	117	6	µ	µ	NUM
ejde-681	117	7	∫	∫	X
ejde-681	117	8	v+w	v+w	NUM
ejde-681	117	9	,	,	PUNCT
ejde-681	117	10	f	f	PROPN
ejde-681	117	11	′	′	NUM
ejde-681	117	12	5(0	5(0	NUM
ejde-681	117	13	)	)	PUNCT
ejde-681	117	14	=	=	PUNCT
ejde-681	118	1	−	−	PROPN
ejde-681	118	2	∫	∫	PROPN
ejde-681	118	3	ω	ω	NUM
ejde-681	118	4	∇v−∇w	∇v−∇w	PROPN
ejde-681	118	5	−	−	PROPN
ejde-681	118	6	µ	µ	PRON
ejde-681	118	7	∫	∫	NOUN
ejde-681	118	8	v−w	v−w	NOUN
ejde-681	118	9	.	.	PUNCT
ejde-681	119	1	it	it	PRON
ejde-681	119	2	is	be	AUX
ejde-681	119	3	important	important	ADJ
ejde-681	119	4	to	to	PART
ejde-681	119	5	observe	observe	VERB
ejde-681	119	6	that	that	SCONJ
ejde-681	119	7	∥z∥	∥z∥	NOUN
ejde-681	119	8	,	,	PUNCT
ejde-681	119	9	∥w∥	∥w∥	VERB
ejde-681	119	10	≤	≤	NUM
ejde-681	119	11	1	1	NUM
ejde-681	119	12	and	and	CCONJ
ejde-681	119	13	∥u∥	∥u∥	NOUN
ejde-681	119	14	,	,	PUNCT
ejde-681	119	15	∥v∥	∥v∥	ADJ
ejde-681	119	16	≤	≤	ADJ
ejde-681	119	17	m1	m1	NOUN
ejde-681	119	18	.	.	PUNCT
ejde-681	120	1	by	by	ADP
ejde-681	120	2	the	the	DET
ejde-681	120	3	sobolev	sobolev	NOUN
ejde-681	120	4	embedding	embed	VERB
ejde-681	120	5	theorems	theorem	NOUN
ejde-681	120	6	,	,	PUNCT
ejde-681	120	7	there	there	PRON
ejde-681	120	8	exists	exist	VERB
ejde-681	120	9	a	a	DET
ejde-681	120	10	constant	constant	ADJ
ejde-681	120	11	k3	k3	NOUN
ejde-681	120	12	=	=	SYM
ejde-681	120	13	k3(p	k3(p	PROPN
ejde-681	120	14	,	,	PUNCT
ejde-681	120	15	q	q	NOUN
ejde-681	120	16	,	,	PUNCT
ejde-681	120	17	λ	λ	PROPN
ejde-681	120	18	,	,	PUNCT
ejde-681	120	19	µ	µ	NUM
ejde-681	120	20	,	,	PUNCT
ejde-681	120	21	λ1(ω),m1	λ1(ω),m1	PROPN
ejde-681	120	22	,	,	PUNCT
ejde-681	120	23	n	n	CCONJ
ejde-681	120	24	)	)	PUNCT
ejde-681	120	25	>	>	X
ejde-681	120	26	0	0	PUNCT
ejde-681	121	1	such	such	ADJ
ejde-681	121	2	that	that	PRON
ejde-681	121	3	|f	|f	PROPN
ejde-681	121	4	′	′	NUM
ejde-681	122	1	i(0)|	i(0)|	SCONJ
ejde-681	122	2	≤	≤	NOUN
ejde-681	122	3	k3	k3	VERB
ejde-681	122	4	,	,	PUNCT
ejde-681	122	5	1	1	NUM
ejde-681	122	6	≤	≤	NUM
ejde-681	122	7	i	i	X
ejde-681	122	8	≤	≤	NOUN
ejde-681	122	9	5	5	NUM
ejde-681	122	10	.	.	PUNCT
ejde-681	123	1	(	(	PUNCT
ejde-681	123	2	2.11	2.11	NUM
ejde-681	123	3	)	)	PUNCT
ejde-681	123	4	from	from	ADP
ejde-681	123	5	the	the	DET
ejde-681	123	6	explicit	explicit	ADJ
ejde-681	123	7	expression	expression	NOUN
ejde-681	123	8	of	of	ADP
ejde-681	123	9	t(δ	t(δ	NOUN
ejde-681	123	10	)	)	PUNCT
ejde-681	123	11	given	give	VERB
ejde-681	123	12	by	by	ADP
ejde-681	123	13	in	in	ADP
ejde-681	123	14	(	(	PUNCT
ejde-681	123	15	2.8	2.8	NUM
ejde-681	123	16	)	)	PUNCT
ejde-681	123	17	it	it	PRON
ejde-681	123	18	follows	follow	VERB
ejde-681	123	19	that	that	SCONJ
ejde-681	123	20	for	for	ADP
ejde-681	123	21	a	a	DET
ejde-681	123	22	certain	certain	ADJ
ejde-681	123	23	ψ	ψ	X
ejde-681	123	24	∈	∈	PROPN
ejde-681	123	25	c1(r5	c1(r5	NOUN
ejde-681	123	26	+	+	NOUN
ejde-681	123	27	)	)	PUNCT
ejde-681	123	28	(	(	PUNCT
ejde-681	123	29	and	and	CCONJ
ejde-681	123	30	ψ	ψ	NOUN
ejde-681	123	31	/∈	/∈	PUNCT
ejde-681	123	32	c1(r5	c1(r5	NOUN
ejde-681	123	33	+	+	NOUN
ejde-681	123	34	)	)	PUNCT
ejde-681	123	35	)	)	PUNCT
ejde-681	124	1	we	we	PRON
ejde-681	124	2	can	can	AUX
ejde-681	124	3	write	write	VERB
ejde-681	124	4	t(δ	t(δ	PROPN
ejde-681	124	5	)	)	PUNCT
ejde-681	124	6	=	=	SYM
ejde-681	124	7	ψ(f1(δ	ψ(f1(δ	PROPN
ejde-681	124	8	)	)	PUNCT
ejde-681	124	9	,	,	PUNCT
ejde-681	124	10	.	.	PUNCT
ejde-681	124	11	.	.	PUNCT
ejde-681	125	1	.	.	PUNCT
ejde-681	126	1	,	,	PUNCT
ejde-681	126	2	f5(δ	f5(δ	X
ejde-681	126	3	)	)	PUNCT
ejde-681	126	4	)	)	PUNCT
ejde-681	126	5	.	.	PUNCT
ejde-681	127	1	therefore	therefore	ADV
ejde-681	127	2	t′(0	t′(0	NOUN
ejde-681	127	3	)	)	PUNCT
ejde-681	127	4	=	=	PUNCT
ejde-681	128	1	∑	∑	PUNCT
ejde-681	128	2	f	f	PROPN
ejde-681	128	3	′	′	NUM
ejde-681	128	4	i(0)ψxi(f1(0	i(0)ψxi(f1(0	PROPN
ejde-681	128	5	)	)	PUNCT
ejde-681	128	6	,	,	PUNCT
ejde-681	128	7	.	.	PUNCT
ejde-681	128	8	.	.	PUNCT
ejde-681	128	9	.	.	PUNCT
ejde-681	129	1	,	,	PUNCT
ejde-681	129	2	f5(0	f5(0	PROPN
ejde-681	129	3	)	)	PUNCT
ejde-681	129	4	)	)	PUNCT
ejde-681	129	5	,	,	PUNCT
ejde-681	129	6	and	and	CCONJ
ejde-681	129	7	from	from	ADP
ejde-681	129	8	this	this	DET
ejde-681	129	9	equality	equality	NOUN
ejde-681	129	10	,	,	PUNCT
ejde-681	129	11	together	together	ADV
ejde-681	129	12	with	with	ADP
ejde-681	129	13	(	(	PUNCT
ejde-681	129	14	2.10	2.10	NUM
ejde-681	129	15	)	)	PUNCT
ejde-681	129	16	and	and	CCONJ
ejde-681	129	17	(	(	PUNCT
ejde-681	129	18	2.11	2.11	NUM
ejde-681	129	19	)	)	PUNCT
ejde-681	129	20	we	we	PRON
ejde-681	129	21	conclude	conclude	VERB
ejde-681	129	22	that	that	SCONJ
ejde-681	129	23	there	there	PRON
ejde-681	129	24	exist	exist	VERB
ejde-681	129	25	ci	ci	NOUN
ejde-681	129	26	=	=	PUNCT
ejde-681	129	27	ci(p	ci(p	NOUN
ejde-681	129	28	,	,	PUNCT
ejde-681	129	29	q	q	X
ejde-681	129	30	,	,	PUNCT
ejde-681	129	31	λ	λ	PROPN
ejde-681	129	32	,	,	PUNCT
ejde-681	129	33	µ	µ	NOUN
ejde-681	129	34	,	,	PUNCT
ejde-681	129	35	λ1(ω),ω	λ1(ω),ω	NOUN
ejde-681	129	36	,	,	PUNCT
ejde-681	129	37	m1	m1	NOUN
ejde-681	129	38	,	,	PUNCT
ejde-681	129	39	n	n	CCONJ
ejde-681	129	40	)	)	PUNCT
ejde-681	130	1	>	>	X
ejde-681	130	2	0	0	PUNCT
ejde-681	131	1	such	such	ADJ
ejde-681	131	2	that	that	DET
ejde-681	131	3	|t′(0)|	|t′(0)|	NOUN
ejde-681	131	4	≤	≤	PROPN
ejde-681	131	5	c2	c2	PROPN
ejde-681	131	6	and	and	CCONJ
ejde-681	131	7	c1	c1	PROPN
ejde-681	131	8	≤	≤	PROPN
ejde-681	131	9	t(0	t(0	PROPN
ejde-681	131	10	)	)	PUNCT
ejde-681	131	11	≤	≤	PROPN
ejde-681	131	12	c2	c2	PROPN
ejde-681	131	13	.	.	PUNCT
ejde-681	132	1	the	the	DET
ejde-681	132	2	other	other	ADJ
ejde-681	132	3	inequalities	inequality	NOUN
ejde-681	132	4	can	can	AUX
ejde-681	132	5	be	be	AUX
ejde-681	132	6	derived	derive	VERB
ejde-681	132	7	from	from	ADP
ejde-681	132	8	combining	combine	VERB
ejde-681	132	9	the	the	DET
ejde-681	132	10	last	last	ADJ
ejde-681	132	11	estimates	estimate	NOUN
ejde-681	132	12	with	with	ADP
ejde-681	132	13	(	(	PUNCT
ejde-681	132	14	2.6	2.6	NUM
ejde-681	132	15	)	)	PUNCT
ejde-681	132	16	and	and	CCONJ
ejde-681	132	17	(	(	PUNCT
ejde-681	132	18	2.7	2.7	NUM
ejde-681	132	19	)	)	PUNCT
ejde-681	132	20	.	.	PUNCT
ejde-681	133	1	□	□	PUNCT
ejde-681	133	2	the	the	DET
ejde-681	133	3	following	follow	VERB
ejde-681	133	4	proposition	proposition	NOUN
ejde-681	133	5	shows	show	VERB
ejde-681	133	6	the	the	DET
ejde-681	133	7	existence	existence	NOUN
ejde-681	133	8	of	of	ADP
ejde-681	133	9	a	a	DET
ejde-681	133	10	palais	palais	ADJ
ejde-681	133	11	-	-	PUNCT
ejde-681	133	12	smale	smale	ADJ
ejde-681	133	13	sequence	sequence	NOUN
ejde-681	133	14	that	that	PRON
ejde-681	133	15	converges	converge	VERB
ejde-681	133	16	to	to	ADP
ejde-681	133	17	the	the	DET
ejde-681	133	18	infimum	infimum	NOUN
ejde-681	133	19	of	of	ADP
ejde-681	133	20	iλµ	iλµ	NOUN
ejde-681	133	21	over	over	ADP
ejde-681	133	22	mλµ.	mλµ.	NOUN
ejde-681	133	23	notice	notice	NOUN
ejde-681	133	24	also	also	ADV
ejde-681	133	25	that	that	SCONJ
ejde-681	133	26	p+	p+	VERB
ejde-681	133	27	q	q	X
ejde-681	133	28	>	>	X
ejde-681	133	29	2	2	NUM
ejde-681	133	30	and	and	CCONJ
ejde-681	133	31	iλµ(u	iλµ(u	NOUN
ejde-681	133	32	,	,	PUNCT
ejde-681	133	33	v	v	NOUN
ejde-681	133	34	)	)	PUNCT
ejde-681	133	35	=	=	PUNCT
ejde-681	134	1	(	(	PUNCT
ejde-681	134	2	1	1	NUM
ejde-681	134	3	2	2	NUM
ejde-681	134	4	−	−	NUM
ejde-681	134	5	1	1	NUM
ejde-681	134	6	p+	p+	NOUN
ejde-681	134	7	q	q	NOUN
ejde-681	134	8	)	)	PUNCT
ejde-681	134	9	(	(	PUNCT
ejde-681	134	10	∥u∥2λ	∥u∥2λ	PROPN
ejde-681	134	11	+	+	CCONJ
ejde-681	134	12	∥v∥2µ	∥v∥2µ	ADJ
ejde-681	134	13	)	)	PUNCT
ejde-681	135	1	for	for	ADP
ejde-681	135	2	all	all	DET
ejde-681	135	3	(	(	PUNCT
ejde-681	135	4	u	u	NOUN
ejde-681	135	5	,	,	PUNCT
ejde-681	135	6	v	v	NOUN
ejde-681	135	7	)	)	PUNCT
ejde-681	135	8	∈	∈	PROPN
ejde-681	135	9	mλµ.	mλµ.	NOUN
ejde-681	135	10	(	(	PUNCT
ejde-681	135	11	2.12	2.12	NUM
ejde-681	135	12	)	)	PUNCT
ejde-681	135	13	hence	hence	ADV
ejde-681	135	14	,	,	PUNCT
ejde-681	135	15	inf(u	inf(u	PROPN
ejde-681	135	16	,	,	PUNCT
ejde-681	135	17	v)∈mλµ	v)∈mλµ	NOUN
ejde-681	135	18	iλµ(u	iλµ(u	NOUN
ejde-681	135	19	,	,	PUNCT
ejde-681	135	20	v	v	NOUN
ejde-681	135	21	)	)	PUNCT
ejde-681	135	22	>	>	X
ejde-681	135	23	−∞.	−∞.	PROPN
ejde-681	135	24	in	in	ADP
ejde-681	135	25	what	what	PRON
ejde-681	135	26	follows	follow	VERB
ejde-681	135	27	,	,	PUNCT
ejde-681	135	28	we	we	PRON
ejde-681	135	29	will	will	AUX
ejde-681	135	30	use	use	VERB
ejde-681	135	31	the	the	DET
ejde-681	135	32	notation	notation	NOUN
ejde-681	135	33	∥(φ	∥(φ	NOUN
ejde-681	135	34	,	,	PUNCT
ejde-681	135	35	ϕ)∥	ϕ)∥	NOUN
ejde-681	135	36	:	:	PUNCT
ejde-681	135	37	=	=	PUNCT
ejde-681	135	38	∥φ∥+	∥φ∥+	VERB
ejde-681	135	39	∥ϕ∥	∥ϕ∥	NOUN
ejde-681	135	40	for	for	ADP
ejde-681	135	41	all	all	DET
ejde-681	135	42	φ	φ	NOUN
ejde-681	135	43	,	,	PUNCT
ejde-681	135	44	ϕ	ϕ	PROPN
ejde-681	135	45	∈	∈	PROPN
ejde-681	135	46	h1	h1	NOUN
ejde-681	135	47	0	0	NUM
ejde-681	135	48	(	(	PUNCT
ejde-681	135	49	ω	ω	NOUN
ejde-681	135	50	)	)	PUNCT
ejde-681	135	51	.	.	PUNCT
ejde-681	136	1	proposition	proposition	NOUN
ejde-681	136	2	2.2	2.2	NUM
ejde-681	136	3	.	.	PUNCT
ejde-681	137	1	let	let	AUX
ejde-681	137	2	cλµ	cλµ	VERB
ejde-681	137	3	:	:	PUNCT
ejde-681	137	4	=	=	SYM
ejde-681	137	5	inf(u	inf(u	ADJ
ejde-681	137	6	,	,	PUNCT
ejde-681	137	7	v)∈mλµ	v)∈mλµ	NOUN
ejde-681	137	8	iλµ(u	iλµ(u	NOUN
ejde-681	137	9	,	,	PUNCT
ejde-681	137	10	v	v	NOUN
ejde-681	137	11	)	)	PUNCT
ejde-681	137	12	.	.	PUNCT
ejde-681	138	1	then	then	ADV
ejde-681	138	2	there	there	PRON
ejde-681	138	3	exists	exist	VERB
ejde-681	138	4	a	a	DET
ejde-681	138	5	sequence	sequence	NOUN
ejde-681	138	6	(	(	PUNCT
ejde-681	138	7	un	un	PROPN
ejde-681	138	8	,	,	PUNCT
ejde-681	138	9	vn	vn	NOUN
ejde-681	138	10	)	)	PUNCT
ejde-681	138	11	∈	∈	NOUN
ejde-681	138	12	mλµ	mλµ	NOUN
ejde-681	138	13	such	such	ADJ
ejde-681	138	14	that	that	SCONJ
ejde-681	138	15	iλµ(un	iλµ(un	NOUN
ejde-681	138	16	,	,	PUNCT
ejde-681	138	17	vn	vn	NOUN
ejde-681	138	18	)	)	PUNCT
ejde-681	138	19	→	→	SYM
ejde-681	138	20	cλµ	cλµ	PROPN
ejde-681	138	21	and	and	CCONJ
ejde-681	138	22	i	i	PRON
ejde-681	138	23	′λµ(un	′λµ(un	PROPN
ejde-681	138	24	,	,	PUNCT
ejde-681	138	25	vn	vn	PROPN
ejde-681	138	26	)	)	PUNCT
ejde-681	138	27	→	→	SYM
ejde-681	138	28	0	0	X
ejde-681	138	29	.	.	PUNCT
ejde-681	139	1	moreover	moreover	ADV
ejde-681	139	2	,	,	PUNCT
ejde-681	139	3	there	there	PRON
ejde-681	139	4	exist	exist	VERB
ejde-681	139	5	m0,m1	m0,m1	PROPN
ejde-681	139	6	>	>	X
ejde-681	139	7	0	0	PUNCT
ejde-681	140	1	such	such	ADJ
ejde-681	140	2	that	that	DET
ejde-681	140	3	∥un∥	∥un∥	NOUN
ejde-681	140	4	,	,	PUNCT
ejde-681	140	5	∥v±n	∥v±n	PUNCT
ejde-681	140	6	∥	∥	PUNCT
ejde-681	140	7	∈	∈	PROPN
ejde-681	141	1	[	[	X
ejde-681	141	2	m0,m1	m0,m1	X
ejde-681	141	3	]	]	X
ejde-681	141	4	for	for	ADP
ejde-681	141	5	all	all	DET
ejde-681	141	6	n	n	PRON
ejde-681	141	7	∈	∈	PROPN
ejde-681	141	8	n.	n.	NOUN
ejde-681	141	9	proof	proof	NOUN
ejde-681	141	10	.	.	PUNCT
ejde-681	142	1	by	by	ADP
ejde-681	142	2	applying	apply	VERB
ejde-681	142	3	the	the	DET
ejde-681	142	4	ekeland	ekeland	NOUN
ejde-681	142	5	’s	’s	PART
ejde-681	142	6	variational	variational	ADJ
ejde-681	142	7	principle	principle	NOUN
ejde-681	142	8	[	[	X
ejde-681	142	9	12	12	NUM
ejde-681	142	10	]	]	PUNCT
ejde-681	142	11	,	,	PUNCT
ejde-681	142	12	we	we	PRON
ejde-681	142	13	construct	construct	VERB
ejde-681	142	14	a	a	DET
ejde-681	142	15	sequence	sequence	NOUN
ejde-681	142	16	(	(	PUNCT
ejde-681	142	17	un	un	PROPN
ejde-681	142	18	,	,	PUNCT
ejde-681	142	19	vn	vn	NOUN
ejde-681	142	20	)	)	PUNCT
ejde-681	142	21	∈	∈	NOUN
ejde-681	142	22	mλµ	mλµ	NOUN
ejde-681	142	23	such	such	ADJ
ejde-681	143	1	that	that	SCONJ
ejde-681	143	2	iλµ(un	iλµ(un	NOUN
ejde-681	143	3	,	,	PUNCT
ejde-681	143	4	vn	vn	NOUN
ejde-681	143	5	)	)	PUNCT
ejde-681	143	6	→	→	SYM
ejde-681	143	7	cλµ	cλµ	PROPN
ejde-681	143	8	,	,	PUNCT
ejde-681	143	9	iλµ(un	iλµ(un	NOUN
ejde-681	143	10	,	,	PUNCT
ejde-681	143	11	vn	vn	NOUN
ejde-681	143	12	)	)	PUNCT
ejde-681	143	13	<	<	X
ejde-681	143	14	iλµ(φ	iλµ(φ	PROPN
ejde-681	143	15	,	,	PUNCT
ejde-681	143	16	ϕ	ϕ	PROPN
ejde-681	143	17	)	)	PUNCT
ejde-681	143	18	+	+	CCONJ
ejde-681	143	19	1	1	NUM
ejde-681	143	20	n	n	NOUN
ejde-681	143	21	∥(un	∥(un	ADJ
ejde-681	143	22	−	−	PROPN
ejde-681	143	23	u	u	PROPN
ejde-681	143	24	,	,	PUNCT
ejde-681	143	25	vn	vn	PROPN
ejde-681	143	26	−	−	PROPN
ejde-681	143	27	v)∥	v)∥	NUM
ejde-681	143	28	,	,	PUNCT
ejde-681	143	29	∀(φ	∀(φ	NUM
ejde-681	143	30	,	,	PUNCT
ejde-681	143	31	ϕ	ϕ	NOUN
ejde-681	143	32	)	)	PUNCT
ejde-681	143	33	∈	∈	PROPN
ejde-681	143	34	mλµ.	mλµ.	NOUN
ejde-681	143	35	(	(	PUNCT
ejde-681	143	36	2.13	2.13	NUM
ejde-681	143	37	)	)	PUNCT
ejde-681	143	38	as	as	ADP
ejde-681	143	39	(	(	PUNCT
ejde-681	143	40	un	un	PROPN
ejde-681	143	41	,	,	PUNCT
ejde-681	143	42	vn	vn	NOUN
ejde-681	143	43	)	)	PUNCT
ejde-681	143	44	∈	∈	PROPN
ejde-681	143	45	mλµ	mλµ	NOUN
ejde-681	143	46	,	,	PUNCT
ejde-681	143	47	then	then	ADV
ejde-681	143	48	∥un∥2λ	∥un∥2λ	X
ejde-681	143	49	+	+	CCONJ
ejde-681	143	50	∥vn∥2µ	∥vn∥2µ	PROPN
ejde-681	143	51	=	=	SYM
ejde-681	143	52	∫	∫	PROPN
ejde-681	143	53	ω	ω	PROPN
ejde-681	143	54	|un|p|vn|q	|un|p|vn|q	PROPN
ejde-681	143	55	which	which	PRON
ejde-681	143	56	leads	lead	VERB
ejde-681	143	57	us	we	PRON
ejde-681	143	58	to	to	PART
ejde-681	143	59	p+	p+	VERB
ejde-681	143	60	q	q	NOUN
ejde-681	143	61	−	−	PROPN
ejde-681	143	62	1	1	NUM
ejde-681	143	63	2(p+	2(p+	NUM
ejde-681	143	64	q	q	NOUN
ejde-681	143	65	)	)	PUNCT
ejde-681	143	66	(	(	PUNCT
ejde-681	143	67	∥un∥2λ	∥un∥2λ	NOUN
ejde-681	143	68	+	+	CCONJ
ejde-681	143	69	∥vn∥2µ	∥vn∥2µ	NOUN
ejde-681	143	70	)	)	PUNCT
ejde-681	143	71	=	=	SYM
ejde-681	143	72	1	1	NUM
ejde-681	143	73	2	2	NUM
ejde-681	143	74	(	(	PUNCT
ejde-681	143	75	∥un∥2λ	∥un∥2λ	NOUN
ejde-681	143	76	+	+	CCONJ
ejde-681	143	77	∥vn∥2µ	∥vn∥2µ	PROPN
ejde-681	143	78	)	)	PUNCT
ejde-681	143	79	−	−	PROPN
ejde-681	143	80	1	1	NUM
ejde-681	143	81	p+	p+	VERB
ejde-681	143	82	q	q	PROPN
ejde-681	143	83	∫	∫	PROPN
ejde-681	143	84	ω	ω	PROPN
ejde-681	143	85	|un|p|vn|q	|un|p|vn|q	PROPN
ejde-681	143	86	=	=	SYM
ejde-681	143	87	iλµ(un	iλµ(un	PROPN
ejde-681	143	88	,	,	PUNCT
ejde-681	143	89	vn	vn	NOUN
ejde-681	143	90	)	)	PUNCT
ejde-681	143	91	=	=	VERB
ejde-681	143	92	cλµ	cλµ	VERB
ejde-681	143	93	+	+	CCONJ
ejde-681	143	94	on(1	on(1	NOUN
ejde-681	143	95	)	)	PUNCT
ejde-681	143	96	.	.	PUNCT
ejde-681	144	1	the	the	DET
ejde-681	144	2	above	above	ADJ
ejde-681	144	3	expression	expression	NOUN
ejde-681	144	4	and	and	CCONJ
ejde-681	144	5	(	(	PUNCT
ejde-681	144	6	2.1	2.1	NUM
ejde-681	144	7	)	)	PUNCT
ejde-681	144	8	gives	give	VERB
ejde-681	144	9	us	we	PRON
ejde-681	144	10	2cλµ	2cλµ	NUM
ejde-681	144	11	(	(	PUNCT
ejde-681	144	12	∥un∥2	∥un∥2	NUM
ejde-681	144	13	+	+	CCONJ
ejde-681	144	14	∥vn∥2	∥vn∥2	NOUN
ejde-681	144	15	)	)	PUNCT
ejde-681	144	16	≤	≤	NOUN
ejde-681	144	17	(	(	PUNCT
ejde-681	144	18	∥un∥2λ	∥un∥2λ	NOUN
ejde-681	144	19	+	+	CCONJ
ejde-681	144	20	∥vn∥2µ	∥vn∥2µ	NOUN
ejde-681	144	21	)	)	PUNCT
ejde-681	145	1	=	=	SYM
ejde-681	145	2	2(p+	2(p+	NUM
ejde-681	146	1	q)cλµ	q)cλµ	PROPN
ejde-681	146	2	p+	p+	NOUN
ejde-681	146	3	q	q	NOUN
ejde-681	146	4	−	−	PROPN
ejde-681	146	5	1	1	NUM
ejde-681	146	6	+	+	SYM
ejde-681	146	7	on(1	on(1	NOUN
ejde-681	146	8	)	)	PUNCT
ejde-681	146	9	;	;	PUNCT
ejde-681	146	10	therefore	therefore	ADV
ejde-681	146	11	(	(	PUNCT
ejde-681	146	12	un	un	PROPN
ejde-681	146	13	,	,	PUNCT
ejde-681	146	14	vn	vn	NOUN
ejde-681	146	15	)	)	PUNCT
ejde-681	146	16	is	be	AUX
ejde-681	146	17	a	a	DET
ejde-681	146	18	bounded	bounded	ADJ
ejde-681	146	19	sequence	sequence	NOUN
ejde-681	146	20	,	,	PUNCT
ejde-681	146	21	i.e	i.e	PRON
ejde-681	146	22	,	,	PUNCT
ejde-681	146	23	there	there	PRON
ejde-681	146	24	exists	exist	VERB
ejde-681	146	25	m1	m1	PROPN
ejde-681	146	26	>	>	X
ejde-681	146	27	0	0	NUM
ejde-681	146	28	such	such	ADJ
ejde-681	146	29	that	that	SCONJ
ejde-681	146	30	∥(un	∥(un	PROPN
ejde-681	146	31	,	,	PUNCT
ejde-681	146	32	vn)∥	vn)∥	NOUN
ejde-681	146	33	≤	≤	NOUN
ejde-681	146	34	m1	m1	NOUN
ejde-681	146	35	for	for	ADP
ejde-681	146	36	all	all	DET
ejde-681	146	37	n	n	PRON
ejde-681	146	38	∈	∈	PROPN
ejde-681	146	39	n	n	CCONJ
ejde-681	146	40	(	(	PUNCT
ejde-681	146	41	2.14	2.14	NUM
ejde-681	146	42	)	)	PUNCT
ejde-681	146	43	by	by	ADP
ejde-681	146	44	the	the	DET
ejde-681	146	45	riesz	riesz	PROPN
ejde-681	146	46	representation	representation	NOUN
ejde-681	146	47	theorem	theorem	NOUN
ejde-681	146	48	,	,	PUNCT
ejde-681	146	49	it	it	PRON
ejde-681	146	50	follows	follow	VERB
ejde-681	146	51	that	that	SCONJ
ejde-681	146	52	for	for	ADP
ejde-681	146	53	every	every	DET
ejde-681	146	54	fixed	fix	VERB
ejde-681	146	55	n	n	NOUN
ejde-681	146	56	∈	∈	NOUN
ejde-681	146	57	n	n	AUX
ejde-681	146	58	there	there	PRON
ejde-681	146	59	exist	exist	VERB
ejde-681	146	60	zn	zn	PROPN
ejde-681	146	61	,	,	PUNCT
ejde-681	146	62	wn	wn	PROPN
ejde-681	146	63	∈	∈	PROPN
ejde-681	146	64	h1	h1	PROPN
ejde-681	146	65	0	0	NUM
ejde-681	146	66	(	(	PUNCT
ejde-681	146	67	ω	ω	NOUN
ejde-681	146	68	)	)	PUNCT
ejde-681	146	69	such	such	ADJ
ejde-681	146	70	that	that	SCONJ
ejde-681	146	71	(	(	PUNCT
ejde-681	146	72	zn	zn	PROPN
ejde-681	146	73	,	,	PUNCT
ejde-681	146	74	wn	wn	PROPN
ejde-681	146	75	)	)	PUNCT
ejde-681	146	76	∼=	∼=	PROPN
ejde-681	146	77	i	i	PRON
ejde-681	146	78	′λµ(un	′λµ(un	NOUN
ejde-681	146	79	,	,	PUNCT
ejde-681	146	80	vn)/∥i	vn)/∥i	VERB
ejde-681	146	81	′λµ(un	′λµ(un	NOUN
ejde-681	146	82	,	,	PUNCT
ejde-681	146	83	vn)∥	vn)∥	NOUN
ejde-681	146	84	;	;	PUNCT
ejde-681	146	85	moreover	moreover	ADV
ejde-681	146	86	∥(zn	∥(zn	NOUN
ejde-681	146	87	,	,	PUNCT
ejde-681	146	88	wn)∥	wn)∥	X
ejde-681	146	89	=	=	SYM
ejde-681	146	90	1	1	NUM
ejde-681	146	91	and	and	CCONJ
ejde-681	146	92	i	i	PRON
ejde-681	146	93	′λµ(un	′λµ(un	PROPN
ejde-681	146	94	,	,	PUNCT
ejde-681	146	95	vn)(zn	vn)(zn	PROPN
ejde-681	146	96	,	,	PUNCT
ejde-681	146	97	wn	wn	PROPN
ejde-681	146	98	)	)	PUNCT
ejde-681	146	99	=	=	SYM
ejde-681	147	1	∥i	∥i	PROPN
ejde-681	147	2	′λµ(un	′λµ(un	PROPN
ejde-681	147	3	,	,	PUNCT
ejde-681	147	4	vn)∥.	vn)∥.	NUM
ejde-681	147	5	(	(	PUNCT
ejde-681	147	6	2.15	2.15	NUM
ejde-681	147	7	)	)	PUNCT
ejde-681	147	8	6	6	NUM
ejde-681	148	1	j.	j.	PROPN
ejde-681	148	2	p.	p.	PROPN
ejde-681	148	3	p.	p.	PROPN
ejde-681	148	4	d.	d.	PROPN
ejde-681	148	5	silva	silva	PROPN
ejde-681	148	6	,	,	PUNCT
ejde-681	148	7	e.	e.	PROPN
ejde-681	148	8	d.	d.	PROPN
ejde-681	148	9	silva	silva	PROPN
ejde-681	148	10	ejde-2024/32	ejde-2024/32	PROPN
ejde-681	148	11	from	from	ADP
ejde-681	148	12	now	now	ADV
ejde-681	148	13	on	on	ADV
ejde-681	148	14	,	,	PUNCT
ejde-681	148	15	we	we	PRON
ejde-681	148	16	will	will	AUX
ejde-681	148	17	assume	assume	VERB
ejde-681	148	18	that	that	SCONJ
ejde-681	148	19	n	n	PRON
ejde-681	148	20	∈	∈	PROPN
ejde-681	148	21	n	n	NOUN
ejde-681	148	22	is	be	AUX
ejde-681	148	23	fixed	fix	VERB
ejde-681	148	24	.	.	PUNCT
ejde-681	149	1	let	let	VERB
ejde-681	149	2	t(δ	t(δ	NOUN
ejde-681	149	3	)	)	PUNCT
ejde-681	149	4	:	:	PUNCT
ejde-681	150	1	=	=	X
ejde-681	150	2	tn(δ	tn(δ	NUM
ejde-681	150	3	)	)	PUNCT
ejde-681	150	4	,	,	PUNCT
ejde-681	150	5	r(δ	r(δ	PROPN
ejde-681	150	6	)	)	PUNCT
ejde-681	150	7	:	:	PUNCT
ejde-681	151	1	=	=	SYM
ejde-681	151	2	rn(δ	rn(δ	X
ejde-681	151	3	)	)	PUNCT
ejde-681	151	4	,	,	PUNCT
ejde-681	151	5	s(δ	s(δ	NOUN
ejde-681	151	6	)	)	PUNCT
ejde-681	151	7	:	:	PUNCT
ejde-681	151	8	=	=	SYM
ejde-681	151	9	sn(δ	sn(δ	X
ejde-681	151	10	)	)	PUNCT
ejde-681	151	11	be	be	AUX
ejde-681	151	12	given	give	VERB
ejde-681	151	13	as	as	SCONJ
ejde-681	151	14	stated	state	VERB
ejde-681	151	15	in	in	ADP
ejde-681	151	16	lemma	lemma	PROPN
ejde-681	151	17	2.1	2.1	NUM
ejde-681	151	18	and	and	CCONJ
ejde-681	151	19	u	u	NOUN
ejde-681	151	20	:	:	PUNCT
ejde-681	151	21	=	=	SYM
ejde-681	151	22	un	un	PROPN
ejde-681	151	23	,	,	PUNCT
ejde-681	151	24	v	v	ADP
ejde-681	151	25	:	:	PUNCT
ejde-681	151	26	=	=	SYM
ejde-681	151	27	vn	vn	X
ejde-681	151	28	,	,	PUNCT
ejde-681	151	29	z	z	NOUN
ejde-681	151	30	:	:	PUNCT
ejde-681	151	31	=	=	SYM
ejde-681	151	32	zn	zn	X
ejde-681	151	33	,	,	PUNCT
ejde-681	151	34	w	w	PROPN
ejde-681	151	35	:	:	PUNCT
ejde-681	151	36	=	=	NOUN
ejde-681	151	37	wn	wn	INTJ
ejde-681	151	38	we	we	PRON
ejde-681	151	39	will	will	AUX
ejde-681	151	40	define	define	VERB
ejde-681	151	41	(	(	PUNCT
ejde-681	151	42	u(δ	u(δ	PROPN
ejde-681	151	43	)	)	PUNCT
ejde-681	151	44	,	,	PUNCT
ejde-681	151	45	v(δ	v(δ	PROPN
ejde-681	151	46	)	)	PUNCT
ejde-681	151	47	)	)	PUNCT
ejde-681	152	1	:	:	PUNCT
ejde-681	152	2	=	=	SYM
ejde-681	152	3	(	(	PUNCT
ejde-681	152	4	un(δ	un(δ	PROPN
ejde-681	152	5	)	)	PUNCT
ejde-681	152	6	,	,	PUNCT
ejde-681	152	7	vn(δ	vn(δ	PUNCT
ejde-681	152	8	)	)	PUNCT
ejde-681	152	9	)	)	PUNCT
ejde-681	153	1	by	by	ADP
ejde-681	153	2	(	(	PUNCT
ejde-681	153	3	u(δ	u(δ	PROPN
ejde-681	153	4	)	)	PUNCT
ejde-681	153	5	,	,	PUNCT
ejde-681	153	6	v(δ	v(δ	PROPN
ejde-681	153	7	)	)	PUNCT
ejde-681	153	8	)	)	PUNCT
ejde-681	153	9	:	:	PUNCT
ejde-681	154	1	=	=	SYM
ejde-681	154	2	(	(	PUNCT
ejde-681	154	3	t(δ)[u−	t(δ)[u−	NOUN
ejde-681	154	4	δz	δz	X
ejde-681	154	5	]	]	X
ejde-681	154	6	,	,	PUNCT
ejde-681	154	7	r(δ)[v	r(δ)[v	ADJ
ejde-681	154	8	−	−	PROPN
ejde-681	154	9	δw]+	δw]+	NOUN
ejde-681	154	10	−	−	PROPN
ejde-681	154	11	s(δ)[v	s(δ)[v	NOUN
ejde-681	154	12	−	−	PROPN
ejde-681	154	13	δw]−	δw]−	NOUN
ejde-681	154	14	)	)	PUNCT
ejde-681	154	15	∈	∈	PROPN
ejde-681	154	16	mλµ.	mλµ.	NOUN
ejde-681	154	17	recall	recall	VERB
ejde-681	154	18	also	also	ADV
ejde-681	154	19	that	that	SCONJ
ejde-681	154	20	iλµ	iλµ	PROPN
ejde-681	154	21	∈	∈	PROPN
ejde-681	154	22	c1(h	c1(h	PROPN
ejde-681	154	23	,	,	PUNCT
ejde-681	154	24	r	r	NOUN
ejde-681	154	25	)	)	PUNCT
ejde-681	154	26	,	,	PUNCT
ejde-681	154	27	where	where	SCONJ
ejde-681	154	28	h	h	NOUN
ejde-681	154	29	=	=	X
ejde-681	154	30	h1	h1	PROPN
ejde-681	154	31	0	0	NUM
ejde-681	154	32	(	(	PUNCT
ejde-681	154	33	ω)×h1	ω)×h1	NUM
ejde-681	154	34	0	0	NUM
ejde-681	154	35	(	(	PUNCT
ejde-681	154	36	ω	ω	NOUN
ejde-681	154	37	)	)	PUNCT
ejde-681	154	38	.	.	PUNCT
ejde-681	155	1	setting	set	VERB
ejde-681	155	2	r(x−y	r(x−y	NOUN
ejde-681	155	3	)	)	PUNCT
ejde-681	155	4	:	:	PUNCT
ejde-681	155	5	=	=	PUNCT
ejde-681	155	6	iλµ(x	iλµ(x	NOUN
ejde-681	155	7	)	)	PUNCT
ejde-681	155	8	−	−	PROPN
ejde-681	156	1	iλµ(y	iλµ(y	PROPN
ejde-681	156	2	)	)	PUNCT
ejde-681	157	1	−	−	PROPN
ejde-681	158	1	i	i	PRON
ejde-681	158	2	′λµ(x)(x	′λµ(x)(x	PROPN
ejde-681	158	3	−	−	PROPN
ejde-681	158	4	y	y	PROPN
ejde-681	158	5	)	)	PUNCT
ejde-681	158	6	for	for	ADP
ejde-681	158	7	any	any	DET
ejde-681	158	8	x	x	NOUN
ejde-681	158	9	,	,	PUNCT
ejde-681	158	10	y	y	PROPN
ejde-681	158	11	∈	∈	PROPN
ejde-681	158	12	h	h	NOUN
ejde-681	158	13	,	,	PUNCT
ejde-681	158	14	we	we	PRON
ejde-681	158	15	have	have	AUX
ejde-681	158	16	limx→y	limx→y	VERB
ejde-681	158	17	(	(	PUNCT
ejde-681	158	18	r(x	r(x	PROPN
ejde-681	158	19	−	−	PROPN
ejde-681	158	20	y	y	PROPN
ejde-681	158	21	)	)	PUNCT
ejde-681	158	22	/∥x	/∥x	NOUN
ejde-681	159	1	−	−	PROPN
ejde-681	159	2	y	y	NOUN
ejde-681	159	3	∥	∥	PUNCT
ejde-681	159	4	)	)	PUNCT
ejde-681	160	1	=	=	PUNCT
ejde-681	160	2	0	0	X
ejde-681	160	3	.	.	PUNCT
ejde-681	160	4	since	since	SCONJ
ejde-681	160	5	limδ→0+(u(δ	limδ→0+(u(δ	PROPN
ejde-681	160	6	)	)	PUNCT
ejde-681	160	7	,	,	PUNCT
ejde-681	160	8	v(δ	v(δ	PROPN
ejde-681	160	9	)	)	PUNCT
ejde-681	160	10	)	)	PUNCT
ejde-681	161	1	=	=	PRON
ejde-681	161	2	(	(	PUNCT
ejde-681	161	3	u	u	NOUN
ejde-681	161	4	,	,	PUNCT
ejde-681	161	5	v	v	NOUN
ejde-681	161	6	)	)	PUNCT
ejde-681	161	7	,	,	PUNCT
ejde-681	161	8	it	it	PRON
ejde-681	161	9	is	be	AUX
ejde-681	161	10	not	not	PART
ejde-681	161	11	difficult	difficult	ADJ
ejde-681	161	12	to	to	PART
ejde-681	161	13	see	see	VERB
ejde-681	161	14	that	that	SCONJ
ejde-681	161	15	(	(	PUNCT
ejde-681	161	16	∥u(δ)−	∥u(δ)−	NOUN
ejde-681	161	17	u∥+	u∥+	ADJ
ejde-681	161	18	∥v(δ)−	∥v(δ)−	PROPN
ejde-681	161	19	v∥	v∥	NOUN
ejde-681	161	20	)	)	PUNCT
ejde-681	161	21	/δ	/δ	PUNCT
ejde-681	162	1	→	→	SYM
ejde-681	162	2	∥t′(0)u−	∥t′(0)u−	PROPN
ejde-681	162	3	z∥+	z∥+	NOUN
ejde-681	162	4	∥r′(0)v+	∥r′(0)v+	NOUN
ejde-681	162	5	−	−	PROPN
ejde-681	162	6	s′(0)v−	s′(0)v−	NOUN
ejde-681	162	7	−	−	PROPN
ejde-681	162	8	w∥	w∥	NOUN
ejde-681	162	9	as	as	ADP
ejde-681	162	10	δ	δ	PROPN
ejde-681	162	11	→	→	X
ejde-681	162	12	0	0	NUM
ejde-681	163	1	+	+	NOUN
ejde-681	163	2	.	.	PUNCT
ejde-681	164	1	therefore	therefore	ADV
ejde-681	164	2	,	,	PUNCT
ejde-681	164	3	o(δ	o(δ	PROPN
ejde-681	164	4	)	)	PUNCT
ejde-681	164	5	:	:	PUNCT
ejde-681	165	1	=	=	X
ejde-681	165	2	r(u(δ)−	r(u(δ)−	PUNCT
ejde-681	165	3	u	u	NOUN
ejde-681	165	4	,	,	PUNCT
ejde-681	165	5	v(δ)−	v(δ)−	PROPN
ejde-681	165	6	v	v	NOUN
ejde-681	165	7	)	)	PUNCT
ejde-681	165	8	satisfies	satisfy	VERB
ejde-681	165	9	o(δ)/δ	o(δ)/δ	PROPN
ejde-681	165	10	→	→	SYM
ejde-681	165	11	0	0	PUNCT
ejde-681	165	12	as	as	ADP
ejde-681	165	13	δ	δ	PROPN
ejde-681	165	14	→	→	X
ejde-681	165	15	0	0	NUM
ejde-681	165	16	+	+	NUM
ejde-681	165	17	and	and	CCONJ
ejde-681	165	18	iλµ(u(δ	iλµ(u(δ	NOUN
ejde-681	165	19	)	)	PUNCT
ejde-681	165	20	,	,	PUNCT
ejde-681	165	21	v(δ	v(δ	PROPN
ejde-681	165	22	)	)	PUNCT
ejde-681	165	23	)	)	PUNCT
ejde-681	166	1	=	=	SYM
ejde-681	166	2	iλµ(u	iλµ(u	NOUN
ejde-681	166	3	,	,	PUNCT
ejde-681	166	4	v	v	NOUN
ejde-681	166	5	)	)	PUNCT
ejde-681	166	6	+	+	CCONJ
ejde-681	166	7	i	i	PRON
ejde-681	166	8	′λµ(u(δ	′λµ(u(δ	NOUN
ejde-681	166	9	)	)	PUNCT
ejde-681	166	10	,	,	PUNCT
ejde-681	166	11	v(δ))(u(δ)−	v(δ))(u(δ)−	NOUN
ejde-681	166	12	u	u	NOUN
ejde-681	166	13	,	,	PUNCT
ejde-681	166	14	v(δ)−	v(δ)−	PROPN
ejde-681	166	15	v	v	NOUN
ejde-681	166	16	)	)	PUNCT
ejde-681	166	17	+	+	CCONJ
ejde-681	166	18	o(δ	o(δ	PROPN
ejde-681	166	19	)	)	PUNCT
ejde-681	166	20	(	(	PUNCT
ejde-681	166	21	2.16	2.16	NUM
ejde-681	166	22	)	)	PUNCT
ejde-681	166	23	setting	set	VERB
ejde-681	166	24	tδ(φ	tδ(φ	NUM
ejde-681	166	25	,	,	PUNCT
ejde-681	166	26	ϕ	ϕ	NOUN
ejde-681	166	27	)	)	PUNCT
ejde-681	166	28	:	:	PUNCT
ejde-681	167	1	=	=	PUNCT
ejde-681	167	2	i	i	PRON
ejde-681	167	3	′λµ(u(δ	′λµ(u(δ	VERB
ejde-681	167	4	)	)	PUNCT
ejde-681	167	5	,	,	PUNCT
ejde-681	167	6	v(δ))(φ	v(δ))(φ	PROPN
ejde-681	167	7	,	,	PUNCT
ejde-681	167	8	ϕ	ϕ	NOUN
ejde-681	167	9	)	)	PUNCT
ejde-681	167	10	,	,	PUNCT
ejde-681	167	11	by	by	ADP
ejde-681	167	12	(	(	PUNCT
ejde-681	167	13	2.13	2.13	NUM
ejde-681	167	14	)	)	PUNCT
ejde-681	167	15	and	and	CCONJ
ejde-681	167	16	(	(	PUNCT
ejde-681	167	17	2.16	2.16	NUM
ejde-681	167	18	)	)	PUNCT
ejde-681	167	19	we	we	PRON
ejde-681	167	20	have	have	VERB
ejde-681	167	21	1	1	NUM
ejde-681	167	22	n	n	NOUN
ejde-681	167	23	∥u(δ)−	∥u(δ)−	NOUN
ejde-681	167	24	u	u	NOUN
ejde-681	167	25	,	,	PUNCT
ejde-681	167	26	v(δ)−	v(δ)−	PROPN
ejde-681	167	27	v∥	v∥	PROPN
ejde-681	167	28	≥	≥	NOUN
ejde-681	167	29	iλµ(u	iλµ(u	NOUN
ejde-681	167	30	,	,	PUNCT
ejde-681	167	31	v)−	v)−	PROPN
ejde-681	167	32	iλµ(u(δ	iλµ(u(δ	NOUN
ejde-681	167	33	)	)	PUNCT
ejde-681	167	34	,	,	PUNCT
ejde-681	167	35	v(δ	v(δ	PROPN
ejde-681	167	36	)	)	PUNCT
ejde-681	167	37	)	)	PUNCT
ejde-681	168	1	=	=	SYM
ejde-681	168	2	tδ(u−	tδ(u−	X
ejde-681	168	3	u(δ	u(δ	PROPN
ejde-681	168	4	)	)	PUNCT
ejde-681	168	5	,	,	PUNCT
ejde-681	168	6	v	v	ADP
ejde-681	168	7	−	−	PROPN
ejde-681	168	8	v(δ	v(δ	PROPN
ejde-681	168	9	)	)	PUNCT
ejde-681	168	10	)	)	PUNCT
ejde-681	169	1	+	+	CCONJ
ejde-681	169	2	o(δ	o(δ	NOUN
ejde-681	169	3	)	)	PUNCT
ejde-681	169	4	=	=	PUNCT
ejde-681	170	1	=	=	PUNCT
ejde-681	170	2	(	(	PUNCT
ejde-681	170	3	1−	1−	NUM
ejde-681	170	4	t(δ))tδ(u−	t(δ))tδ(u−	PROPN
ejde-681	170	5	δz	δz	PROPN
ejde-681	170	6	,	,	PUNCT
ejde-681	170	7	0	0	NUM
ejde-681	170	8	)	)	PUNCT
ejde-681	170	9	+	+	CCONJ
ejde-681	170	10	tδ(u	tδ(u	NUM
ejde-681	170	11	,	,	PUNCT
ejde-681	170	12	0)−	0)−	NUM
ejde-681	170	13	tδ(u−	tδ(u−	NUM
ejde-681	170	14	δz	δz	NOUN
ejde-681	170	15	,	,	PUNCT
ejde-681	170	16	0	0	NUM
ejde-681	170	17	)	)	PUNCT
ejde-681	170	18	+	+	CCONJ
ejde-681	170	19	(	(	PUNCT
ejde-681	170	20	1−	1−	NUM
ejde-681	170	21	r(δ))tδ(0	r(δ))tδ(0	NOUN
ejde-681	170	22	,	,	PUNCT
ejde-681	170	23	[	[	X
ejde-681	170	24	vn	vn	X
ejde-681	170	25	−	−	PROPN
ejde-681	170	26	δw]+	δw]+	NOUN
ejde-681	170	27	)	)	PUNCT
ejde-681	170	28	+	+	CCONJ
ejde-681	170	29	tδ(0	tδ(0	NOUN
ejde-681	170	30	,	,	PUNCT
ejde-681	170	31	v	v	ADP
ejde-681	170	32	+	+	NOUN
ejde-681	170	33	)	)	PUNCT
ejde-681	170	34	−	−	PROPN
ejde-681	170	35	tδ(0	tδ(0	PROPN
ejde-681	170	36	,	,	PUNCT
ejde-681	170	37	[	[	X
ejde-681	170	38	v	v	ADP
ejde-681	170	39	−	−	PROPN
ejde-681	170	40	δw]+	δw]+	NOUN
ejde-681	170	41	)	)	PUNCT
ejde-681	170	42	−	−	PROPN
ejde-681	170	43	(	(	PUNCT
ejde-681	170	44	1−	1−	NUM
ejde-681	170	45	s(δ))tδ(0	s(δ))tδ(0	NOUN
ejde-681	170	46	,	,	PUNCT
ejde-681	170	47	[	[	X
ejde-681	170	48	v	v	ADP
ejde-681	170	49	−	−	PROPN
ejde-681	170	50	δw]−)−	δw]−)−	PROPN
ejde-681	170	51	tδ(0	tδ(0	PROPN
ejde-681	170	52	,	,	PUNCT
ejde-681	170	53	v	v	ADP
ejde-681	170	54	−	−	NOUN
ejde-681	170	55	)	)	PUNCT
ejde-681	170	56	+	+	CCONJ
ejde-681	170	57	tδ(0	tδ(0	NOUN
ejde-681	170	58	,	,	PUNCT
ejde-681	170	59	[	[	X
ejde-681	170	60	v	v	ADP
ejde-681	170	61	−	−	NOUN
ejde-681	170	62	δw]−	δw]−	NOUN
ejde-681	170	63	)	)	PUNCT
ejde-681	170	64	+	+	CCONJ
ejde-681	170	65	o(δ	o(δ	NOUN
ejde-681	170	66	)	)	PUNCT
ejde-681	170	67	=	=	PUNCT
ejde-681	170	68	(	(	PUNCT
ejde-681	170	69	1−	1−	NUM
ejde-681	170	70	t(δ))tδ(u−	t(δ))tδ(u−	PROPN
ejde-681	170	71	δz	δz	PROPN
ejde-681	170	72	,	,	PUNCT
ejde-681	170	73	0	0	NUM
ejde-681	170	74	)	)	PUNCT
ejde-681	170	75	+	+	CCONJ
ejde-681	170	76	(	(	PUNCT
ejde-681	170	77	1−	1−	NUM
ejde-681	170	78	r(δ))tδ(0	r(δ))tδ(0	NOUN
ejde-681	170	79	,	,	PUNCT
ejde-681	170	80	[	[	X
ejde-681	170	81	v	v	ADP
ejde-681	170	82	−	−	PROPN
ejde-681	170	83	δw]+	δw]+	NOUN
ejde-681	170	84	)	)	PUNCT
ejde-681	170	85	−	−	PROPN
ejde-681	171	1	(	(	PUNCT
ejde-681	171	2	1−	1−	NUM
ejde-681	171	3	s(δ))tδ(0	s(δ))tδ(0	NOUN
ejde-681	171	4	,	,	PUNCT
ejde-681	171	5	[	[	X
ejde-681	171	6	v	v	ADP
ejde-681	171	7	−	−	NOUN
ejde-681	171	8	δw]−	δw]−	NOUN
ejde-681	171	9	)	)	PUNCT
ejde-681	171	10	+	+	CCONJ
ejde-681	171	11	δtδ(z	δtδ(z	PROPN
ejde-681	171	12	,	,	PUNCT
ejde-681	171	13	w	w	NOUN
ejde-681	171	14	)	)	PUNCT
ejde-681	171	15	+	+	CCONJ
ejde-681	171	16	o(δ	o(δ	PROPN
ejde-681	171	17	)	)	PUNCT
ejde-681	171	18	.	.	PUNCT
ejde-681	172	1	as	as	ADP
ejde-681	172	2	a	a	DET
ejde-681	172	3	consequence	consequence	NOUN
ejde-681	172	4	,	,	PUNCT
ejde-681	172	5	1	1	NUM
ejde-681	172	6	n	n	PRON
ejde-681	172	7	∥u(δ)−	∥u(δ)−	NOUN
ejde-681	172	8	u	u	PROPN
ejde-681	172	9	δ	δ	PROPN
ejde-681	172	10	,	,	PUNCT
ejde-681	172	11	v(δ)−	v(δ)−	PROPN
ejde-681	172	12	v	v	NUM
ejde-681	172	13	δ	δ	PROPN
ejde-681	172	14	∥	∥	X
ejde-681	172	15	≥	≥	X
ejde-681	172	16	(	(	PUNCT
ejde-681	172	17	1−	1−	NUM
ejde-681	172	18	t(δ	t(δ	NOUN
ejde-681	172	19	)	)	PUNCT
ejde-681	172	20	δ	δ	PROPN
ejde-681	172	21	)	)	PUNCT
ejde-681	172	22	tδ(u−	tδ(u−	X
ejde-681	172	23	δz	δz	NOUN
ejde-681	172	24	,	,	PUNCT
ejde-681	172	25	0	0	NUM
ejde-681	172	26	)	)	PUNCT
ejde-681	172	27	+	+	CCONJ
ejde-681	172	28	(	(	PUNCT
ejde-681	172	29	1−	1−	NUM
ejde-681	172	30	r(δ	r(δ	NOUN
ejde-681	172	31	)	)	PUNCT
ejde-681	172	32	δ	δ	PROPN
ejde-681	172	33	)	)	PUNCT
ejde-681	172	34	tδ(0	tδ(0	PROPN
ejde-681	172	35	,	,	PUNCT
ejde-681	172	36	[	[	X
ejde-681	172	37	v	v	ADP
ejde-681	172	38	−	−	PROPN
ejde-681	172	39	δw]+	δw]+	NOUN
ejde-681	172	40	)	)	PUNCT
ejde-681	172	41	−	−	PROPN
ejde-681	173	1	(	(	PUNCT
ejde-681	173	2	1−	1−	NUM
ejde-681	173	3	s(δ	s(δ	NOUN
ejde-681	173	4	)	)	PUNCT
ejde-681	173	5	δ	δ	PROPN
ejde-681	173	6	)	)	PUNCT
ejde-681	173	7	tδ(0	tδ(0	PROPN
ejde-681	173	8	,	,	PUNCT
ejde-681	173	9	[	[	X
ejde-681	173	10	v	v	ADP
ejde-681	173	11	−	−	NOUN
ejde-681	173	12	δw]−	δw]−	NOUN
ejde-681	173	13	)	)	PUNCT
ejde-681	173	14	+	+	NUM
ejde-681	173	15	tδ(z	tδ(z	NOUN
ejde-681	173	16	,	,	PUNCT
ejde-681	173	17	w	w	NOUN
ejde-681	173	18	)	)	PUNCT
ejde-681	173	19	+	+	CCONJ
ejde-681	173	20	o(δ	o(δ	PROPN
ejde-681	173	21	)	)	PUNCT
ejde-681	173	22	δ	δ	PROPN
ejde-681	173	23	.	.	PUNCT
ejde-681	174	1	given	give	VERB
ejde-681	174	2	that	that	SCONJ
ejde-681	174	3	limδ→0	limδ→0	PROPN
ejde-681	174	4	+	+	PROPN
ejde-681	174	5	t(δ	t(δ	PROPN
ejde-681	174	6	)	)	PUNCT
ejde-681	174	7	=	=	SYM
ejde-681	175	1	limδ→0	limδ→0	NOUN
ejde-681	175	2	+	+	NOUN
ejde-681	175	3	r(δ	r(δ	PROPN
ejde-681	175	4	)	)	PUNCT
ejde-681	175	5	=	=	SYM
ejde-681	176	1	limδ→0	limδ→0	NOUN
ejde-681	176	2	+	+	NOUN
ejde-681	176	3	s(δ	s(δ	NOUN
ejde-681	176	4	)	)	PUNCT
ejde-681	176	5	=	=	SYM
ejde-681	176	6	1	1	NUM
ejde-681	176	7	,	,	PUNCT
ejde-681	176	8	taking	take	VERB
ejde-681	176	9	the	the	DET
ejde-681	176	10	limit	limit	NOUN
ejde-681	176	11	as	as	ADP
ejde-681	176	12	δ	δ	PROPN
ejde-681	176	13	→	→	X
ejde-681	176	14	0	0	PROPN
ejde-681	176	15	+	+	CCONJ
ejde-681	176	16	,	,	PUNCT
ejde-681	176	17	the	the	DET
ejde-681	176	18	above	above	ADJ
ejde-681	176	19	inequality	inequality	NOUN
ejde-681	176	20	gives	give	VERB
ejde-681	176	21	us	we	PRON
ejde-681	176	22	1	1	NUM
ejde-681	176	23	n	n	PROPN
ejde-681	176	24	∥t′(0)u−	∥t′(0)u−	PROPN
ejde-681	176	25	z	z	PROPN
ejde-681	176	26	,	,	PUNCT
ejde-681	176	27	r′(0)v+	r′(0)v+	VERB
ejde-681	176	28	−	−	PROPN
ejde-681	176	29	s′(0)v−	s′(0)v−	NOUN
ejde-681	176	30	−	−	PROPN
ejde-681	176	31	w∥	w∥	X
ejde-681	176	32	≥	≥	NOUN
ejde-681	176	33	−t′(0)t0(u	−t′(0)t0(u	ADJ
ejde-681	176	34	,	,	PUNCT
ejde-681	176	35	0)−	0)−	PUNCT
ejde-681	177	1	r′(0)t0(0	r′(0)t0(0	NOUN
ejde-681	177	2	,	,	PUNCT
ejde-681	177	3	v	v	ADP
ejde-681	177	4	+	+	NOUN
ejde-681	177	5	)	)	PUNCT
ejde-681	177	6	+	+	CCONJ
ejde-681	177	7	s′(0)t0(0	s′(0)t0(0	NOUN
ejde-681	177	8	,	,	PUNCT
ejde-681	177	9	v	v	ADP
ejde-681	177	10	−	−	NOUN
ejde-681	177	11	)	)	PUNCT
ejde-681	177	12	+	+	SYM
ejde-681	178	1	t0(z	t0(z	NUM
ejde-681	178	2	,	,	PUNCT
ejde-681	178	3	w	w	NOUN
ejde-681	178	4	)	)	PUNCT
ejde-681	178	5	=	=	VERB
ejde-681	179	1	−t′(0)t0(u	−t′(0)t0(u	ADJ
ejde-681	179	2	,	,	PUNCT
ejde-681	179	3	0)−	0)−	PUNCT
ejde-681	179	4	r′(0)t0(0	r′(0)t0(0	NOUN
ejde-681	179	5	,	,	PUNCT
ejde-681	179	6	v	v	ADP
ejde-681	179	7	+	+	NOUN
ejde-681	179	8	)	)	PUNCT
ejde-681	179	9	+	+	CCONJ
ejde-681	179	10	s′(0)t0(0	s′(0)t0(0	NOUN
ejde-681	179	11	,	,	PUNCT
ejde-681	179	12	v	v	ADP
ejde-681	179	13	−	−	NOUN
ejde-681	179	14	)	)	PUNCT
ejde-681	179	15	+	+	SYM
ejde-681	180	1	t0(z	t0(z	NUM
ejde-681	180	2	,	,	PUNCT
ejde-681	180	3	w	w	NOUN
ejde-681	180	4	)	)	PUNCT
ejde-681	180	5	.	.	PUNCT
ejde-681	181	1	(	(	PUNCT
ejde-681	181	2	2.17	2.17	NUM
ejde-681	181	3	)	)	PUNCT
ejde-681	181	4	since	since	SCONJ
ejde-681	181	5	(	(	PUNCT
ejde-681	181	6	u	u	NOUN
ejde-681	181	7	,	,	PUNCT
ejde-681	181	8	v	v	NOUN
ejde-681	181	9	)	)	PUNCT
ejde-681	181	10	∈	∈	NOUN
ejde-681	181	11	mλµ	mλµ	NOUN
ejde-681	181	12	,	,	PUNCT
ejde-681	181	13	it	it	PRON
ejde-681	181	14	follows	follow	VERB
ejde-681	181	15	that	that	SCONJ
ejde-681	181	16	t0(u	t0(u	ADV
ejde-681	181	17	,	,	PUNCT
ejde-681	181	18	0	0	NUM
ejde-681	181	19	)	)	PUNCT
ejde-681	181	20	=	=	SYM
ejde-681	181	21	t0(0	t0(0	PROPN
ejde-681	181	22	,	,	PUNCT
ejde-681	181	23	v	v	ADP
ejde-681	181	24	+	+	NOUN
ejde-681	181	25	)	)	PUNCT
ejde-681	181	26	=	=	SYM
ejde-681	181	27	t0(0	t0(0	PROPN
ejde-681	181	28	,	,	PUNCT
ejde-681	181	29	v	v	ADP
ejde-681	181	30	−	−	NOUN
ejde-681	181	31	)	)	PUNCT
ejde-681	181	32	=	=	SYM
ejde-681	181	33	0	0	NUM
ejde-681	181	34	;	;	PUNCT
ejde-681	181	35	therefore	therefore	ADV
ejde-681	181	36	,	,	PUNCT
ejde-681	181	37	from	from	ADP
ejde-681	181	38	(	(	PUNCT
ejde-681	181	39	2.17	2.17	NUM
ejde-681	181	40	)	)	PUNCT
ejde-681	181	41	and	and	CCONJ
ejde-681	181	42	(	(	PUNCT
ejde-681	181	43	2.15	2.15	NUM
ejde-681	181	44	)	)	PUNCT
ejde-681	181	45	we	we	PRON
ejde-681	181	46	conclude	conclude	VERB
ejde-681	181	47	that	that	SCONJ
ejde-681	181	48	|t′(0)|+	|t′(0)|+	PROPN
ejde-681	181	49	|r′(0)|+	|r′(0)|+	ADJ
ejde-681	181	50	|s′(0)|	|s′(0)|	NOUN
ejde-681	181	51	n	n	PROPN
ejde-681	181	52	(	(	PUNCT
ejde-681	181	53	∥u	∥u	PROPN
ejde-681	181	54	,	,	PUNCT
ejde-681	181	55	v∥+	v∥+	ADV
ejde-681	181	56	∥z	∥z	PROPN
ejde-681	181	57	,	,	PUNCT
ejde-681	181	58	w∥	w∥	NOUN
ejde-681	181	59	)	)	PUNCT
ejde-681	181	60	≥	≥	X
ejde-681	181	61	t0(z	t0(z	NOUN
ejde-681	181	62	,	,	PUNCT
ejde-681	181	63	w	w	NOUN
ejde-681	181	64	)	)	PUNCT
ejde-681	181	65	=	=	VERB
ejde-681	182	1	i	i	PRON
ejde-681	182	2	′λµ(u	′λµ(u	PROPN
ejde-681	182	3	,	,	PUNCT
ejde-681	182	4	v)(z	v)(z	NOUN
ejde-681	182	5	,	,	PUNCT
ejde-681	182	6	w	w	NOUN
ejde-681	182	7	)	)	PUNCT
ejde-681	183	1	=	=	SYM
ejde-681	183	2	∥i	∥i	PROPN
ejde-681	183	3	′λµ(u	′λµ(u	PROPN
ejde-681	183	4	,	,	PUNCT
ejde-681	183	5	v)∥.	v)∥.	NOUN
ejde-681	183	6	(	(	PUNCT
ejde-681	183	7	2.18	2.18	NUM
ejde-681	183	8	)	)	PUNCT
ejde-681	183	9	by	by	ADP
ejde-681	183	10	lemma	lemma	PROPN
ejde-681	183	11	2.1	2.1	NUM
ejde-681	183	12	there	there	ADV
ejde-681	183	13	exists	exist	VERB
ejde-681	183	14	c2	c2	PROPN
ejde-681	183	15	>	>	X
ejde-681	183	16	0	0	PUNCT
ejde-681	184	1	(	(	PUNCT
ejde-681	184	2	that	that	PRON
ejde-681	184	3	does	do	AUX
ejde-681	184	4	not	not	PART
ejde-681	184	5	depend	depend	VERB
ejde-681	184	6	on	on	ADP
ejde-681	184	7	the	the	DET
ejde-681	184	8	index	index	NOUN
ejde-681	184	9	n	n	CCONJ
ejde-681	184	10	)	)	PUNCT
ejde-681	184	11	such	such	ADJ
ejde-681	184	12	that	that	DET
ejde-681	184	13	|t′(0)|	|t′(0)|	NOUN
ejde-681	184	14	+	+	CCONJ
ejde-681	184	15	|r′(0)|	|r′(0)|	NOUN
ejde-681	184	16	+	+	CCONJ
ejde-681	184	17	|s′(0)|	|s′(0)|	NOUN
ejde-681	184	18	≤	≤	NOUN
ejde-681	184	19	3c2	3c2	NUM
ejde-681	184	20	.	.	PUNCT
ejde-681	185	1	from	from	ADP
ejde-681	185	2	(	(	PUNCT
ejde-681	185	3	2.18	2.18	NUM
ejde-681	185	4	)	)	PUNCT
ejde-681	185	5	,	,	PUNCT
ejde-681	185	6	(	(	PUNCT
ejde-681	185	7	2.14	2.14	NUM
ejde-681	185	8	)	)	PUNCT
ejde-681	185	9	and	and	CCONJ
ejde-681	185	10	(	(	PUNCT
ejde-681	185	11	2.15	2.15	NUM
ejde-681	185	12	)	)	PUNCT
ejde-681	185	13	we	we	PRON
ejde-681	185	14	obtain	obtain	VERB
ejde-681	185	15	∥i	∥i	PROPN
ejde-681	185	16	′λµ(un	′λµ(un	NOUN
ejde-681	185	17	,	,	PUNCT
ejde-681	185	18	vn)∥	vn)∥	NOUN
ejde-681	185	19	≤	≤	NUM
ejde-681	185	20	3(2m1	3(2m1	NUM
ejde-681	185	21	+1)c2	+1)c2	NOUN
ejde-681	185	22	/	/	SYM
ejde-681	185	23	n.	n.	NOUN
ejde-681	185	24	the	the	DET
ejde-681	185	25	existence	existence	NOUN
ejde-681	185	26	of	of	ADP
ejde-681	185	27	the	the	DET
ejde-681	185	28	constant	constant	ADJ
ejde-681	185	29	m0	m0	NOUN
ejde-681	185	30	>	>	X
ejde-681	185	31	0	0	NUM
ejde-681	185	32	is	be	AUX
ejde-681	185	33	guaranteed	guarantee	VERB
ejde-681	185	34	by	by	ADP
ejde-681	185	35	lemma	lemma	PROPN
ejde-681	185	36	2.1	2.1	NUM
ejde-681	185	37	.	.	PUNCT
ejde-681	186	1	this	this	PRON
ejde-681	186	2	completes	complete	VERB
ejde-681	186	3	the	the	DET
ejde-681	186	4	proof	proof	NOUN
ejde-681	186	5	.	.	PUNCT
ejde-681	187	1	□	□	PUNCT
ejde-681	187	2	ejde-2024/32	ejde-2024/32	VERB
ejde-681	187	3	solutions	solution	NOUN
ejde-681	187	4	to	to	ADP
ejde-681	187	5	semi	semi	ADJ
ejde-681	187	6	-	-	ADJ
ejde-681	187	7	nodal	nodal	ADJ
ejde-681	187	8	solutions	solution	NOUN
ejde-681	187	9	7	7	NUM
ejde-681	187	10	proof	proof	NOUN
ejde-681	187	11	of	of	ADP
ejde-681	187	12	theorem	theorem	ADJ
ejde-681	187	13	1.1	1.1	NUM
ejde-681	187	14	.	.	PUNCT
ejde-681	188	1	firstly	firstly	ADV
ejde-681	188	2	,	,	PUNCT
ejde-681	188	3	we	we	PRON
ejde-681	188	4	deal	deal	VERB
ejde-681	188	5	with	with	ADP
ejde-681	188	6	the	the	DET
ejde-681	188	7	case	case	NOUN
ejde-681	188	8	n	n	X
ejde-681	188	9	∈	∈	PROPN
ejde-681	188	10	{	{	PUNCT
ejde-681	188	11	3	3	NUM
ejde-681	188	12	,	,	PUNCT
ejde-681	188	13	4	4	NUM
ejde-681	188	14	,	,	PUNCT
ejde-681	188	15	5	5	NUM
ejde-681	188	16	}	}	PUNCT
ejde-681	188	17	.	.	PUNCT
ejde-681	189	1	let	let	VERB
ejde-681	189	2	(	(	PUNCT
ejde-681	189	3	un	un	PROPN
ejde-681	189	4	,	,	PUNCT
ejde-681	189	5	vn	vn	PROPN
ejde-681	189	6	)	)	PUNCT
ejde-681	189	7	the	the	DET
ejde-681	189	8	sequence	sequence	NOUN
ejde-681	189	9	obtained	obtain	VERB
ejde-681	189	10	in	in	ADP
ejde-681	189	11	proposition	proposition	NOUN
ejde-681	189	12	2.2	2.2	NUM
ejde-681	189	13	,	,	PUNCT
ejde-681	189	14	by	by	ADP
ejde-681	189	15	(	(	PUNCT
ejde-681	189	16	2.12	2.12	NUM
ejde-681	189	17	)	)	PUNCT
ejde-681	189	18	,	,	PUNCT
ejde-681	189	19	∥un∥	∥un∥	NUM
ejde-681	189	20	,	,	PUNCT
ejde-681	189	21	∥v±n	∥v±n	PUNCT
ejde-681	190	1	∥	∥	PUNCT
ejde-681	190	2	∈	∈	PROPN
ejde-681	191	1	[	[	X
ejde-681	191	2	m0,m1	m0,m1	PROPN
ejde-681	191	3	]	]	PUNCT
ejde-681	191	4	,	,	PUNCT
ejde-681	191	5	m0	m0	PROPN
ejde-681	191	6	>	>	X
ejde-681	191	7	0	0	PUNCT
ejde-681	191	8	and	and	CCONJ
ejde-681	191	9	λ	λ	PROPN
ejde-681	191	10	,	,	PUNCT
ejde-681	191	11	µ	µ	X
ejde-681	191	12	<	<	X
ejde-681	191	13	λ1(ω	λ1(ω	PROPN
ejde-681	191	14	)	)	PUNCT
ejde-681	191	15	,	,	PUNCT
ejde-681	191	16	we	we	PRON
ejde-681	191	17	can	can	AUX
ejde-681	191	18	deduce	deduce	VERB
ejde-681	191	19	that	that	PRON
ejde-681	191	20	cλµ	cλµ	VERB
ejde-681	191	21	>	>	X
ejde-681	191	22	0	0	X
ejde-681	191	23	.	.	PUNCT
ejde-681	192	1	it	it	PRON
ejde-681	192	2	follows	follow	VERB
ejde-681	192	3	from	from	ADP
ejde-681	192	4	the	the	DET
ejde-681	192	5	boundedness	boundedness	NOUN
ejde-681	192	6	of	of	ADP
ejde-681	192	7	un	un	PROPN
ejde-681	192	8	,	,	PUNCT
ejde-681	192	9	vn	vn	VERB
ejde-681	192	10	in	in	ADP
ejde-681	192	11	h1	h1	PROPN
ejde-681	192	12	0	0	NUM
ejde-681	192	13	(	(	PUNCT
ejde-681	192	14	ω	ω	NOUN
ejde-681	192	15	)	)	PUNCT
ejde-681	192	16	that	that	SCONJ
ejde-681	192	17	there	there	PRON
ejde-681	192	18	exists	exist	VERB
ejde-681	192	19	u0	u0	ADJ
ejde-681	192	20	,	,	PUNCT
ejde-681	192	21	v0	v0	PROPN
ejde-681	192	22	∈	∈	PROPN
ejde-681	192	23	h1	h1	PROPN
ejde-681	192	24	0	0	NUM
ejde-681	192	25	(	(	PUNCT
ejde-681	192	26	ω	ω	NOUN
ejde-681	192	27	)	)	PUNCT
ejde-681	192	28	such	such	ADJ
ejde-681	192	29	that	that	SCONJ
ejde-681	192	30	,	,	PUNCT
ejde-681	192	31	up	up	ADP
ejde-681	192	32	to	to	ADP
ejde-681	192	33	a	a	DET
ejde-681	192	34	subsequence	subsequence	NOUN
ejde-681	192	35	,	,	PUNCT
ejde-681	192	36	un	un	PROPN
ejde-681	192	37	⇀	⇀	PROPN
ejde-681	192	38	u0	u0	ADJ
ejde-681	192	39	and	and	CCONJ
ejde-681	192	40	vn	vn	VERB
ejde-681	192	41	⇀	⇀	NUM
ejde-681	192	42	v0	v0	NOUN
ejde-681	192	43	weakly	weakly	ADV
ejde-681	192	44	in	in	ADP
ejde-681	192	45	h1	h1	PROPN
ejde-681	192	46	0	0	NUM
ejde-681	192	47	(	(	PUNCT
ejde-681	192	48	ω	ω	NOUN
ejde-681	192	49	)	)	PUNCT
ejde-681	192	50	.	.	PUNCT
ejde-681	193	1	since	since	SCONJ
ejde-681	193	2	i	i	PRON
ejde-681	193	3	′λµ(un	′λµ(un	PROPN
ejde-681	193	4	,	,	PUNCT
ejde-681	193	5	vn	vn	PROPN
ejde-681	193	6	)	)	PUNCT
ejde-681	193	7	→	→	SYM
ejde-681	193	8	0	0	NUM
ejde-681	193	9	and	and	CCONJ
ejde-681	193	10	(	(	PUNCT
ejde-681	193	11	v±n	v±n	PROPN
ejde-681	193	12	−	−	NOUN
ejde-681	193	13	v±0	v±0	NUM
ejde-681	193	14	)	)	PUNCT
ejde-681	193	15	is	be	AUX
ejde-681	193	16	bounded	bound	VERB
ejde-681	193	17	in	in	ADP
ejde-681	193	18	h1	h1	PROPN
ejde-681	193	19	0	0	NUM
ejde-681	193	20	(	(	PUNCT
ejde-681	193	21	ω	ω	NOUN
ejde-681	193	22	)	)	PUNCT
ejde-681	193	23	,	,	PUNCT
ejde-681	193	24	it	it	PRON
ejde-681	193	25	follows	follow	VERB
ejde-681	193	26	that	that	SCONJ
ejde-681	193	27	∥v±n	∥v±n	NUM
ejde-681	193	28	∥2µ	∥2µ	ADV
ejde-681	194	1	−	−	PROPN
ejde-681	194	2	∫	∫	PROPN
ejde-681	194	3	ω	ω	PROPN
ejde-681	194	4	(	(	PUNCT
ejde-681	194	5	∇vn∇v±0	∇vn∇v±0	X
ejde-681	194	6	−	−	PROPN
ejde-681	194	7	µvnv	µvnv	PROPN
ejde-681	194	8	±	±	PROPN
ejde-681	194	9	0	0	NUM
ejde-681	194	10	)	)	PUNCT
ejde-681	194	11	−	−	NOUN
ejde-681	195	1	γn	γn	NOUN
ejde-681	195	2	=	=	NOUN
ejde-681	196	1	i	i	PRON
ejde-681	196	2	′λµ(un	′λµ(un	PROPN
ejde-681	196	3	,	,	PUNCT
ejde-681	196	4	vn)(0	vn)(0	PROPN
ejde-681	196	5	,	,	PUNCT
ejde-681	196	6	v	v	NOUN
ejde-681	196	7	±	±	NUM
ejde-681	196	8	n	n	DET
ejde-681	196	9	−	−	NOUN
ejde-681	196	10	v±0	v±0	NUM
ejde-681	196	11	)	)	PUNCT
ejde-681	196	12	→	→	SYM
ejde-681	196	13	0	0	NUM
ejde-681	196	14	,	,	PUNCT
ejde-681	196	15	(	(	PUNCT
ejde-681	196	16	2.19	2.19	NUM
ejde-681	196	17	)	)	PUNCT
ejde-681	196	18	where	where	SCONJ
ejde-681	196	19	γn	γn	X
ejde-681	196	20	:	:	PUNCT
ejde-681	196	21	=	=	PUNCT
ejde-681	196	22	q	q	X
ejde-681	196	23	p+	p+	ADJ
ejde-681	196	24	q	q	PROPN
ejde-681	196	25	∫	∫	PROPN
ejde-681	196	26	ω	ω	NUM
ejde-681	196	27	|un|p||v±n	|un|p||v±n	PROPN
ejde-681	196	28	|q−2v±n	|q−2v±n	PROPN
ejde-681	196	29	(	(	PUNCT
ejde-681	196	30	v	v	NOUN
ejde-681	196	31	±	±	NUM
ejde-681	196	32	n	n	PRON
ejde-681	196	33	−	−	NOUN
ejde-681	196	34	v±0	v±0	NUM
ejde-681	196	35	)	)	PUNCT
ejde-681	197	1	dx	dx	PROPN
ejde-681	197	2	.	.	PUNCT
ejde-681	198	1	then	then	ADV
ejde-681	198	2	hölder	hölder	PROPN
ejde-681	198	3	’s	’s	PART
ejde-681	198	4	inequality	inequality	NOUN
ejde-681	198	5	gives	give	VERB
ejde-681	198	6	us∣∣	us∣∣	PROPN
ejde-681	198	7	∫	∫	PROPN
ejde-681	198	8	ω	ω	NUM
ejde-681	198	9	|un|p||v±n	|un|p||v±n	PROPN
ejde-681	198	10	|q−2v±n	|q−2v±n	PROPN
ejde-681	198	11	(	(	PUNCT
ejde-681	198	12	v	v	NOUN
ejde-681	198	13	±	±	NUM
ejde-681	198	14	n	n	PRON
ejde-681	198	15	−	−	NOUN
ejde-681	198	16	v±0	v±0	NUM
ejde-681	198	17	)	)	PUNCT
ejde-681	198	18	dx	dx	PROPN
ejde-681	199	1	∣∣	∣∣	NUM
ejde-681	199	2	≤	≤	ADV
ejde-681	199	3	|un|pp+q|v±n	|un|pp+q|v±n	NOUN
ejde-681	200	1	|	|	NOUN
ejde-681	200	2	q−1	q−1	PROPN
ejde-681	200	3	p+q|v±n	p+q|v±n	NOUN
ejde-681	200	4	−	−	NUM
ejde-681	200	5	v±0	v±0	ADJ
ejde-681	200	6	|p+q	|p+q	NUM
ejde-681	200	7	.	.	PUNCT
ejde-681	201	1	(	(	PUNCT
ejde-681	201	2	2.20	2.20	NUM
ejde-681	201	3	)	)	PUNCT
ejde-681	201	4	since	since	SCONJ
ejde-681	201	5	2	2	NUM
ejde-681	201	6	<	<	X
ejde-681	201	7	p	p	NOUN
ejde-681	202	1	+	+	NOUN
ejde-681	202	2	q	q	ADJ
ejde-681	202	3	<	<	X
ejde-681	202	4	2∗	2∗	NUM
ejde-681	202	5	,	,	PUNCT
ejde-681	202	6	it	it	PRON
ejde-681	202	7	follows	follow	VERB
ejde-681	202	8	that	that	SCONJ
ejde-681	202	9	h1	h1	PROPN
ejde-681	202	10	0	0	NUM
ejde-681	202	11	(	(	PUNCT
ejde-681	202	12	ω	ω	NOUN
ejde-681	202	13	)	)	PUNCT
ejde-681	202	14	↪	↪	PROPN
ejde-681	202	15	→	→	SYM
ejde-681	202	16	lp+q(ω	lp+q(ω	PROPN
ejde-681	202	17	)	)	PUNCT
ejde-681	202	18	is	be	AUX
ejde-681	202	19	a	a	DET
ejde-681	202	20	compact	compact	ADJ
ejde-681	202	21	embedding	embed	VERB
ejde-681	202	22	;	;	PUNCT
ejde-681	202	23	therefore	therefore	ADV
ejde-681	202	24	vn	vn	PROPN
ejde-681	202	25	⇀	⇀	NUM
ejde-681	202	26	v0	v0	NOUN
ejde-681	202	27	weakly	weakly	ADV
ejde-681	202	28	in	in	ADP
ejde-681	202	29	h1	h1	PROPN
ejde-681	202	30	0	0	NUM
ejde-681	202	31	(	(	PUNCT
ejde-681	202	32	ω	ω	NOUN
ejde-681	202	33	)	)	PUNCT
ejde-681	202	34	imply	imply	VERB
ejde-681	202	35	that	that	SCONJ
ejde-681	202	36	|v±n	|v±n	ADJ
ejde-681	202	37	−	−	NUM
ejde-681	202	38	v±0	v±0	PUNCT
ejde-681	202	39	|p+q	|p+q	NUM
ejde-681	202	40	→	→	SYM
ejde-681	202	41	0	0	NUM
ejde-681	202	42	,	,	PUNCT
ejde-681	202	43	which	which	PRON
ejde-681	202	44	combined	combine	VERB
ejde-681	202	45	with	with	ADP
ejde-681	202	46	the	the	DET
ejde-681	202	47	boundedness	boundedness	NOUN
ejde-681	202	48	of	of	ADP
ejde-681	202	49	un	un	PROPN
ejde-681	202	50	,	,	PUNCT
ejde-681	202	51	vn	vn	VERB
ejde-681	202	52	in	in	ADP
ejde-681	202	53	h1	h1	PROPN
ejde-681	202	54	0	0	NUM
ejde-681	202	55	(	(	PUNCT
ejde-681	202	56	ω	ω	NOUN
ejde-681	202	57	)	)	PUNCT
ejde-681	202	58	and	and	CCONJ
ejde-681	202	59	(	(	PUNCT
ejde-681	202	60	2.20	2.20	NUM
ejde-681	202	61	)	)	PUNCT
ejde-681	202	62	gives	give	VERB
ejde-681	202	63	us	we	PRON
ejde-681	202	64	γn	γn	ADP
ejde-681	202	65	→	→	SYM
ejde-681	202	66	0	0	X
ejde-681	202	67	.	.	PUNCT
ejde-681	203	1	as∫	as∫	PROPN
ejde-681	203	2	ω	ω	PROPN
ejde-681	203	3	(	(	PUNCT
ejde-681	203	4	∇vn∇v±0	∇vn∇v±0	X
ejde-681	203	5	−	−	PROPN
ejde-681	203	6	µvnv	µvnv	PROPN
ejde-681	203	7	±	±	PROPN
ejde-681	203	8	0	0	NUM
ejde-681	203	9	)	)	PUNCT
ejde-681	203	10	dx	dx	PROPN
ejde-681	203	11	→	→	SYM
ejde-681	203	12	∥v±0	∥v±0	X
ejde-681	203	13	∥2µ	∥2µ	ADJ
ejde-681	203	14	from	from	ADP
ejde-681	203	15	(	(	PUNCT
ejde-681	203	16	2.19	2.19	NUM
ejde-681	203	17	)	)	PUNCT
ejde-681	203	18	we	we	PRON
ejde-681	203	19	obtain	obtain	VERB
ejde-681	203	20	∥v±n	∥v±n	PUNCT
ejde-681	203	21	∥2µ	∥2µ	ADJ
ejde-681	203	22	→	→	SYM
ejde-681	203	23	∥v±0	∥v±0	NOUN
ejde-681	204	1	∥2µ.	∥2µ.	NOUN
ejde-681	204	2	since	since	SCONJ
ejde-681	204	3	v±n	v±n	PROPN
ejde-681	204	4	→	→	PUNCT
ejde-681	204	5	v±0	v±0	X
ejde-681	204	6	strongly	strongly	ADV
ejde-681	204	7	in	in	ADP
ejde-681	204	8	l2(ω	l2(ω	NOUN
ejde-681	204	9	)	)	PUNCT
ejde-681	204	10	it	it	PRON
ejde-681	204	11	follows	follow	VERB
ejde-681	204	12	that	that	SCONJ
ejde-681	204	13	∥v±n	∥v±n	NUM
ejde-681	204	14	∥2	∥2	X
ejde-681	204	15	→	→	SYM
ejde-681	204	16	∥v±0	∥v±0	NUM
ejde-681	204	17	∥2	∥2	NOUN
ejde-681	204	18	and	and	CCONJ
ejde-681	204	19	therefore	therefore	ADV
ejde-681	204	20	v±n	v±n	PROPN
ejde-681	204	21	→	→	PUNCT
ejde-681	204	22	v±0	v±0	X
ejde-681	204	23	strongly	strongly	ADV
ejde-681	204	24	in	in	ADP
ejde-681	204	25	h1	h1	PROPN
ejde-681	204	26	0	0	NUM
ejde-681	204	27	(	(	PUNCT
ejde-681	204	28	ω	ω	NOUN
ejde-681	204	29	)	)	PUNCT
ejde-681	204	30	.	.	PUNCT
ejde-681	205	1	in	in	ADP
ejde-681	205	2	a	a	DET
ejde-681	205	3	completely	completely	ADV
ejde-681	205	4	analogous	analogous	ADJ
ejde-681	205	5	manner	manner	NOUN
ejde-681	205	6	,	,	PUNCT
ejde-681	205	7	we	we	PRON
ejde-681	205	8	can	can	AUX
ejde-681	205	9	conclude	conclude	VERB
ejde-681	205	10	that	that	DET
ejde-681	205	11	un	un	PROPN
ejde-681	205	12	→	→	SYM
ejde-681	205	13	u0	u0	ADJ
ejde-681	205	14	strongly	strongly	ADV
ejde-681	205	15	inh1	inh1	NOUN
ejde-681	205	16	0	0	PUNCT
ejde-681	206	1	(	(	PUNCT
ejde-681	206	2	ω	ω	NOUN
ejde-681	206	3	)	)	PUNCT
ejde-681	206	4	.	.	PUNCT
ejde-681	207	1	it	it	PRON
ejde-681	207	2	follows	follow	VERB
ejde-681	207	3	from	from	ADP
ejde-681	207	4	proposition	proposition	NOUN
ejde-681	207	5	2.2	2.2	NUM
ejde-681	207	6	that	that	SCONJ
ejde-681	207	7	iλµ(u0	iλµ(u0	PROPN
ejde-681	207	8	,	,	PUNCT
ejde-681	207	9	v0	v0	PROPN
ejde-681	207	10	)	)	PUNCT
ejde-681	207	11	=	=	PRON
ejde-681	207	12	cλµ	cλµ	PROPN
ejde-681	207	13	,	,	PUNCT
ejde-681	207	14	i	i	PRON
ejde-681	207	15	′	′	VERB
ejde-681	207	16	λµ(u0	λµ(u0	NOUN
ejde-681	207	17	,	,	PUNCT
ejde-681	207	18	v0	v0	PROPN
ejde-681	207	19	)	)	PUNCT
ejde-681	207	20	=	=	SYM
ejde-681	207	21	0	0	NUM
ejde-681	207	22	and	and	CCONJ
ejde-681	207	23	∥u0∥	∥u0∥	PROPN
ejde-681	207	24	>	>	X
ejde-681	207	25	0	0	PUNCT
ejde-681	207	26	and	and	CCONJ
ejde-681	207	27	∥v±0	∥v±0	PUNCT
ejde-681	207	28	∥	∥	PUNCT
ejde-681	207	29	>	>	X
ejde-681	208	1	0	0	X
ejde-681	208	2	.	.	PUNCT
ejde-681	208	3	notice	notice	NOUN
ejde-681	208	4	also	also	ADV
ejde-681	208	5	that	that	SCONJ
ejde-681	208	6	we	we	PRON
ejde-681	208	7	can	can	AUX
ejde-681	208	8	replaced	replace	VERB
ejde-681	208	9	un	un	PROPN
ejde-681	208	10	by	by	ADP
ejde-681	208	11	|un|	|un|	NOUN
ejde-681	208	12	and	and	CCONJ
ejde-681	208	13	still	still	ADV
ejde-681	208	14	have	have	VERB
ejde-681	208	15	iλµ(|un|	iλµ(|un|	NOUN
ejde-681	208	16	,	,	PUNCT
ejde-681	208	17	vn	vn	PROPN
ejde-681	208	18	)	)	PUNCT
ejde-681	208	19	→	→	SYM
ejde-681	208	20	cλµ.	cλµ.	NOUN
ejde-681	208	21	without	without	ADP
ejde-681	208	22	loss	loss	NOUN
ejde-681	208	23	of	of	ADP
ejde-681	208	24	generality	generality	NOUN
ejde-681	208	25	we	we	PRON
ejde-681	208	26	assume	assume	VERB
ejde-681	208	27	that	that	SCONJ
ejde-681	208	28	un	un	PROPN
ejde-681	208	29	≥	≥	PROPN
ejde-681	208	30	0	0	NUM
ejde-681	208	31	which	which	PRON
ejde-681	208	32	implies	imply	VERB
ejde-681	208	33	that	that	SCONJ
ejde-681	208	34	u0	u0	ADJ
ejde-681	208	35	≥	≥	NOUN
ejde-681	208	36	0	0	NUM
ejde-681	208	37	.	.	PUNCT
ejde-681	209	1	since	since	SCONJ
ejde-681	209	2	i	i	PRON
ejde-681	209	3	′λµ(u0	′λµ(u0	PROPN
ejde-681	209	4	,	,	PUNCT
ejde-681	209	5	v0	v0	PROPN
ejde-681	209	6	)	)	PUNCT
ejde-681	209	7	=	=	SYM
ejde-681	209	8	0	0	NUM
ejde-681	210	1	we	we	PRON
ejde-681	210	2	deduce	deduce	VERB
ejde-681	210	3	that	that	SCONJ
ejde-681	210	4	u0	u0	PROPN
ejde-681	210	5	,	,	PUNCT
ejde-681	210	6	v0	v0	PROPN
ejde-681	210	7	are	be	AUX
ejde-681	210	8	the	the	DET
ejde-681	210	9	weak	weak	ADJ
ejde-681	210	10	solutions	solution	NOUN
ejde-681	210	11	of	of	ADP
ejde-681	210	12	the	the	DET
ejde-681	210	13	system	system	NOUN
ejde-681	210	14	−∆u0	−∆u0	NOUN
ejde-681	210	15	=	=	PUNCT
ejde-681	211	1	λu0	λu0	ADJ
ejde-681	212	1	+	+	CCONJ
ejde-681	212	2	p	p	X
ejde-681	212	3	p+	p+	ADJ
ejde-681	212	4	q	q	ADJ
ejde-681	212	5	|u0|p−2u0|v0|q	|u0|p−2u0|v0|q	NOUN
ejde-681	212	6	,	,	PUNCT
ejde-681	212	7	in	in	ADP
ejde-681	212	8	ω	ω	NUM
ejde-681	212	9	,	,	PUNCT
ejde-681	212	10	−∆v0	−∆v0	NOUN
ejde-681	212	11	=	=	PUNCT
ejde-681	212	12	µv0	µv0	PROPN
ejde-681	212	13	+	+	CCONJ
ejde-681	212	14	q	q	PROPN
ejde-681	212	15	p+	p+	PROPN
ejde-681	212	16	q	q	PUNCT
ejde-681	212	17	|u0|p|v0|q−2v0	|u0|p|v0|q−2v0	PROPN
ejde-681	212	18	,	,	PUNCT
ejde-681	212	19	in	in	ADP
ejde-681	212	20	ω	ω	NUM
ejde-681	212	21	,	,	PUNCT
ejde-681	212	22	u0	u0	ADJ
ejde-681	212	23	=	=	PROPN
ejde-681	212	24	v0	v0	NOUN
ejde-681	212	25	=	=	SYM
ejde-681	212	26	0	0	NUM
ejde-681	212	27	,	,	PUNCT
ejde-681	212	28	on	on	ADP
ejde-681	212	29	∂ω	∂ω	PROPN
ejde-681	212	30	,	,	PUNCT
ejde-681	212	31	u0	u0	ADJ
ejde-681	212	32	≥	≥	NOUN
ejde-681	212	33	0	0	NUM
ejde-681	212	34	,	,	PUNCT
ejde-681	212	35	v±0	v±0	X
ejde-681	212	36	̸≡	̸≡	X
ejde-681	212	37	0	0	NUM
ejde-681	212	38	in	in	ADP
ejde-681	212	39	ω	ω	PROPN
ejde-681	212	40	.	.	PUNCT
ejde-681	213	1	(	(	PUNCT
ejde-681	213	2	2.21	2.21	NUM
ejde-681	213	3	)	)	PUNCT
ejde-681	213	4	it	it	PRON
ejde-681	213	5	follows	follow	VERB
ejde-681	213	6	from	from	ADP
ejde-681	213	7	the	the	DET
ejde-681	213	8	standard	standard	ADJ
ejde-681	213	9	theory	theory	NOUN
ejde-681	213	10	of	of	ADP
ejde-681	213	11	elliptic	elliptic	ADJ
ejde-681	213	12	regularity	regularity	NOUN
ejde-681	213	13	and	and	CCONJ
ejde-681	213	14	a	a	DET
ejde-681	213	15	bootstrap	bootstrap	NOUN
ejde-681	213	16	argument	argument	NOUN
ejde-681	213	17	that	that	SCONJ
ejde-681	213	18	u0	u0	PROPN
ejde-681	213	19	,	,	PUNCT
ejde-681	213	20	v0	v0	PROPN
ejde-681	213	21	∈	∈	PROPN
ejde-681	213	22	c2(ω	c2(ω	PRON
ejde-681	213	23	)	)	PUNCT
ejde-681	213	24	.	.	PUNCT
ejde-681	214	1	furthermore	furthermore	ADV
ejde-681	214	2	,	,	PUNCT
ejde-681	214	3	by	by	ADP
ejde-681	214	4	using	use	VERB
ejde-681	214	5	that	that	DET
ejde-681	214	6	−∆u0	−∆u0	NOUN
ejde-681	214	7	≥	≥	NOUN
ejde-681	214	8	0	0	NUM
ejde-681	214	9	in	in	ADP
ejde-681	214	10	ω	ω	PROPN
ejde-681	214	11	and	and	CCONJ
ejde-681	214	12	∥u0∥	∥u0∥	PROPN
ejde-681	214	13	>	>	X
ejde-681	214	14	0	0	NUM
ejde-681	214	15	,	,	PUNCT
ejde-681	214	16	the	the	DET
ejde-681	214	17	strong	strong	ADJ
ejde-681	214	18	maximum	maximum	ADJ
ejde-681	214	19	principle	principle	NOUN
ejde-681	214	20	implies	imply	VERB
ejde-681	214	21	that	that	SCONJ
ejde-681	214	22	u0	u0	VERB
ejde-681	214	23	>	>	X
ejde-681	214	24	0	0	PUNCT
ejde-681	214	25	in	in	ADP
ejde-681	214	26	ω	ω	PROPN
ejde-681	214	27	.	.	PUNCT
ejde-681	215	1	once	once	ADV
ejde-681	215	2	again	again	ADV
ejde-681	215	3	by	by	ADP
ejde-681	215	4	using	use	VERB
ejde-681	215	5	that	that	DET
ejde-681	215	6	p+	p+	NOUN
ejde-681	215	7	q	q	X
ejde-681	215	8	>	>	X
ejde-681	215	9	2	2	NUM
ejde-681	215	10	,	,	PUNCT
ejde-681	215	11	there	there	PRON
ejde-681	215	12	exist	exist	VERB
ejde-681	215	13	t	t	PROPN
ejde-681	215	14	,	,	PUNCT
ejde-681	215	15	s	s	PART
ejde-681	215	16	>	>	X
ejde-681	215	17	0	0	PUNCT
ejde-681	216	1	satisfying	satisfy	VERB
ejde-681	216	2	(	(	PUNCT
ejde-681	216	3	p	p	PROPN
ejde-681	216	4	p+	p+	NOUN
ejde-681	216	5	q	q	X
ejde-681	216	6	)	)	PUNCT
ejde-681	216	7	1	1	NUM
ejde-681	216	8	tp−2sq	tp−2sq	NUM
ejde-681	216	9	=	=	SYM
ejde-681	216	10	ξ	ξ	PROPN
ejde-681	216	11	and	and	CCONJ
ejde-681	216	12	(	(	PUNCT
ejde-681	216	13	q	q	X
ejde-681	216	14	p+	p+	PROPN
ejde-681	216	15	q	q	X
ejde-681	216	16	)	)	PUNCT
ejde-681	216	17	1	1	NUM
ejde-681	216	18	tpsq−2	tpsq−2	X
ejde-681	216	19	=	=	SYM
ejde-681	216	20	τ	τ	X
ejde-681	216	21	it	it	PRON
ejde-681	216	22	is	be	AUX
ejde-681	216	23	easy	easy	ADJ
ejde-681	216	24	to	to	PART
ejde-681	216	25	verify	verify	VERB
ejde-681	216	26	that	that	PRON
ejde-681	216	27	u	u	NOUN
ejde-681	216	28	=	=	PROPN
ejde-681	216	29	tu0	tu0	PROPN
ejde-681	216	30	and	and	CCONJ
ejde-681	216	31	v	v	X
ejde-681	216	32	=	=	SYM
ejde-681	216	33	sv0	sv0	ADJ
ejde-681	216	34	satisfy	satisfy	NOUN
ejde-681	216	35	(	(	PUNCT
ejde-681	216	36	1.3	1.3	NUM
ejde-681	216	37	)	)	PUNCT
ejde-681	216	38	.	.	PUNCT
ejde-681	217	1	the	the	DET
ejde-681	217	2	cases	case	NOUN
ejde-681	217	3	n	n	NOUN
ejde-681	217	4	=	=	SYM
ejde-681	217	5	1	1	NUM
ejde-681	217	6	,	,	PUNCT
ejde-681	217	7	2	2	NUM
ejde-681	217	8	with	with	ADP
ejde-681	217	9	p	p	NOUN
ejde-681	217	10	+	+	NOUN
ejde-681	217	11	q	q	ADJ
ejde-681	217	12	<	<	X
ejde-681	217	13	+	+	NOUN
ejde-681	217	14	∞	∞	PROPN
ejde-681	217	15	follows	follow	VERB
ejde-681	217	16	in	in	ADP
ejde-681	217	17	a	a	DET
ejde-681	217	18	similar	similar	ADJ
ejde-681	217	19	way	way	NOUN
ejde-681	217	20	by	by	ADP
ejde-681	217	21	using	use	VERB
ejde-681	217	22	that	that	DET
ejde-681	217	23	h1	h1	PROPN
ejde-681	217	24	0	0	NUM
ejde-681	217	25	(	(	PUNCT
ejde-681	217	26	ω	ω	NOUN
ejde-681	217	27	)	)	PUNCT
ejde-681	217	28	↪	↪	PROPN
ejde-681	217	29	→	→	SYM
ejde-681	217	30	lq(ω	lq(ω	NOUN
ejde-681	217	31	)	)	PUNCT
ejde-681	217	32	is	be	AUX
ejde-681	217	33	a	a	DET
ejde-681	217	34	compact	compact	ADJ
ejde-681	217	35	embedding	embed	VERB
ejde-681	217	36	for	for	ADP
ejde-681	217	37	each	each	DET
ejde-681	217	38	q	q	ADJ
ejde-681	217	39	≥	≥	NOUN
ejde-681	217	40	1	1	NUM
ejde-681	217	41	.	.	PUNCT
ejde-681	218	1	□	□	PUNCT
ejde-681	218	2	acknowledgements	acknowledgement	NOUN
ejde-681	218	3	.	.	PUNCT
ejde-681	219	1	e.	e.	PROPN
ejde-681	219	2	d.	d.	PROPN
ejde-681	219	3	da	da	PROPN
ejde-681	219	4	silva	silva	PROPN
ejde-681	219	5	was	be	AUX
ejde-681	219	6	partially	partially	ADV
ejde-681	219	7	supported	support	VERB
ejde-681	219	8	by	by	ADP
ejde-681	219	9	cnpq	cnpq	NOUN
ejde-681	219	10	grants	grant	NOUN
ejde-681	219	11	309026/2020	309026/2020	PROPN
ejde-681	219	12	-	-	SYM
ejde-681	219	13	2	2	NUM
ejde-681	219	14	.	.	PUNCT
ejde-681	220	1	the	the	DET
ejde-681	220	2	authors	author	NOUN
ejde-681	220	3	would	would	AUX
ejde-681	220	4	like	like	VERB
ejde-681	220	5	to	to	PART
ejde-681	220	6	express	express	VERB
ejde-681	220	7	their	their	PRON
ejde-681	220	8	sincere	sincere	ADJ
ejde-681	220	9	gratitude	gratitude	NOUN
ejde-681	220	10	to	to	ADP
ejde-681	220	11	the	the	DET
ejde-681	220	12	referees	referee	NOUN
ejde-681	220	13	for	for	ADP
ejde-681	220	14	their	their	PRON
ejde-681	220	15	carefully	carefully	ADV
ejde-681	220	16	reading	read	VERB
ejde-681	220	17	the	the	DET
ejde-681	220	18	manuscript	manuscript	NOUN
ejde-681	220	19	and	and	CCONJ
ejde-681	220	20	valuable	valuable	ADJ
ejde-681	220	21	suggestions	suggestion	NOUN
ejde-681	220	22	.	.	PUNCT
ejde-681	221	1	8	8	NUM
ejde-681	222	1	j.	j.	PROPN
ejde-681	222	2	p.	p.	PROPN
ejde-681	222	3	p.	p.	PROPN
ejde-681	223	1	d.	d.	PROPN
ejde-681	223	2	silva	silva	PROPN
ejde-681	223	3	,	,	PUNCT
ejde-681	223	4	e.	e.	PROPN
ejde-681	223	5	d.	d.	PROPN
ejde-681	223	6	silva	silva	PROPN
ejde-681	223	7	ejde-2024/32	ejde-2024/32	PROPN
ejde-681	223	8	references	reference	NOUN
ejde-681	223	9	[	[	X
ejde-681	223	10	1	1	NUM
ejde-681	223	11	]	]	PUNCT
ejde-681	223	12	a.	a.	NOUN
ejde-681	223	13	ambrosetti	ambrosetti	PROPN
ejde-681	223	14	,	,	PUNCT
ejde-681	223	15	e.	e.	PROPN
ejde-681	223	16	colorado	colorado	PROPN
ejde-681	223	17	;	;	PUNCT
ejde-681	223	18	standing	stand	VERB
ejde-681	223	19	waves	wave	NOUN
ejde-681	223	20	of	of	ADP
ejde-681	223	21	some	some	DET
ejde-681	223	22	coupled	couple	VERB
ejde-681	223	23	nonlinear	nonlinear	PROPN
ejde-681	223	24	schrödinger	schrödinger	NOUN
ejde-681	223	25	equations	equation	NOUN
ejde-681	223	26	.	.	PUNCT
ejde-681	224	1	j.	j.	PROPN
ejde-681	224	2	lond	lond	PROPN
ejde-681	224	3	.	.	PUNCT
ejde-681	225	1	math	math	PROPN
ejde-681	225	2	.	.	PUNCT
ejde-681	226	1	soc	soc	PROPN
ejde-681	226	2	.	.	PUNCT
ejde-681	227	1	(	(	PUNCT
ejde-681	227	2	2	2	NUM
ejde-681	227	3	)	)	PUNCT
ejde-681	227	4	75	75	NUM
ejde-681	227	5	(	(	PUNCT
ejde-681	227	6	2007	2007	NUM
ejde-681	227	7	)	)	PUNCT
ejde-681	227	8	,	,	PUNCT
ejde-681	227	9	no	no	INTJ
ejde-681	227	10	.	.	NOUN
ejde-681	227	11	1	1	NUM
ejde-681	227	12	,	,	PUNCT
ejde-681	227	13	67	67	NUM
ejde-681	227	14	-	-	SYM
ejde-681	227	15	82	82	NUM
ejde-681	227	16	.	.	PUNCT
ejde-681	228	1	[	[	X
ejde-681	228	2	2	2	NUM
ejde-681	228	3	]	]	X
ejde-681	228	4	n.	n.	NOUN
ejde-681	228	5	akhmediev	akhmediev	PROPN
ejde-681	228	6	,	,	PUNCT
ejde-681	228	7	a.	a.	NOUN
ejde-681	228	8	ankiewicz	ankiewicz	NOUN
ejde-681	228	9	;	;	PUNCT
ejde-681	228	10	partially	partially	ADV
ejde-681	228	11	coherent	coherent	ADJ
ejde-681	228	12	solitons	soliton	NOUN
ejde-681	228	13	on	on	ADP
ejde-681	228	14	a	a	DET
ejde-681	228	15	finite	finite	ADJ
ejde-681	228	16	background	background	NOUN
ejde-681	228	17	,	,	PUNCT
ejde-681	228	18	phys	phy	NOUN
ejde-681	228	19	.	.	PUNCT
ejde-681	229	1	rev	rev	PROPN
ejde-681	229	2	.	.	PROPN
ejde-681	229	3	lett	lett	PROPN
ejde-681	229	4	.	.	PROPN
ejde-681	229	5	,	,	PUNCT
ejde-681	229	6	82	82	NUM
ejde-681	229	7	(	(	PUNCT
ejde-681	229	8	1999	1999	NUM
ejde-681	229	9	)	)	PUNCT
ejde-681	229	10	,	,	PUNCT
ejde-681	229	11	2661	2661	NUM
ejde-681	229	12	-	-	SYM
ejde-681	229	13	2664	2664	NUM
ejde-681	229	14	.	.	PUNCT
ejde-681	230	1	[	[	X
ejde-681	230	2	3	3	X
ejde-681	230	3	]	]	X
ejde-681	230	4	t.	t.	PROPN
ejde-681	230	5	bartsch	bartsch	PROPN
ejde-681	230	6	,	,	PUNCT
ejde-681	230	7	n.	n.	NOUN
ejde-681	230	8	dancer	dancer	NOUN
ejde-681	230	9	,	,	PUNCT
ejde-681	230	10	z	z	PROPN
ejde-681	230	11	-	-	PUNCT
ejde-681	230	12	q	q	NOUN
ejde-681	230	13	,	,	PUNCT
ejde-681	230	14	wang	wang	PROPN
ejde-681	230	15	;	;	PUNCT
ejde-681	230	16	a	a	DET
ejde-681	230	17	liouville	liouville	NOUN
ejde-681	230	18	theorem	theorem	NOUN
ejde-681	230	19	,	,	PUNCT
ejde-681	230	20	a	a	PRON
ejde-681	230	21	-	-	PUNCT
ejde-681	230	22	priori	priori	ADJ
ejde-681	230	23	bounds	bound	NOUN
ejde-681	230	24	,	,	PUNCT
ejde-681	230	25	and	and	CCONJ
ejde-681	230	26	bifurcating	bifurcate	VERB
ejde-681	230	27	branches	branch	NOUN
ejde-681	230	28	of	of	ADP
ejde-681	230	29	positive	positive	ADJ
ejde-681	230	30	solutions	solution	NOUN
ejde-681	230	31	for	for	ADP
ejde-681	230	32	a	a	DET
ejde-681	230	33	nonlinear	nonlinear	ADJ
ejde-681	230	34	elliptic	elliptic	ADJ
ejde-681	230	35	system	system	NOUN
ejde-681	230	36	.	.	PUNCT
ejde-681	231	1	calc	calc	PROPN
ejde-681	231	2	.	.	PUNCT
ejde-681	232	1	var	var	PROPN
ejde-681	232	2	.	.	PUNCT
ejde-681	233	1	partial	partial	ADJ
ejde-681	233	2	differential	differential	ADJ
ejde-681	233	3	equations	equation	NOUN
ejde-681	233	4	37	37	NUM
ejde-681	233	5	(	(	PUNCT
ejde-681	233	6	2010	2010	NUM
ejde-681	233	7	)	)	PUNCT
ejde-681	233	8	,	,	PUNCT
ejde-681	233	9	no	no	INTJ
ejde-681	233	10	.	.	NOUN
ejde-681	234	1	3	3	NUM
ejde-681	234	2	-	-	SYM
ejde-681	234	3	4	4	NUM
ejde-681	234	4	,	,	PUNCT
ejde-681	234	5	345	345	NUM
ejde-681	234	6	-	-	SYM
ejde-681	234	7	361	361	NUM
ejde-681	234	8	.	.	PUNCT
ejde-681	235	1	[	[	X
ejde-681	235	2	4	4	NUM
ejde-681	235	3	]	]	X
ejde-681	235	4	g.	g.	PROPN
ejde-681	235	5	cerami	cerami	PROPN
ejde-681	235	6	,	,	PUNCT
ejde-681	235	7	s.	s.	PROPN
ejde-681	235	8	solimini	solimini	PROPN
ejde-681	235	9	,	,	PUNCT
ejde-681	235	10	m.	m.	NOUN
ejde-681	235	11	struwe	struwe	PROPN
ejde-681	235	12	;	;	PUNCT
ejde-681	235	13	some	some	DET
ejde-681	235	14	existence	existence	NOUN
ejde-681	235	15	results	result	VERB
ejde-681	235	16	for	for	ADP
ejde-681	235	17	superlinear	superlinear	ADJ
ejde-681	235	18	elliptic	elliptic	ADJ
ejde-681	235	19	boundary	boundary	ADJ
ejde-681	235	20	value	value	NOUN
ejde-681	235	21	problems	problem	NOUN
ejde-681	235	22	involving	involve	VERB
ejde-681	235	23	critical	critical	ADJ
ejde-681	235	24	exponents	exponent	NOUN
ejde-681	235	25	.	.	PUNCT
ejde-681	236	1	j.	j.	PROPN
ejde-681	236	2	funct	funct	PROPN
ejde-681	236	3	.	.	PUNCT
ejde-681	237	1	anal	anal	PROPN
ejde-681	237	2	.	.	PUNCT
ejde-681	238	1	69	69	NUM
ejde-681	238	2	(	(	PUNCT
ejde-681	238	3	1986	1986	NUM
ejde-681	238	4	)	)	PUNCT
ejde-681	238	5	,	,	PUNCT
ejde-681	239	1	no	no	INTJ
ejde-681	239	2	.	.	NOUN
ejde-681	239	3	3	3	NUM
ejde-681	239	4	,	,	PUNCT
ejde-681	239	5	289	289	NUM
ejde-681	239	6	-	-	SYM
ejde-681	239	7	306	306	NUM
ejde-681	239	8	.	.	PUNCT
ejde-681	240	1	[	[	X
ejde-681	240	2	5	5	X
ejde-681	240	3	]	]	PUNCT
ejde-681	240	4	z.	z.	PROPN
ejde-681	240	5	chen	chen	PROPN
ejde-681	240	6	,	,	PUNCT
ejde-681	240	7	c	c	PROPN
ejde-681	240	8	-	-	PUNCT
ejde-681	240	9	s.	s.	PROPN
ejde-681	240	10	lin	lin	PROPN
ejde-681	240	11	,	,	PUNCT
ejde-681	240	12	w.	w.	PROPN
ejde-681	240	13	zou	zou	PROPN
ejde-681	240	14	;	;	PUNCT
ejde-681	240	15	multiple	multiple	ADJ
ejde-681	240	16	sign	sign	NOUN
ejde-681	240	17	-	-	PUNCT
ejde-681	240	18	changing	change	VERB
ejde-681	240	19	and	and	CCONJ
ejde-681	240	20	semi	semi	ADJ
ejde-681	240	21	-	-	ADJ
ejde-681	240	22	nodal	nodal	ADJ
ejde-681	240	23	solutions	solution	NOUN
ejde-681	240	24	for	for	ADP
ejde-681	240	25	coupled	couple	VERB
ejde-681	240	26	schrödinger	schrödinger	NOUN
ejde-681	240	27	equations	equation	NOUN
ejde-681	240	28	.	.	PUNCT
ejde-681	241	1	j.	j.	PROPN
ejde-681	241	2	differential	differential	PROPN
ejde-681	241	3	equations	equation	NOUN
ejde-681	241	4	255	255	NUM
ejde-681	241	5	(	(	PUNCT
ejde-681	241	6	2013	2013	NUM
ejde-681	241	7	)	)	PUNCT
ejde-681	241	8	,	,	PUNCT
ejde-681	241	9	no	no	INTJ
ejde-681	241	10	.	.	NOUN
ejde-681	241	11	11	11	NUM
ejde-681	241	12	,	,	PUNCT
ejde-681	241	13	4289	4289	NUM
ejde-681	241	14	-	-	SYM
ejde-681	241	15	4311	4311	NUM
ejde-681	241	16	.	.	PUNCT
ejde-681	242	1	[	[	X
ejde-681	242	2	6	6	NUM
ejde-681	242	3	]	]	PUNCT
ejde-681	242	4	z.	z.	PROPN
ejde-681	242	5	chen	chen	PROPN
ejde-681	242	6	,	,	PUNCT
ejde-681	242	7	c.-s	c.-	NOUN
ejde-681	242	8	.	.	PUNCT
ejde-681	243	1	lin	lin	PROPN
ejde-681	243	2	,	,	PUNCT
ejde-681	243	3	w.	w.	PROPN
ejde-681	243	4	zou	zou	PROPN
ejde-681	243	5	;	;	PUNCT
ejde-681	243	6	infinitely	infinitely	ADV
ejde-681	243	7	many	many	ADJ
ejde-681	243	8	sign	sign	NOUN
ejde-681	243	9	-	-	PUNCT
ejde-681	243	10	changing	change	VERB
ejde-681	243	11	and	and	CCONJ
ejde-681	243	12	semi	semi	ADJ
ejde-681	243	13	-	-	ADJ
ejde-681	243	14	nodal	nodal	ADJ
ejde-681	243	15	solutions	solution	NOUN
ejde-681	243	16	for	for	ADP
ejde-681	243	17	a	a	DET
ejde-681	243	18	nonlinear	nonlinear	ADJ
ejde-681	243	19	schrödinger	schrödinger	NOUN
ejde-681	243	20	system	system	NOUN
ejde-681	243	21	.	.	PUNCT
ejde-681	244	1	ann	ann	PROPN
ejde-681	244	2	.	.	PROPN
ejde-681	244	3	sc	sc	PROPN
ejde-681	244	4	.	.	PROPN
ejde-681	244	5	norm	norm	PROPN
ejde-681	244	6	.	.	PUNCT
ejde-681	245	1	super	super	ADJ
ejde-681	245	2	.	.	PUNCT
ejde-681	245	3	pisa	pisa	PROPN
ejde-681	245	4	cl	cl	PROPN
ejde-681	245	5	.	.	PUNCT
ejde-681	246	1	sci	sci	PROPN
ejde-681	246	2	.	.	PUNCT
ejde-681	247	1	(	(	PUNCT
ejde-681	247	2	5	5	NUM
ejde-681	247	3	)	)	SYM
ejde-681	247	4	15	15	NUM
ejde-681	247	5	(	(	PUNCT
ejde-681	247	6	2016	2016	NUM
ejde-681	247	7	)	)	PUNCT
ejde-681	247	8	,	,	PUNCT
ejde-681	247	9	859	859	NUM
ejde-681	247	10	-	-	SYM
ejde-681	247	11	897	897	NUM
ejde-681	247	12	[	[	X
ejde-681	247	13	7	7	NUM
ejde-681	247	14	]	]	PUNCT
ejde-681	247	15	z.	z.	PROPN
ejde-681	247	16	chen	chen	PROPN
ejde-681	247	17	,	,	PUNCT
ejde-681	247	18	c.-s	c.-	NOUN
ejde-681	247	19	.	.	PUNCT
ejde-681	248	1	lin	lin	PROPN
ejde-681	248	2	,	,	PUNCT
ejde-681	248	3	w.	w.	PROPN
ejde-681	248	4	zou	zou	PROPN
ejde-681	248	5	;	;	PUNCT
ejde-681	248	6	sign	sign	NOUN
ejde-681	248	7	-	-	PUNCT
ejde-681	248	8	changing	change	VERB
ejde-681	248	9	solutions	solution	NOUN
ejde-681	248	10	and	and	CCONJ
ejde-681	248	11	phase	phase	NOUN
ejde-681	248	12	separation	separation	NOUN
ejde-681	248	13	for	for	ADP
ejde-681	248	14	an	an	DET
ejde-681	248	15	elliptic	elliptic	ADJ
ejde-681	248	16	system	system	NOUN
ejde-681	248	17	with	with	ADP
ejde-681	248	18	critical	critical	ADJ
ejde-681	248	19	exponent	exponent	NOUN
ejde-681	248	20	.	.	PUNCT
ejde-681	249	1	comm	comm	NOUN
ejde-681	249	2	.	.	PUNCT
ejde-681	250	1	partial	partial	ADJ
ejde-681	250	2	differential	differential	ADJ
ejde-681	250	3	equations	equation	NOUN
ejde-681	250	4	39	39	NUM
ejde-681	250	5	(	(	PUNCT
ejde-681	250	6	2014	2014	NUM
ejde-681	250	7	)	)	PUNCT
ejde-681	250	8	,	,	PUNCT
ejde-681	250	9	no	no	INTJ
ejde-681	250	10	.	.	NOUN
ejde-681	250	11	10	10	NUM
ejde-681	250	12	,	,	PUNCT
ejde-681	250	13	18271859	18271859	NUM
ejde-681	250	14	.	.	PUNCT
ejde-681	251	1	[	[	X
ejde-681	251	2	8	8	NUM
ejde-681	251	3	]	]	PUNCT
ejde-681	251	4	z.	z.	PROPN
ejde-681	251	5	chen	chen	PROPN
ejde-681	251	6	,	,	PUNCT
ejde-681	251	7	c.-s	c.-	NOUN
ejde-681	251	8	.	.	PUNCT
ejde-681	252	1	lin	lin	PROPN
ejde-681	252	2	,	,	PUNCT
ejde-681	252	3	w.	w.	PROPN
ejde-681	252	4	zou	zou	PROPN
ejde-681	252	5	;	;	PUNCT
ejde-681	252	6	infinitely	infinitely	ADV
ejde-681	252	7	many	many	ADJ
ejde-681	252	8	sign	sign	NOUN
ejde-681	252	9	-	-	PUNCT
ejde-681	252	10	changing	change	VERB
ejde-681	252	11	and	and	CCONJ
ejde-681	252	12	semi	semi	ADJ
ejde-681	252	13	-	-	ADJ
ejde-681	252	14	nodal	nodal	ADJ
ejde-681	252	15	solutions	solution	NOUN
ejde-681	252	16	for	for	ADP
ejde-681	252	17	a	a	DET
ejde-681	252	18	nonlinear	nonlinear	ADJ
ejde-681	252	19	schrödinger	schrödinger	NOUN
ejde-681	252	20	system	system	NOUN
ejde-681	252	21	.	.	PUNCT
ejde-681	253	1	ann	ann	PROPN
ejde-681	253	2	.	.	PROPN
ejde-681	253	3	sc	sc	PROPN
ejde-681	253	4	.	.	PROPN
ejde-681	253	5	norm	norm	PROPN
ejde-681	253	6	.	.	PUNCT
ejde-681	254	1	super	super	ADJ
ejde-681	254	2	.	.	PUNCT
ejde-681	254	3	pisa	pisa	PROPN
ejde-681	254	4	cl	cl	PROPN
ejde-681	254	5	.	.	PUNCT
ejde-681	255	1	sci	sci	PROPN
ejde-681	255	2	.	.	PUNCT
ejde-681	256	1	(	(	PUNCT
ejde-681	256	2	5	5	NUM
ejde-681	256	3	)	)	SYM
ejde-681	256	4	15	15	NUM
ejde-681	256	5	(	(	PUNCT
ejde-681	256	6	2016	2016	NUM
ejde-681	256	7	)	)	PUNCT
ejde-681	256	8	,	,	PUNCT
ejde-681	256	9	859	859	NUM
ejde-681	256	10	-	-	SYM
ejde-681	256	11	897	897	NUM
ejde-681	256	12	.	.	PUNCT
ejde-681	257	1	[	[	X
ejde-681	257	2	9	9	NUM
ejde-681	257	3	]	]	PUNCT
ejde-681	257	4	z.	z.	PROPN
ejde-681	257	5	chen	chen	PROPN
ejde-681	257	6	,	,	PUNCT
ejde-681	257	7	c.-s	c.-	NOUN
ejde-681	257	8	.	.	PUNCT
ejde-681	258	1	lin	lin	PROPN
ejde-681	258	2	,	,	PUNCT
ejde-681	258	3	w.	w.	PROPN
ejde-681	258	4	zou	zou	PROPN
ejde-681	258	5	;	;	PUNCT
ejde-681	258	6	multiple	multiple	ADJ
ejde-681	258	7	sign	sign	NOUN
ejde-681	258	8	-	-	PUNCT
ejde-681	258	9	changing	change	VERB
ejde-681	258	10	and	and	CCONJ
ejde-681	258	11	semi	semi	ADJ
ejde-681	258	12	-	-	ADJ
ejde-681	258	13	nodal	nodal	ADJ
ejde-681	258	14	solutions	solution	NOUN
ejde-681	258	15	for	for	ADP
ejde-681	258	16	coupled	couple	VERB
ejde-681	258	17	schrödinger	schrödinger	NOUN
ejde-681	258	18	equations	equation	NOUN
ejde-681	258	19	.	.	PUNCT
ejde-681	259	1	j.	j.	PROPN
ejde-681	259	2	differential	differential	PROPN
ejde-681	259	3	equations	equation	NOUN
ejde-681	259	4	255	255	NUM
ejde-681	259	5	(	(	PUNCT
ejde-681	259	6	2013	2013	NUM
ejde-681	259	7	)	)	PUNCT
ejde-681	259	8	,	,	PUNCT
ejde-681	259	9	no	no	INTJ
ejde-681	259	10	.	.	NOUN
ejde-681	259	11	11	11	NUM
ejde-681	259	12	,	,	PUNCT
ejde-681	259	13	4289	4289	NUM
ejde-681	259	14	-	-	SYM
ejde-681	259	15	4311	4311	NUM
ejde-681	259	16	.	.	PUNCT
ejde-681	260	1	[	[	X
ejde-681	260	2	10	10	NUM
ejde-681	260	3	]	]	PUNCT
ejde-681	260	4	z.	z.	PROPN
ejde-681	260	5	chen	chen	PROPN
ejde-681	260	6	,	,	PUNCT
ejde-681	260	7	w.	w.	PROPN
ejde-681	260	8	zou	zou	PROPN
ejde-681	260	9	;	;	PUNCT
ejde-681	260	10	an	an	DET
ejde-681	260	11	optimal	optimal	ADJ
ejde-681	260	12	constant	constant	NOUN
ejde-681	260	13	for	for	ADP
ejde-681	260	14	the	the	DET
ejde-681	260	15	existence	existence	NOUN
ejde-681	260	16	of	of	ADP
ejde-681	260	17	least	least	ADJ
ejde-681	260	18	energy	energy	NOUN
ejde-681	260	19	solutions	solution	NOUN
ejde-681	260	20	of	of	ADP
ejde-681	260	21	a	a	DET
ejde-681	260	22	coupled	couple	VERB
ejde-681	260	23	schrödinger	schrödinger	NOUN
ejde-681	260	24	system	system	NOUN
ejde-681	260	25	.	.	PUNCT
ejde-681	261	1	calc	calc	PROPN
ejde-681	261	2	.	.	PUNCT
ejde-681	262	1	var	var	PROPN
ejde-681	262	2	.	.	PUNCT
ejde-681	263	1	partial	partial	ADJ
ejde-681	263	2	differential	differential	ADJ
ejde-681	263	3	equations	equation	NOUN
ejde-681	263	4	48	48	NUM
ejde-681	263	5	(	(	PUNCT
ejde-681	263	6	2013	2013	NUM
ejde-681	263	7	)	)	PUNCT
ejde-681	263	8	,	,	PUNCT
ejde-681	263	9	no	no	INTJ
ejde-681	263	10	.	.	NOUN
ejde-681	264	1	3	3	NUM
ejde-681	264	2	-	-	SYM
ejde-681	264	3	4	4	NUM
ejde-681	264	4	,	,	PUNCT
ejde-681	264	5	695	695	NUM
ejde-681	264	6	-	-	SYM
ejde-681	264	7	711	711	NUM
ejde-681	264	8	.	.	PUNCT
ejde-681	265	1	[	[	X
ejde-681	265	2	11	11	NUM
ejde-681	265	3	]	]	PUNCT
ejde-681	265	4	m.	m.	NOUN
ejde-681	265	5	clapp	clapp	PROPN
ejde-681	265	6	,	,	PUNCT
ejde-681	265	7	m.	m.	NOUN
ejde-681	265	8	soares	soares	PROPN
ejde-681	265	9	;	;	PUNCT
ejde-681	265	10	energy	energy	NOUN
ejde-681	265	11	estimates	estimate	NOUN
ejde-681	265	12	for	for	ADP
ejde-681	265	13	seminodal	seminodal	NOUN
ejde-681	265	14	solutions	solution	NOUN
ejde-681	265	15	to	to	ADP
ejde-681	265	16	an	an	DET
ejde-681	265	17	elliptic	elliptic	ADJ
ejde-681	265	18	system	system	NOUN
ejde-681	265	19	with	with	ADP
ejde-681	265	20	mixed	mixed	ADJ
ejde-681	265	21	couplings	coupling	NOUN
ejde-681	265	22	.	.	PUNCT
ejde-681	266	1	nodea	nodea	ADJ
ejde-681	266	2	nonlinear	nonlinear	PROPN
ejde-681	266	3	differential	differential	PROPN
ejde-681	266	4	equations	equation	NOUN
ejde-681	266	5	appl	appl	PROPN
ejde-681	266	6	.	.	PROPN
ejde-681	266	7	30	30	NUM
ejde-681	266	8	(	(	PUNCT
ejde-681	266	9	2023	2023	NUM
ejde-681	266	10	)	)	PUNCT
ejde-681	266	11	,	,	PUNCT
ejde-681	267	1	no	no	INTJ
ejde-681	267	2	.	.	NOUN
ejde-681	267	3	1	1	NUM
ejde-681	267	4	,	,	PUNCT
ejde-681	267	5	paper	paper	NOUN
ejde-681	267	6	no	no	NOUN
ejde-681	267	7	.	.	PROPN
ejde-681	267	8	11	11	NUM
ejde-681	267	9	,	,	PUNCT
ejde-681	267	10	33	33	NUM
ejde-681	267	11	pp	pp	NOUN
ejde-681	267	12	.	.	PUNCT
ejde-681	268	1	[	[	X
ejde-681	268	2	12	12	NUM
ejde-681	268	3	]	]	X
ejde-681	268	4	i.	i.	NOUN
ejde-681	268	5	ekeland	ekeland	NOUN
ejde-681	268	6	;	;	PUNCT
ejde-681	268	7	on	on	ADP
ejde-681	268	8	the	the	DET
ejde-681	268	9	variational	variational	ADJ
ejde-681	268	10	principle	principle	NOUN
ejde-681	268	11	,	,	PUNCT
ejde-681	268	12	j.	j.	PROPN
ejde-681	268	13	anal	anal	PROPN
ejde-681	268	14	.	.	PUNCT
ejde-681	269	1	appl	appl	PROPN
ejde-681	269	2	.	.	PROPN
ejde-681	270	1	17	17	NUM
ejde-681	270	2	(	(	PUNCT
ejde-681	270	3	1974	1974	NUM
ejde-681	270	4	)	)	PUNCT
ejde-681	270	5	,	,	PUNCT
ejde-681	270	6	324	324	NUM
ejde-681	270	7	-	-	SYM
ejde-681	270	8	353	353	NUM
ejde-681	270	9	.	.	PUNCT
ejde-681	271	1	[	[	X
ejde-681	271	2	13	13	NUM
ejde-681	271	3	]	]	X
ejde-681	271	4	b.	b.	PROPN
ejde-681	271	5	esry	esry	PROPN
ejde-681	271	6	,	,	PUNCT
ejde-681	271	7	c.	c.	PROPN
ejde-681	271	8	greene	greene	PROPN
ejde-681	271	9	,	,	PUNCT
ejde-681	271	10	j.	j.	PROPN
ejde-681	271	11	burke	burke	PROPN
ejde-681	271	12	,	,	PUNCT
ejde-681	271	13	j.	j.	PROPN
ejde-681	271	14	bohn	bohn	PROPN
ejde-681	271	15	;	;	PUNCT
ejde-681	271	16	hartree	hartree	ADJ
ejde-681	271	17	-	-	PUNCT
ejde-681	271	18	fock	fock	ADJ
ejde-681	271	19	theory	theory	NOUN
ejde-681	271	20	for	for	ADP
ejde-681	271	21	double	double	ADJ
ejde-681	271	22	condesates	condesate	NOUN
ejde-681	271	23	,	,	PUNCT
ejde-681	271	24	phys	phy	NOUN
ejde-681	271	25	.	.	PUNCT
ejde-681	272	1	rev	rev	PROPN
ejde-681	272	2	.	.	PROPN
ejde-681	272	3	lett	lett	PROPN
ejde-681	272	4	.	.	PROPN
ejde-681	272	5	,	,	PUNCT
ejde-681	272	6	78	78	NUM
ejde-681	272	7	(	(	PUNCT
ejde-681	272	8	1997	1997	NUM
ejde-681	272	9	)	)	PUNCT
ejde-681	272	10	,	,	PUNCT
ejde-681	272	11	3594	3594	NUM
ejde-681	272	12	-	-	SYM
ejde-681	272	13	3597	3597	NUM
ejde-681	272	14	.	.	PUNCT
ejde-681	273	1	[	[	X
ejde-681	273	2	14	14	NUM
ejde-681	273	3	]	]	X
ejde-681	273	4	d.	d.	PROPN
ejde-681	273	5	j.	j.	PROPN
ejde-681	273	6	frantzeskakis	frantzeskakis	PROPN
ejde-681	273	7	;	;	PUNCT
ejde-681	273	8	dark	dark	ADJ
ejde-681	273	9	solitons	soliton	NOUN
ejde-681	273	10	in	in	ADP
ejde-681	273	11	atomic	atomic	ADJ
ejde-681	273	12	bose	bose	PROPN
ejde-681	273	13	-	-	PUNCT
ejde-681	273	14	einstein	einstein	NOUN
ejde-681	273	15	condesates	condesate	NOUN
ejde-681	273	16	:	:	PUNCT
ejde-681	273	17	from	from	ADP
ejde-681	273	18	theory	theory	NOUN
ejde-681	273	19	to	to	ADP
ejde-681	273	20	experiments	experiment	NOUN
ejde-681	273	21	.	.	PUNCT
ejde-681	274	1	j.	j.	PROPN
ejde-681	274	2	phys	phys	PROPN
ejde-681	274	3	.	.	PUNCT
ejde-681	275	1	a	a	PRON
ejde-681	275	2	(	(	PUNCT
ejde-681	275	3	2010	2010	NUM
ejde-681	275	4	)	)	PUNCT
ejde-681	275	5	43:213001	43:213001	NUM
ejde-681	275	6	.	.	PUNCT
ejde-681	276	1	[	[	X
ejde-681	276	2	15	15	NUM
ejde-681	276	3	]	]	X
ejde-681	276	4	v.	v.	ADP
ejde-681	276	5	n.	n.	PROPN
ejde-681	276	6	ginzburg	ginzburg	NOUN
ejde-681	276	7	,	,	PUNCT
ejde-681	276	8	a.	a.	NOUN
ejde-681	276	9	a.	a.	PROPN
ejde-681	276	10	kochetkov	kochetkov	PROPN
ejde-681	276	11	,	,	PUNCT
ejde-681	276	12	a.	a.	PROPN
ejde-681	276	13	k.	k.	PROPN
ejde-681	276	14	potemkin	potemkin	PROPN
ejde-681	276	15	,	,	PUNCT
ejde-681	276	16	e.a	e.a	PROPN
ejde-681	276	17	.	.	PROPN
ejde-681	276	18	khazanov	khazanov	PROPN
ejde-681	276	19	;	;	PUNCT
ejde-681	276	20	suppression	suppression	NOUN
ejde-681	276	21	of	of	ADP
ejde-681	276	22	smallscale	smallscale	NOUN
ejde-681	276	23	self	self	NOUN
ejde-681	276	24	-	-	PUNCT
ejde-681	276	25	focusing	focus	VERB
ejde-681	276	26	of	of	ADP
ejde-681	276	27	high	high	ADJ
ejde-681	276	28	-	-	PUNCT
ejde-681	276	29	power	power	NOUN
ejde-681	276	30	laser	laser	NOUN
ejde-681	276	31	beams	beam	NOUN
ejde-681	276	32	due	due	ADP
ejde-681	276	33	to	to	ADP
ejde-681	276	34	their	their	PRON
ejde-681	276	35	self	self	NOUN
ejde-681	276	36	-	-	PUNCT
ejde-681	276	37	filtration	filtration	NOUN
ejde-681	276	38	during	during	ADP
ejde-681	276	39	propagation	propagation	NOUN
ejde-681	276	40	in	in	ADP
ejde-681	276	41	free	free	ADJ
ejde-681	276	42	space	space	NOUN
ejde-681	276	43	quantum	quantum	NOUN
ejde-681	276	44	electron	electron	NOUN
ejde-681	276	45	.	.	PUNCT
ejde-681	277	1	48	48	NUM
ejde-681	277	2	(	(	PUNCT
ejde-681	277	3	2018	2018	NUM
ejde-681	277	4	)	)	PUNCT
ejde-681	277	5	325	325	NUM
ejde-681	277	6	.	.	PUNCT
ejde-681	278	1	[	[	X
ejde-681	278	2	16	16	NUM
ejde-681	278	3	]	]	X
ejde-681	278	4	e.	e.	PROPN
ejde-681	278	5	khazanov	khazanov	PROPN
ejde-681	278	6	,	,	PUNCT
ejde-681	278	7	v.	v.	ADP
ejde-681	278	8	ginzburg	ginzburg	NOUN
ejde-681	278	9	,	,	PUNCT
ejde-681	278	10	a.	a.	NOUN
ejde-681	278	11	kochetkov	kochetkov	PROPN
ejde-681	278	12	;	;	PUNCT
ejde-681	278	13	self	self	NOUN
ejde-681	278	14	-	-	PUNCT
ejde-681	278	15	focusing	focus	VERB
ejde-681	278	16	suppression	suppression	NOUN
ejde-681	278	17	in	in	ADP
ejde-681	278	18	ultrahigh	ultrahigh	NOUN
ejde-681	278	19	-	-	PUNCT
ejde-681	278	20	intensity	intensity	NOUN
ejde-681	278	21	lasers	laser	NOUN
ejde-681	278	22	,	,	PUNCT
ejde-681	278	23	2018	2018	NUM
ejde-681	278	24	conference	conference	NOUN
ejde-681	278	25	on	on	ADP
ejde-681	278	26	lasers	laser	NOUN
ejde-681	278	27	and	and	CCONJ
ejde-681	278	28	electro	electro	ADJ
ejde-681	278	29	-	-	PUNCT
ejde-681	278	30	optics	optic	NOUN
ejde-681	278	31	pacific	pacific	ADJ
ejde-681	278	32	rim	rim	NOUN
ejde-681	278	33	(	(	PUNCT
ejde-681	278	34	cleo	cleo	PROPN
ejde-681	278	35	-	-	PUNCT
ejde-681	278	36	pr	pr	NOUN
ejde-681	278	37	)	)	PUNCT
ejde-681	278	38	,	,	PUNCT
ejde-681	278	39	hong	hong	PROPN
ejde-681	278	40	kong	kong	PROPN
ejde-681	278	41	,	,	PUNCT
ejde-681	278	42	china	china	PROPN
ejde-681	278	43	,	,	PUNCT
ejde-681	278	44	2018	2018	NUM
ejde-681	278	45	,	,	PUNCT
ejde-681	278	46	pp	pp	ADJ
ejde-681	278	47	.	.	PUNCT
ejde-681	279	1	1	1	NUM
ejde-681	279	2	-	-	SYM
ejde-681	279	3	2	2	NUM
ejde-681	279	4	.	.	PUNCT
ejde-681	280	1	[	[	X
ejde-681	280	2	17	17	NUM
ejde-681	280	3	]	]	X
ejde-681	280	4	y.	y.	PROPN
ejde-681	280	5	s.	s.	PROPN
ejde-681	280	6	kivshar	kivshar	PROPN
ejde-681	280	7	,	,	PUNCT
ejde-681	280	8	b.	b.	PROPN
ejde-681	280	9	luther	luther	PROPN
ejde-681	280	10	-	-	PUNCT
ejde-681	280	11	davies	davy	NOUN
ejde-681	280	12	;	;	PUNCT
ejde-681	280	13	dark	dark	ADJ
ejde-681	280	14	optical	optical	ADJ
ejde-681	280	15	solitons	soliton	NOUN
ejde-681	280	16	:	:	PUNCT
ejde-681	280	17	physics	physics	NOUN
ejde-681	280	18	and	and	CCONJ
ejde-681	280	19	applications	application	NOUN
ejde-681	280	20	.	.	PUNCT
ejde-681	281	1	physics	physics	NOUN
ejde-681	281	2	reports	report	NOUN
ejde-681	281	3	(	(	PUNCT
ejde-681	281	4	1998	1998	NUM
ejde-681	281	5	)	)	PUNCT
ejde-681	281	6	298:81	298:81	NUM
ejde-681	281	7	-	-	SYM
ejde-681	281	8	197	197	NUM
ejde-681	281	9	.	.	PUNCT
ejde-681	282	1	[	[	X
ejde-681	282	2	18	18	NUM
ejde-681	282	3	]	]	PUNCT
ejde-681	282	4	t.-c	t.-c	PROPN
ejde-681	282	5	.	.	PUNCT
ejde-681	283	1	lin	lin	PROPN
ejde-681	283	2	,	,	PUNCT
ejde-681	283	3	j.	j.	PROPN
ejde-681	283	4	wei	wei	PROPN
ejde-681	283	5	;	;	PUNCT
ejde-681	283	6	ground	ground	NOUN
ejde-681	283	7	state	state	NOUN
ejde-681	283	8	of	of	ADP
ejde-681	283	9	n	n	PROPN
ejde-681	283	10	coupled	couple	VERB
ejde-681	283	11	nonlinear	nonlinear	PROPN
ejde-681	283	12	schrödinger	schrödinger	NOUN
ejde-681	283	13	equations	equation	NOUN
ejde-681	283	14	in	in	ADP
ejde-681	283	15	rn	rn	PROPN
ejde-681	283	16	,	,	PUNCT
ejde-681	283	17	n	n	ADV
ejde-681	283	18	≤	≤	NOUN
ejde-681	283	19	3	3	NUM
ejde-681	283	20	.	.	PUNCT
ejde-681	283	21	comm	comm	NOUN
ejde-681	283	22	.	.	PUNCT
ejde-681	283	23	math	math	NOUN
ejde-681	283	24	.	.	PUNCT
ejde-681	284	1	phys	phy	NOUN
ejde-681	284	2	.	.	PUNCT
ejde-681	285	1	255	255	NUM
ejde-681	285	2	(	(	PUNCT
ejde-681	285	3	2005	2005	NUM
ejde-681	285	4	)	)	PUNCT
ejde-681	285	5	,	,	PUNCT
ejde-681	285	6	no	no	INTJ
ejde-681	285	7	.	.	NOUN
ejde-681	285	8	3	3	NUM
ejde-681	285	9	,	,	PUNCT
ejde-681	285	10	629	629	NUM
ejde-681	285	11	-	-	SYM
ejde-681	285	12	653	653	NUM
ejde-681	285	13	.	.	PUNCT
ejde-681	286	1	[	[	X
ejde-681	286	2	19	19	NUM
ejde-681	286	3	]	]	PUNCT
ejde-681	286	4	z.	z.	PROPN
ejde-681	286	5	liu	liu	PROPN
ejde-681	286	6	,	,	PUNCT
ejde-681	287	1	z.-q	z.-q	PROPN
ejde-681	287	2	.	.	PUNCT
ejde-681	287	3	wang	wang	PROPN
ejde-681	287	4	;	;	PUNCT
ejde-681	287	5	multiple	multiple	ADJ
ejde-681	287	6	bound	bind	VERB
ejde-681	287	7	states	state	NOUN
ejde-681	287	8	of	of	ADP
ejde-681	287	9	nonlinear	nonlinear	ADJ
ejde-681	287	10	schrödinger	schrödinger	NOUN
ejde-681	287	11	systems	system	NOUN
ejde-681	287	12	.	.	PUNCT
ejde-681	288	1	comm	comm	NOUN
ejde-681	288	2	.	.	PUNCT
ejde-681	288	3	math	math	NOUN
ejde-681	288	4	.	.	PUNCT
ejde-681	289	1	phys	phy	NOUN
ejde-681	289	2	.	.	PUNCT
ejde-681	290	1	282	282	NUM
ejde-681	290	2	(	(	PUNCT
ejde-681	290	3	2008	2008	NUM
ejde-681	290	4	)	)	PUNCT
ejde-681	290	5	,	,	PUNCT
ejde-681	290	6	no	no	INTJ
ejde-681	290	7	.	.	NOUN
ejde-681	290	8	3	3	NUM
ejde-681	290	9	,	,	PUNCT
ejde-681	290	10	721	721	NUM
ejde-681	290	11	-	-	SYM
ejde-681	290	12	731	731	NUM
ejde-681	290	13	.	.	PUNCT
ejde-681	291	1	[	[	X
ejde-681	291	2	20	20	NUM
ejde-681	291	3	]	]	PUNCT
ejde-681	291	4	s.	s.	PROPN
ejde-681	291	5	g.	g.	PROPN
ejde-681	291	6	lukishova	lukishova	PROPN
ejde-681	291	7	,	,	PUNCT
ejde-681	291	8	y.	y.	PROPN
ejde-681	291	9	v.	v.	PROPN
ejde-681	291	10	senatsky	senatsky	PROPN
ejde-681	291	11	,	,	PUNCT
ejde-681	291	12	n.	n.	PROPN
ejde-681	291	13	e.	e.	PROPN
ejde-681	291	14	bykovsky	bykovsky	PROPN
ejde-681	291	15	,	,	PUNCT
ejde-681	291	16	a.	a.	PROPN
ejde-681	291	17	s.	s.	PROPN
ejde-681	291	18	scheulin	scheulin	PROPN
ejde-681	291	19	;	;	PUNCT
ejde-681	291	20	beam	beam	NOUN
ejde-681	291	21	shaping	shaping	NOUN
ejde-681	291	22	and	and	CCONJ
ejde-681	291	23	suppression	suppression	NOUN
ejde-681	291	24	of	of	ADP
ejde-681	291	25	self	self	NOUN
ejde-681	291	26	-	-	PUNCT
ejde-681	291	27	focusing	focus	VERB
ejde-681	291	28	in	in	ADP
ejde-681	291	29	high	high	ADJ
ejde-681	291	30	-	-	PUNCT
ejde-681	291	31	peak	peak	NOUN
ejde-681	291	32	-	-	PUNCT
ejde-681	291	33	power	power	NOUN
ejde-681	291	34	nd	nd	NOUN
ejde-681	291	35	:	:	PUNCT
ejde-681	291	36	glass	glass	NOUN
ejde-681	291	37	laser	laser	NOUN
ejde-681	291	38	systems	system	NOUN
ejde-681	291	39	part	part	NOUN
ejde-681	291	40	of	of	ADP
ejde-681	291	41	the	the	DET
ejde-681	291	42	book	book	NOUN
ejde-681	291	43	series	series	NOUN
ejde-681	291	44	:	:	PUNCT
ejde-681	291	45	topics	topic	NOUN
ejde-681	291	46	in	in	ADP
ejde-681	291	47	applied	applied	ADJ
ejde-681	291	48	physics	physics	NOUN
ejde-681	291	49	(	(	PUNCT
ejde-681	291	50	tap	tap	NOUN
ejde-681	291	51	,	,	PUNCT
ejde-681	291	52	volume	volume	NOUN
ejde-681	291	53	114	114	NUM
ejde-681	291	54	,	,	PUNCT
ejde-681	291	55	chapter	chapter	NOUN
ejde-681	291	56	8)	8)	NUM
ejde-681	291	57	doi	doi	NOUN
ejde-681	291	58	:	:	PUNCT
ejde-681	291	59	10.1007/978	10.1007/978	NUM
ejde-681	291	60	-	-	SYM
ejde-681	291	61	0	0	NUM
ejde-681	291	62	-	-	PUNCT
ejde-681	291	63	387	387	NUM
ejde-681	291	64	-	-	PUNCT
ejde-681	291	65	34727	34727	NUM
ejde-681	291	66	-	-	SYM
ejde-681	291	67	1	1	NUM
ejde-681	291	68	8	8	NUM
ejde-681	291	69	[	[	X
ejde-681	291	70	21	21	NUM
ejde-681	291	71	]	]	X
ejde-681	291	72	l.	l.	PROPN
ejde-681	291	73	a.	a.	PROPN
ejde-681	291	74	maia	maia	PROPN
ejde-681	291	75	,	,	PUNCT
ejde-681	291	76	e.	e.	PROPN
ejde-681	291	77	montefusco	montefusco	PROPN
ejde-681	291	78	,	,	PUNCT
ejde-681	291	79	b.	b.	PROPN
ejde-681	291	80	pellacci	pellacci	PROPN
ejde-681	291	81	;	;	PUNCT
ejde-681	291	82	positive	positive	ADJ
ejde-681	291	83	solutions	solution	NOUN
ejde-681	291	84	for	for	ADP
ejde-681	291	85	a	a	DET
ejde-681	291	86	weakly	weakly	ADV
ejde-681	291	87	coupled	couple	VERB
ejde-681	291	88	nonlinear	nonlinear	ADJ
ejde-681	291	89	schrödinger	schrödinger	NOUN
ejde-681	291	90	system	system	NOUN
ejde-681	291	91	.	.	PUNCT
ejde-681	292	1	j.	j.	PROPN
ejde-681	292	2	differential	differential	PROPN
ejde-681	292	3	equations	equation	NOUN
ejde-681	292	4	229	229	NUM
ejde-681	292	5	(	(	PUNCT
ejde-681	292	6	2006	2006	NUM
ejde-681	292	7	)	)	PUNCT
ejde-681	292	8	,	,	PUNCT
ejde-681	292	9	no	no	INTJ
ejde-681	292	10	.	.	NOUN
ejde-681	292	11	2	2	NUM
ejde-681	292	12	,	,	PUNCT
ejde-681	292	13	743	743	NUM
ejde-681	292	14	-	-	SYM
ejde-681	292	15	767	767	NUM
ejde-681	292	16	.	.	PUNCT
ejde-681	293	1	[	[	X
ejde-681	293	2	22	22	NUM
ejde-681	293	3	]	]	X
ejde-681	293	4	c.	c.	PROPN
ejde-681	293	5	pethick	pethick	PROPN
ejde-681	293	6	,	,	PUNCT
ejde-681	293	7	h.	h.	PROPN
ejde-681	293	8	smith	smith	PROPN
ejde-681	293	9	;	;	PUNCT
ejde-681	293	10	bose	bose	PROPN
ejde-681	293	11	-	-	PUNCT
ejde-681	293	12	einstein	einstein	NOUN
ejde-681	293	13	condensation	condensation	NOUN
ejde-681	293	14	in	in	ADP
ejde-681	293	15	dilute	dilute	NOUN
ejde-681	293	16	gases	gas	NOUN
ejde-681	293	17	(	(	PUNCT
ejde-681	293	18	2nd	2nd	ADJ
ejde-681	293	19	ed	ed	NOUN
ejde-681	293	20	.	.	PUNCT
ejde-681	293	21	)	)	PUNCT
ejde-681	293	22	.	.	PUNCT
ejde-681	294	1	cambridge	cambridge	PROPN
ejde-681	294	2	:	:	PUNCT
ejde-681	294	3	cambridge	cambridge	PROPN
ejde-681	294	4	university	university	PROPN
ejde-681	294	5	press	press	PROPN
ejde-681	294	6	(	(	PUNCT
ejde-681	294	7	2008	2008	NUM
ejde-681	294	8	)	)	PUNCT
ejde-681	294	9	.	.	PUNCT
ejde-681	295	1	[	[	X
ejde-681	295	2	23	23	NUM
ejde-681	295	3	]	]	X
ejde-681	295	4	b.	b.	PROPN
ejde-681	295	5	sirakov	sirakov	PROPN
ejde-681	295	6	;	;	PUNCT
ejde-681	295	7	least	least	ADJ
ejde-681	295	8	energy	energy	NOUN
ejde-681	295	9	solitary	solitary	ADJ
ejde-681	295	10	waves	wave	NOUN
ejde-681	295	11	for	for	ADP
ejde-681	295	12	a	a	DET
ejde-681	295	13	system	system	NOUN
ejde-681	295	14	of	of	ADP
ejde-681	295	15	nonlinear	nonlinear	ADJ
ejde-681	295	16	schrödinger	schrödinger	NOUN
ejde-681	295	17	equations	equation	NOUN
ejde-681	295	18	in	in	ADP
ejde-681	295	19	rn	rn	PROPN
ejde-681	295	20	.	.	PROPN
ejde-681	295	21	comm	comm	NOUN
ejde-681	295	22	.	.	PUNCT
ejde-681	296	1	math	math	NOUN
ejde-681	296	2	.	.	PUNCT
ejde-681	297	1	phys	phy	NOUN
ejde-681	297	2	.	.	PUNCT
ejde-681	298	1	271	271	NUM
ejde-681	298	2	(	(	PUNCT
ejde-681	298	3	2007	2007	NUM
ejde-681	298	4	)	)	PUNCT
ejde-681	298	5	,	,	PUNCT
ejde-681	298	6	no	no	INTJ
ejde-681	298	7	.	.	NOUN
ejde-681	298	8	1	1	NUM
ejde-681	298	9	,	,	PUNCT
ejde-681	298	10	199	199	NUM
ejde-681	298	11	-	-	SYM
ejde-681	298	12	221	221	NUM
ejde-681	298	13	.	.	PUNCT
ejde-681	299	1	[	[	X
ejde-681	299	2	24	24	NUM
ejde-681	299	3	]	]	X
ejde-681	299	4	g.	g.	PROPN
ejde-681	299	5	tarantello	tarantello	PROPN
ejde-681	299	6	;	;	PUNCT
ejde-681	299	7	on	on	ADP
ejde-681	299	8	nonhomogeneous	nonhomogeneous	ADJ
ejde-681	299	9	elliptic	elliptic	ADJ
ejde-681	299	10	equations	equation	NOUN
ejde-681	299	11	involving	involve	VERB
ejde-681	299	12	critical	critical	ADJ
ejde-681	299	13	sobolev	sobolev	NOUN
ejde-681	299	14	exponent	exponent	NOUN
ejde-681	299	15	.	.	PUNCT
ejde-681	300	1	ann	ann	PROPN
ejde-681	300	2	.	.	PROPN
ejde-681	300	3	inst	inst	PROPN
ejde-681	300	4	.	.	PUNCT
ejde-681	301	1	h.	h.	PROPN
ejde-681	301	2	poincaré	poincaré	PROPN
ejde-681	301	3	anal	anal	PROPN
ejde-681	301	4	.	.	PUNCT
ejde-681	302	1	non	non	PROPN
ejde-681	302	2	lineaire	lineaire	NOUN
ejde-681	302	3	9	9	NUM
ejde-681	302	4	(	(	PUNCT
ejde-681	302	5	1992	1992	NUM
ejde-681	302	6	)	)	PUNCT
ejde-681	302	7	,	,	PUNCT
ejde-681	302	8	no	no	INTJ
ejde-681	302	9	.	.	NOUN
ejde-681	302	10	3	3	NUM
ejde-681	302	11	,	,	PUNCT
ejde-681	302	12	281	281	NUM
ejde-681	302	13	-	-	SYM
ejde-681	302	14	304	304	NUM
ejde-681	302	15	.	.	PUNCT
ejde-681	303	1	[	[	X
ejde-681	303	2	25	25	NUM
ejde-681	303	3	]	]	PUNCT
ejde-681	303	4	j.	j.	PROPN
ejde-681	303	5	wei	wei	PROPN
ejde-681	303	6	,	,	PUNCT
ejde-681	303	7	t.	t.	PROPN
ejde-681	303	8	weth	weth	NOUN
ejde-681	303	9	;	;	PUNCT
ejde-681	303	10	radial	radial	ADJ
ejde-681	303	11	solutions	solution	NOUN
ejde-681	303	12	and	and	CCONJ
ejde-681	303	13	phase	phase	NOUN
ejde-681	303	14	separation	separation	NOUN
ejde-681	303	15	in	in	ADP
ejde-681	303	16	a	a	DET
ejde-681	303	17	system	system	NOUN
ejde-681	303	18	of	of	ADP
ejde-681	303	19	two	two	NUM
ejde-681	303	20	coupled	couple	VERB
ejde-681	303	21	schrödinger	schrödinger	NOUN
ejde-681	303	22	equations	equation	NOUN
ejde-681	303	23	.	.	PUNCT
ejde-681	304	1	arch	arch	NOUN
ejde-681	304	2	.	.	PUNCT
ejde-681	305	1	ration	ration	NOUN
ejde-681	305	2	.	.	PUNCT
ejde-681	306	1	mech	mech	PROPN
ejde-681	306	2	.	.	PUNCT
ejde-681	307	1	anal	anal	PROPN
ejde-681	307	2	.	.	PUNCT
ejde-681	308	1	190	190	NUM
ejde-681	308	2	(	(	PUNCT
ejde-681	308	3	2008	2008	NUM
ejde-681	308	4	)	)	PUNCT
ejde-681	308	5	,	,	PUNCT
ejde-681	308	6	no	no	INTJ
ejde-681	308	7	.	.	NOUN
ejde-681	308	8	1	1	NUM
ejde-681	308	9	,	,	PUNCT
ejde-681	308	10	83	83	NUM
ejde-681	308	11	-	-	SYM
ejde-681	308	12	106	106	NUM
ejde-681	308	13	.	.	PUNCT
ejde-681	309	1	ejde-2024/32	ejde-2024/32	VERB
ejde-681	309	2	solutions	solution	NOUN
ejde-681	309	3	to	to	ADP
ejde-681	309	4	semi	semi	ADJ
ejde-681	309	5	-	-	ADJ
ejde-681	309	6	nodal	nodal	ADJ
ejde-681	309	7	solutions	solution	NOUN
ejde-681	309	8	9	9	NUM
ejde-681	309	9	joão	joão	PROPN
ejde-681	309	10	pablo	pablo	PROPN
ejde-681	309	11	pinheiro	pinheiro	PROPN
ejde-681	309	12	da	da	PROPN
ejde-681	309	13	silva	silva	PROPN
ejde-681	309	14	departamento	departamento	PROPN
ejde-681	309	15	de	de	PROPN
ejde-681	309	16	matemática	matemática	PROPN
ejde-681	309	17	,	,	PUNCT
ejde-681	309	18	universidade	universidade	PROPN
ejde-681	309	19	federal	federal	PROPN
ejde-681	309	20	do	do	VERB
ejde-681	309	21	pará	pará	NOUN
ejde-681	309	22	,	,	PUNCT
ejde-681	309	23	belem	belem	PROPN
ejde-681	309	24	,	,	PUNCT
ejde-681	309	25	brazil	brazil	PROPN
ejde-681	309	26	email	email	NOUN
ejde-681	309	27	address	address	NOUN
ejde-681	309	28	:	:	PUNCT
ejde-681	309	29	jpabloufpa@gmail.com	jpabloufpa@gmail.com	PROPN
ejde-681	309	30	edcarlos	edcarlos	PROPN
ejde-681	309	31	domingos	domingos	PROPN
ejde-681	309	32	da	da	PROPN
ejde-681	309	33	silva	silva	PROPN
ejde-681	309	34	departamento	departamento	PROPN
ejde-681	309	35	de	de	PROPN
ejde-681	309	36	matemática	matemática	PROPN
ejde-681	309	37	,	,	PUNCT
ejde-681	309	38	universidade	universidade	PROPN
ejde-681	309	39	de	de	PROPN
ejde-681	309	40	federal	federal	PROPN
ejde-681	309	41	de	de	X
ejde-681	309	42	goiás	goiás	PROPN
ejde-681	309	43	,	,	PUNCT
ejde-681	309	44	goiánia	goiánia	NOUN
ejde-681	309	45	,	,	PUNCT
ejde-681	309	46	go	go	VERB
ejde-681	309	47	,	,	PUNCT
ejde-681	309	48	74690900	74690900	NUM
ejde-681	309	49	,	,	PUNCT
ejde-681	309	50	brazil	brazil	PROPN
ejde-681	309	51	email	email	NOUN
ejde-681	309	52	address	address	NOUN
ejde-681	309	53	:	:	PUNCT
ejde-681	310	1	edcarlos@ufg.br	edcarlos@ufg.br	NOUN
ejde-681	310	2	1	1	X
ejde-681	310	3	.	.	X
ejde-681	310	4	introduction	introduction	NOUN
ejde-681	310	5	2	2	NUM
ejde-681	310	6	.	.	PUNCT
ejde-681	310	7	main	main	ADJ
ejde-681	310	8	result	result	NOUN
ejde-681	310	9	acknowledgements	acknowledgement	NOUN
ejde-681	310	10	references	reference	NOUN