id	sid	tid	token	lemma	pos
ijassa-294	1	1	82	82	NUM
ijassa-294	1	2	-	-	SYM
ijassa-294	1	3	92	92	NUM
ijassa-294	1	4	advances	advance	NOUN
ijassa-294	1	5	in	in	ADP
ijassa-294	1	6	systems	system	NOUN
ijassa-294	1	7	science	science	NOUN
ijassa-294	1	8	and	and	CCONJ
ijassa-294	1	9	applications	application	NOUN
ijassa-294	1	10	(	(	PUNCT
ijassa-294	1	11	2011	2011	NUM
ijassa-294	1	12	)	)	PUNCT
ijassa-294	1	13	,	,	PUNCT
ijassa-294	1	14	vol	vol	NOUN
ijassa-294	1	15	.	.	PROPN
ijassa-294	1	16	11	11	NUM
ijassa-294	1	17	,	,	PUNCT
ijassa-294	1	18	no	no	INTJ
ijassa-294	1	19	.	.	NOUN
ijassa-294	1	20	1	1	NUM
ijassa-294	1	21	-	-	SYM
ijassa-294	1	22	2	2	NUM
ijassa-294	1	23	existence	existence	NOUN
ijassa-294	1	24	and	and	CCONJ
ijassa-294	1	25	nonexistence	nonexistence	NOUN
ijassa-294	1	26	of	of	ADP
ijassa-294	1	27	positive	positive	ADJ
ijassa-294	1	28	solutions	solution	NOUN
ijassa-294	1	29	for	for	ADP
ijassa-294	1	30	a	a	DET
ijassa-294	1	31	kirchhoff	kirchhoff	NOUN
ijassa-294	1	32	-	-	PUNCT
ijassa-294	1	33	type	type	NOUN
ijassa-294	1	34	equation	equation	NOUN
ijassa-294	1	35	with	with	ADP
ijassa-294	1	36	inhomogeneous	inhomogeneous	ADJ
ijassa-294	1	37	strong	strong	ADJ
ijassa-294	1	38	allee	allee	ADJ
ijassa-294	1	39	effect	effect	NOUN
ijassa-294	1	40	ruyun	ruyun	PROPN
ijassa-294	1	41	ma	ma	PROPN
ijassa-294	1	42	and	and	CCONJ
ijassa-294	1	43	guowei	guowei	PROPN
ijassa-294	1	44	dai	dai	PROPN
ijassa-294	1	45	department	department	PROPN
ijassa-294	1	46	of	of	ADP
ijassa-294	1	47	mathematics	mathematics	PROPN
ijassa-294	1	48	,	,	PUNCT
ijassa-294	1	49	northwest	northwest	PROPN
ijassa-294	1	50	normal	normal	ADJ
ijassa-294	1	51	university	university	NOUN
ijassa-294	1	52	,	,	PUNCT
ijassa-294	1	53	lanzhou	lanzhou	PROPN
ijassa-294	1	54	730070	730070	NUM
ijassa-294	1	55	,	,	PUNCT
ijassa-294	1	56	p.r	p.r	PROPN
ijassa-294	1	57	.	.	PROPN
ijassa-294	1	58	china	china	PROPN
ijassa-294	1	59	email	email	NOUN
ijassa-294	1	60	:	:	PUNCT
ijassa-294	1	61	mary@nwnu.edu.cn	mary@nwnu.edu.cn	NOUN
ijassa-294	1	62	,	,	PUNCT
ijassa-294	1	63	daiguowei@uwnu.edu.cn	daiguowei@uwnu.edu.cn	NOUN
ijassa-294	1	64	abstract	abstract	NOUN
ijassa-294	1	65	in	in	ADP
ijassa-294	1	66	this	this	DET
ijassa-294	1	67	paper	paper	NOUN
ijassa-294	1	68	,	,	PUNCT
ijassa-294	1	69	we	we	PRON
ijassa-294	1	70	deal	deal	VERB
ijassa-294	1	71	with	with	ADP
ijassa-294	1	72	the	the	DET
ijassa-294	1	73	nonlocal	nonlocal	ADJ
ijassa-294	1	74	semilinear	semilinear	ADJ
ijassa-294	1	75	elliptic	elliptic	ADJ
ijassa-294	1	76	equation	equation	NOUN
ijassa-294	1	77	with	with	ADP
ijassa-294	1	78	inhomogeneous	inhomogeneous	ADJ
ijassa-294	1	79	strong	strong	ADJ
ijassa-294	1	80	allee	allee	ADJ
ijassa-294	1	81	effect	effect	NOUN
ijassa-294	1	82	{	{	PUNCT
ijassa-294	1	83	−m	−m	INTJ
ijassa-294	1	84	(	(	PUNCT
ijassa-294	1	85	∫	∫	PROPN
ijassa-294	1	86	ω	ω	PROPN
ijassa-294	1	87	1	1	NUM
ijassa-294	1	88	2	2	NUM
ijassa-294	1	89	|∇u|	|∇u|	ADJ
ijassa-294	1	90	2	2	NUM
ijassa-294	1	91	dx	dx	PROPN
ijassa-294	1	92	)	)	PUNCT
ijassa-294	2	1	∆u	∆u	PROPN
ijassa-294	2	2	=	=	SYM
ijassa-294	2	3	λf(x	λf(x	PROPN
ijassa-294	2	4	,	,	PUNCT
ijassa-294	2	5	u	u	NOUN
ijassa-294	2	6	)	)	PUNCT
ijassa-294	2	7	in	in	ADP
ijassa-294	2	8	ω	ω	PROPN
ijassa-294	2	9	,	,	PUNCT
ijassa-294	2	10	u	u	NOUN
ijassa-294	2	11	=	=	NOUN
ijassa-294	2	12	0	0	NUM
ijassa-294	2	13	on	on	ADP
ijassa-294	2	14	∂ω	∂ω	PROPN
ijassa-294	2	15	,	,	PUNCT
ijassa-294	2	16	where	where	SCONJ
ijassa-294	2	17	the	the	DET
ijassa-294	2	18	nonlocal	nonlocal	ADJ
ijassa-294	2	19	coefficient	coefficient	NOUN
ijassa-294	2	20	m	m	PROPN
ijassa-294	2	21	(	(	PUNCT
ijassa-294	2	22	∫	∫	PROPN
ijassa-294	2	23	ω	ω	PROPN
ijassa-294	2	24	1	1	NUM
ijassa-294	2	25	2	2	NUM
ijassa-294	2	26	|∇u|	|∇u|	ADJ
ijassa-294	2	27	2	2	NUM
ijassa-294	2	28	dx	dx	PROPN
ijassa-294	2	29	)	)	PUNCT
ijassa-294	2	30	is	be	AUX
ijassa-294	2	31	a	a	DET
ijassa-294	2	32	continuous	continuous	ADJ
ijassa-294	2	33	function	function	NOUN
ijassa-294	2	34	of	of	ADP
ijassa-294	2	35	∫	∫	PROPN
ijassa-294	2	36	ω	ω	PROPN
ijassa-294	2	37	1	1	NUM
ijassa-294	2	38	2	2	NUM
ijassa-294	2	39	|∇u|	|∇u|	ADJ
ijassa-294	2	40	2	2	NUM
ijassa-294	2	41	dx	dx	NOUN
ijassa-294	2	42	.	.	PUNCT
ijassa-294	3	1	by	by	ADP
ijassa-294	3	2	means	mean	NOUN
ijassa-294	3	3	of	of	ADP
ijassa-294	3	4	variational	variational	ADJ
ijassa-294	3	5	approach	approach	NOUN
ijassa-294	3	6	,	,	PUNCT
ijassa-294	3	7	we	we	PRON
ijassa-294	3	8	prove	prove	VERB
ijassa-294	3	9	that	that	SCONJ
ijassa-294	3	10	the	the	DET
ijassa-294	3	11	equation	equation	NOUN
ijassa-294	3	12	has	have	VERB
ijassa-294	3	13	at	at	ADV
ijassa-294	3	14	least	least	ADV
ijassa-294	3	15	two	two	NUM
ijassa-294	3	16	positive	positive	ADJ
ijassa-294	3	17	solutions	solution	NOUN
ijassa-294	3	18	for	for	ADP
ijassa-294	3	19	largeλ	largeλ	NOUN
ijassa-294	3	20	under	under	ADP
ijassa-294	3	21	suitable	suitable	ADJ
ijassa-294	3	22	hypotheses	hypothesis	NOUN
ijassa-294	3	23	about	about	ADP
ijassa-294	3	24	nonlinearity	nonlinearity	NOUN
ijassa-294	3	25	.	.	PUNCT
ijassa-294	4	1	we	we	PRON
ijassa-294	4	2	also	also	ADV
ijassa-294	4	3	prove	prove	VERB
ijassa-294	4	4	some	some	DET
ijassa-294	4	5	nonexistence	nonexistence	NOUN
ijassa-294	4	6	results	result	NOUN
ijassa-294	4	7	.	.	PUNCT
ijassa-294	5	1	in	in	ADP
ijassa-294	5	2	particular	particular	ADJ
ijassa-294	5	3	,	,	PUNCT
ijassa-294	5	4	we	we	PRON
ijassa-294	5	5	shall	shall	AUX
ijassa-294	5	6	give	give	VERB
ijassa-294	5	7	a	a	DET
ijassa-294	5	8	positive	positive	ADJ
ijassa-294	5	9	answer	answer	NOUN
ijassa-294	5	10	to	to	ADP
ijassa-294	5	11	the	the	DET
ijassa-294	5	12	conjecture	conjecture	NOUN
ijassa-294	5	13	by	by	ADP
ijassa-294	5	14	liu	liu	PROPN
ijassa-294	5	15	,	,	PUNCT
ijassa-294	5	16	wang	wang	PROPN
ijassa-294	5	17	and	and	CCONJ
ijassa-294	5	18	shi	shi	PROPN
ijassa-294	5	19	’s	’s	NOUN
ijassa-294	5	20	of	of	ADP
ijassa-294	5	21	[	[	X
ijassa-294	5	22	1	1	NUM
ijassa-294	5	23	]	]	PUNCT
ijassa-294	5	24	.	.	PUNCT
ijassa-294	6	1	keywords	keyword	VERB
ijassa-294	6	2	nonlocal	nonlocal	ADJ
ijassa-294	6	3	differential	differential	ADJ
ijassa-294	6	4	equation	equation	NOUN
ijassa-294	6	5	variational	variational	ADJ
ijassa-294	6	6	method	method	NOUN
ijassa-294	6	7	positive	positive	ADJ
ijassa-294	6	8	solutions	solution	NOUN
ijassa-294	6	9	inhomogeneous	inhomogeneous	ADJ
ijassa-294	6	10	strong	strong	ADJ
ijassa-294	6	11	allee	allee	NOUN
ijassa-294	6	12	effect	effect	NOUN
ijassa-294	6	13	.	.	PUNCT
ijassa-294	7	1	1	1	X
ijassa-294	7	2	.	.	X
ijassa-294	7	3	introduction	introduction	NOUN
ijassa-294	7	4	in	in	ADP
ijassa-294	7	5	this	this	DET
ijassa-294	7	6	paper	paper	NOUN
ijassa-294	7	7	we	we	PRON
ijassa-294	7	8	study	study	VERB
ijassa-294	7	9	the	the	DET
ijassa-294	7	10	following	follow	VERB
ijassa-294	7	11	problem	problem	NOUN
ijassa-294	7	12	{	{	PUNCT
ijassa-294	7	13	−m	−m	NOUN
ijassa-294	7	14	(	(	PUNCT
ijassa-294	7	15	∫	∫	PROPN
ijassa-294	7	16	ω	ω	PROPN
ijassa-294	7	17	1	1	NUM
ijassa-294	7	18	2	2	NUM
ijassa-294	7	19	|∇u|	|∇u|	ADJ
ijassa-294	7	20	2	2	NUM
ijassa-294	7	21	dx	dx	PROPN
ijassa-294	7	22	)	)	PUNCT
ijassa-294	8	1	∆u	∆u	PROPN
ijassa-294	8	2	=	=	SYM
ijassa-294	8	3	λf(x	λf(x	PROPN
ijassa-294	8	4	,	,	PUNCT
ijassa-294	8	5	u	u	NOUN
ijassa-294	8	6	)	)	PUNCT
ijassa-294	8	7	in	in	ADP
ijassa-294	8	8	ω	ω	PROPN
ijassa-294	8	9	,	,	PUNCT
ijassa-294	8	10	u	u	NOUN
ijassa-294	8	11	=	=	NOUN
ijassa-294	8	12	0	0	NUM
ijassa-294	8	13	on	on	ADP
ijassa-294	8	14	∂ω	∂ω	PROPN
ijassa-294	8	15	,	,	PUNCT
ijassa-294	8	16	(	(	PUNCT
ijassa-294	8	17	1	1	X
ijassa-294	8	18	)	)	PUNCT
ijassa-294	8	19	where	where	SCONJ
ijassa-294	8	20	ω	ω	PROPN
ijassa-294	8	21	is	be	AUX
ijassa-294	8	22	a	a	DET
ijassa-294	8	23	smooth	smooth	ADJ
ijassa-294	8	24	bounded	bounded	ADJ
ijassa-294	8	25	domain	domain	NOUN
ijassa-294	8	26	in	in	ADP
ijassa-294	8	27	rn	rn	PROPN
ijassa-294	8	28	for	for	ADP
ijassa-294	8	29	n	n	X
ijassa-294	8	30	≥	≥	NUM
ijassa-294	8	31	1	1	NUM
ijassa-294	8	32	,	,	PUNCT
ijassa-294	8	33	the	the	DET
ijassa-294	8	34	nonlocal	nonlocal	ADJ
ijassa-294	8	35	coefficient	coefficient	NOUN
ijassa-294	8	36	m(t	m(t	NOUN
ijassa-294	8	37	)	)	PUNCT
ijassa-294	8	38	is	be	AUX
ijassa-294	8	39	a	a	DET
ijassa-294	8	40	continuous	continuous	ADJ
ijassa-294	8	41	function	function	NOUN
ijassa-294	8	42	of	of	ADP
ijassa-294	8	43	t	t	PROPN
ijassa-294	9	1	=	=	SYM
ijassa-294	9	2	∫	∫	PROPN
ijassa-294	9	3	ω	ω	NUM
ijassa-294	9	4	1	1	NUM
ijassa-294	9	5	2	2	NUM
ijassa-294	9	6	|∇u|	|∇u|	ADJ
ijassa-294	9	7	2	2	NUM
ijassa-294	9	8	dx	dx	NOUN
ijassa-294	9	9	.	.	PUNCT
ijassa-294	10	1	we	we	PRON
ijassa-294	10	2	shall	shall	AUX
ijassa-294	10	3	give	give	VERB
ijassa-294	10	4	a	a	DET
ijassa-294	10	5	positive	positive	ADJ
ijassa-294	10	6	answer	answer	NOUN
ijassa-294	10	7	to	to	ADP
ijassa-294	10	8	a	a	DET
ijassa-294	10	9	conjecture	conjecture	NOUN
ijassa-294	10	10	by	by	ADP
ijassa-294	10	11	liu	liu	PROPN
ijassa-294	10	12	,	,	PUNCT
ijassa-294	10	13	wang	wang	PROPN
ijassa-294	10	14	and	and	CCONJ
ijassa-294	10	15	shi	shi	PROPN
ijassa-294	10	16	’s	’s	NOUN
ijassa-294	10	17	of	of	ADP
ijassa-294	10	18	[	[	X
ijassa-294	10	19	1	1	NUM
ijassa-294	10	20	]	]	PUNCT
ijassa-294	10	21	.	.	PUNCT
ijassa-294	11	1	the	the	DET
ijassa-294	11	2	problem	problem	NOUN
ijassa-294	11	3	(	(	PUNCT
ijassa-294	11	4	1	1	X
ijassa-294	11	5	)	)	PUNCT
ijassa-294	11	6	is	be	AUX
ijassa-294	11	7	a	a	DET
ijassa-294	11	8	generalization	generalization	NOUN
ijassa-294	11	9	of	of	ADP
ijassa-294	11	10	a	a	DET
ijassa-294	11	11	model	model	NOUN
ijassa-294	11	12	introduced	introduce	VERB
ijassa-294	11	13	by	by	ADP
ijassa-294	11	14	kirchhoff[2	kirchhoff[2	PROPN
ijassa-294	11	15	]	]	PUNCT
ijassa-294	11	16	.	.	PUNCT
ijassa-294	12	1	more	more	ADV
ijassa-294	12	2	precisely	precisely	ADV
ijassa-294	12	3	,	,	PUNCT
ijassa-294	12	4	kirchhoff	kirchhoff	PROPN
ijassa-294	12	5	proposed	propose	VERB
ijassa-294	12	6	a	a	DET
ijassa-294	12	7	model	model	NOUN
ijassa-294	12	8	given	give	VERB
ijassa-294	12	9	by	by	ADP
ijassa-294	12	10	the	the	DET
ijassa-294	12	11	equation	equation	NOUN
ijassa-294	12	12	ρ	ρ	PROPN
ijassa-294	12	13	∂2u	∂2u	PROPN
ijassa-294	12	14	∂t2	∂t2	PROPN
ijassa-294	12	15	−	−	PROPN
ijassa-294	13	1	(	(	PUNCT
ijassa-294	13	2	ρ0	ρ0	PROPN
ijassa-294	13	3	h	h	NOUN
ijassa-294	13	4	+	+	CCONJ
ijassa-294	13	5	e	e	X
ijassa-294	13	6	2l	2l	NUM
ijassa-294	13	7	∫	∫	PROPN
ijassa-294	13	8	l	l	NOUN
ijassa-294	13	9	0	0	NUM
ijassa-294	13	10	∣∣∣∣∂u∂x	∣∣∣∣∂u∂x	NOUN
ijassa-294	13	11	∣∣∣∣2	∣∣∣∣2	NOUN
ijassa-294	13	12	dx	dx	PROPN
ijassa-294	13	13	)	)	PUNCT
ijassa-294	13	14	∂2u	∂2u	PROPN
ijassa-294	13	15	∂x2	∂x2	PROPN
ijassa-294	13	16	=	=	SYM
ijassa-294	13	17	0	0	NUM
ijassa-294	13	18	,	,	PUNCT
ijassa-294	13	19	(	(	PUNCT
ijassa-294	13	20	2	2	X
ijassa-294	13	21	)	)	PUNCT
ijassa-294	13	22	where	where	SCONJ
ijassa-294	13	23	ρ	ρ	NOUN
ijassa-294	13	24	,	,	PUNCT
ijassa-294	13	25	ρ0	ρ0	PROPN
ijassa-294	13	26	,	,	PUNCT
ijassa-294	13	27	h	h	NOUN
ijassa-294	13	28	,	,	PUNCT
ijassa-294	13	29	e	e	NOUN
ijassa-294	13	30	,	,	PUNCT
ijassa-294	13	31	l	l	NOUN
ijassa-294	13	32	are	be	AUX
ijassa-294	13	33	constants	constant	NOUN
ijassa-294	13	34	,	,	PUNCT
ijassa-294	13	35	which	which	PRON
ijassa-294	13	36	extends	extend	VERB
ijassa-294	13	37	the	the	DET
ijassa-294	13	38	classical	classical	ADJ
ijassa-294	13	39	d’alembert	d’alembert	NOUN
ijassa-294	13	40	’s	’s	PART
ijassa-294	13	41	wave	wave	NOUN
ijassa-294	13	42	equation	equation	NOUN
ijassa-294	13	43	,	,	PUNCT
ijassa-294	13	44	by	by	ADP
ijassa-294	13	45	considering	consider	VERB
ijassa-294	13	46	the	the	DET
ijassa-294	13	47	effect	effect	NOUN
ijassa-294	13	48	of	of	ADP
ijassa-294	13	49	the	the	DET
ijassa-294	13	50	changing	change	VERB
ijassa-294	13	51	in	in	ADP
ijassa-294	13	52	the	the	DET
ijassa-294	13	53	length	length	NOUN
ijassa-294	13	54	of	of	ADP
ijassa-294	13	55	the	the	DET
ijassa-294	13	56	string	string	NOUN
ijassa-294	13	57	during	during	ADP
ijassa-294	13	58	the	the	DET
ijassa-294	13	59	vibration	vibration	NOUN
ijassa-294	13	60	.	.	PUNCT
ijassa-294	14	1	a	a	DET
ijassa-294	14	2	distinguishing	distinguish	VERB
ijassa-294	14	3	feature	feature	NOUN
ijassa-294	14	4	of	of	ADP
ijassa-294	14	5	equation	equation	NOUN
ijassa-294	14	6	(	(	PUNCT
ijassa-294	14	7	2	2	X
ijassa-294	14	8	)	)	PUNCT
ijassa-294	14	9	is	be	AUX
ijassa-294	14	10	that	that	SCONJ
ijassa-294	14	11	the	the	DET
ijassa-294	14	12	equation	equation	NOUN
ijassa-294	14	13	contains	contain	VERB
ijassa-294	14	14	a	a	DET
ijassa-294	14	15	nonlocal	nonlocal	ADJ
ijassa-294	14	16	coefficient	coefficient	NOUN
ijassa-294	14	17	ρ0	ρ0	PROPN
ijassa-294	14	18	h	h	NOUN
ijassa-294	14	19	+	+	CCONJ
ijassa-294	14	20	e	e	X
ijassa-294	14	21	2l	2l	NUM
ijassa-294	14	22	∫	∫	PROPN
ijassa-294	14	23	l	l	NOUN
ijassa-294	14	24	0	0	NUM
ijassa-294	14	25	∣∣∂u	∣∣∂u	PROPN
ijassa-294	14	26	∂x	∂x	PROPN
ijassa-294	14	27	∣∣2	∣∣2	PROPN
ijassa-294	14	28	dx	dx	PROPN
ijassa-294	14	29	which	which	PRON
ijassa-294	14	30	depends	depend	VERB
ijassa-294	14	31	on	on	ADP
ijassa-294	14	32	the	the	DET
ijassa-294	14	33	average	average	ADJ
ijassa-294	14	34	1	1	NUM
ijassa-294	14	35	2l	2l	NUM
ijassa-294	14	36	∫	∫	PROPN
ijassa-294	14	37	l	l	NOUN
ijassa-294	14	38	0	0	NUM
ijassa-294	14	39	∣∣∂u	∣∣∂u	PROPN
ijassa-294	14	40	∂x	∂x	PROPN
ijassa-294	14	41	∣∣2	∣∣2	PROPN
ijassa-294	14	42	dx	dx	NOUN
ijassa-294	14	43	of	of	ADP
ijassa-294	14	44	the	the	DET
ijassa-294	14	45	kinetic	kinetic	ADJ
ijassa-294	14	46	energy	energy	NOUN
ijassa-294	14	47	1	1	NUM
ijassa-294	14	48	2	2	NUM
ijassa-294	14	49	∣∣∂u	∣∣∂u	NOUN
ijassa-294	14	50	∂x	∂x	PROPN
ijassa-294	14	51	∣∣2	∣∣2	PROPN
ijassa-294	14	52	on	on	ADP
ijassa-294	14	53	[	[	X
ijassa-294	14	54	0	0	NUM
ijassa-294	14	55	,	,	PUNCT
ijassa-294	14	56	l	l	NOUN
ijassa-294	14	57	]	]	X
ijassa-294	14	58	,	,	PUNCT
ijassa-294	14	59	and	and	CCONJ
ijassa-294	14	60	hence	hence	ADV
ijassa-294	14	61	the	the	DET
ijassa-294	14	62	equation	equation	NOUN
ijassa-294	14	63	is	be	AUX
ijassa-294	14	64	no	no	ADV
ijassa-294	14	65	longer	long	ADV
ijassa-294	14	66	a	a	DET
ijassa-294	14	67	pointwise	pointwise	ADJ
ijassa-294	14	68	identity	identity	NOUN
ijassa-294	14	69	.	.	PUNCT
ijassa-294	15	1	the	the	DET
ijassa-294	15	2	equation	equation	NOUN
ijassa-294	15	3	{	{	PUNCT
ijassa-294	15	4	−	−	PROPN
ijassa-294	15	5	(	(	PUNCT
ijassa-294	15	6	a+	a+	SYM
ijassa-294	15	7	b	b	PROPN
ijassa-294	15	8	∫	∫	PROPN
ijassa-294	15	9	ω	ω	PROPN
ijassa-294	15	10	|∇u|	|∇u|	ADJ
ijassa-294	15	11	2	2	NUM
ijassa-294	15	12	dx	dx	PROPN
ijassa-294	15	13	)	)	PUNCT
ijassa-294	16	1	∆u	∆u	PROPN
ijassa-294	16	2	=	=	SYM
ijassa-294	16	3	f(x	f(x	PROPN
ijassa-294	16	4	,	,	PUNCT
ijassa-294	16	5	u	u	NOUN
ijassa-294	16	6	)	)	PUNCT
ijassa-294	16	7	in	in	ADP
ijassa-294	16	8	ω	ω	PROPN
ijassa-294	16	9	,	,	PUNCT
ijassa-294	16	10	u	u	NOUN
ijassa-294	16	11	=	=	NOUN
ijassa-294	16	12	0	0	NUM
ijassa-294	16	13	on	on	ADP
ijassa-294	16	14	∂ω	∂ω	PROPN
ijassa-294	16	15	,	,	PUNCT
ijassa-294	16	16	(	(	PUNCT
ijassa-294	16	17	3	3	X
ijassa-294	16	18	)	)	PUNCT
ijassa-294	16	19	issn	issn	PROPN
ijassa-294	16	20	1078	1078	NUM
ijassa-294	16	21	-	-	PUNCT
ijassa-294	16	22	6236	6236	NUM
ijassa-294	16	23	international	international	PROPN
ijassa-294	16	24	institute	institute	NOUN
ijassa-294	16	25	for	for	ADP
ijassa-294	16	26	general	general	ADJ
ijassa-294	16	27	systems	system	NOUN
ijassa-294	16	28	studies	study	NOUN
ijassa-294	16	29	,	,	PUNCT
ijassa-294	16	30	inc	inc	PROPN
ijassa-294	16	31	.	.	PROPN
ijassa-294	16	32	advances	advance	NOUN
ijassa-294	16	33	in	in	ADP
ijassa-294	16	34	systems	system	NOUN
ijassa-294	16	35	science	science	NOUN
ijassa-294	16	36	and	and	CCONJ
ijassa-294	16	37	applications	application	NOUN
ijassa-294	16	38	(	(	PUNCT
ijassa-294	16	39	2011	2011	NUM
ijassa-294	16	40	)	)	PUNCT
ijassa-294	16	41	,	,	PUNCT
ijassa-294	16	42	vol	vol	NOUN
ijassa-294	16	43	.	.	PROPN
ijassa-294	17	1	11	11	NUM
ijassa-294	17	2	,	,	PUNCT
ijassa-294	17	3	no	no	INTJ
ijassa-294	17	4	.	.	NOUN
ijassa-294	17	5	1	1	NUM
ijassa-294	17	6	-	-	SYM
ijassa-294	17	7	2	2	NUM
ijassa-294	17	8	83	83	NUM
ijassa-294	17	9	is	be	AUX
ijassa-294	17	10	related	relate	VERB
ijassa-294	17	11	to	to	ADP
ijassa-294	17	12	the	the	DET
ijassa-294	17	13	stationary	stationary	ADJ
ijassa-294	17	14	analogue	analogue	NOUN
ijassa-294	17	15	of	of	ADP
ijassa-294	17	16	the	the	DET
ijassa-294	17	17	equation	equation	NOUN
ijassa-294	17	18	(	(	PUNCT
ijassa-294	17	19	2	2	NUM
ijassa-294	17	20	)	)	PUNCT
ijassa-294	17	21	.	.	PUNCT
ijassa-294	18	1	equation	equation	NOUN
ijassa-294	18	2	(	(	PUNCT
ijassa-294	18	3	3	3	X
ijassa-294	18	4	)	)	PUNCT
ijassa-294	18	5	received	receive	VERB
ijassa-294	18	6	much	much	ADJ
ijassa-294	18	7	attention	attention	NOUN
ijassa-294	18	8	only	only	ADV
ijassa-294	18	9	after	after	SCONJ
ijassa-294	18	10	lions	lion	NOUN
ijassa-294	18	11	[	[	X
ijassa-294	18	12	3	3	NUM
ijassa-294	18	13	]	]	PUNCT
ijassa-294	18	14	proposed	propose	VERB
ijassa-294	18	15	an	an	DET
ijassa-294	18	16	abstract	abstract	ADJ
ijassa-294	18	17	framework	framework	NOUN
ijassa-294	18	18	to	to	ADP
ijassa-294	18	19	the	the	DET
ijassa-294	18	20	problem	problem	NOUN
ijassa-294	18	21	.	.	PUNCT
ijassa-294	19	1	some	some	DET
ijassa-294	19	2	important	important	ADJ
ijassa-294	19	3	and	and	CCONJ
ijassa-294	19	4	interesting	interesting	ADJ
ijassa-294	19	5	results	result	NOUN
ijassa-294	19	6	can	can	AUX
ijassa-294	19	7	be	be	AUX
ijassa-294	19	8	found	find	VERB
ijassa-294	19	9	,	,	PUNCT
ijassa-294	19	10	for	for	ADP
ijassa-294	19	11	example	example	NOUN
ijassa-294	19	12	,	,	PUNCT
ijassa-294	19	13	in	in	ADP
ijassa-294	19	14	[	[	PUNCT
ijassa-294	19	15	4	4	NUM
ijassa-294	19	16	-	-	SYM
ijassa-294	19	17	15	15	NUM
ijassa-294	19	18	]	]	PUNCT
ijassa-294	19	19	.	.	PUNCT
ijassa-294	20	1	in	in	ADP
ijassa-294	20	2	the	the	DET
ijassa-294	20	3	context	context	NOUN
ijassa-294	20	4	of	of	ADP
ijassa-294	20	5	population	population	NOUN
ijassa-294	20	6	biology	biology	NOUN
ijassa-294	20	7	,	,	PUNCT
ijassa-294	20	8	the	the	DET
ijassa-294	20	9	nonlinear	nonlinear	ADJ
ijassa-294	20	10	function	function	NOUN
ijassa-294	20	11	f(x	f(x	PROPN
ijassa-294	20	12	,	,	PUNCT
ijassa-294	20	13	u	u	NOUN
ijassa-294	20	14	)	)	PUNCT
ijassa-294	20	15	≡	≡	PROPN
ijassa-294	20	16	ug(x	ug(x	X
ijassa-294	20	17	,	,	PUNCT
ijassa-294	20	18	u	u	NOUN
ijassa-294	20	19	)	)	PUNCT
ijassa-294	20	20	represents	represent	VERB
ijassa-294	20	21	a	a	DET
ijassa-294	20	22	density	density	NOUN
ijassa-294	20	23	dependent	dependent	ADJ
ijassa-294	20	24	growth	growth	NOUN
ijassa-294	20	25	if	if	SCONJ
ijassa-294	20	26	g(x	g(x	NOUN
ijassa-294	20	27	,	,	PUNCT
ijassa-294	20	28	u	u	NOUN
ijassa-294	20	29	)	)	PUNCT
ijassa-294	20	30	is	be	AUX
ijassa-294	20	31	a	a	DET
ijassa-294	20	32	function	function	NOUN
ijassa-294	20	33	depending	depend	VERB
ijassa-294	20	34	on	on	ADP
ijassa-294	20	35	the	the	DET
ijassa-294	20	36	population	population	NOUN
ijassa-294	20	37	density	density	NOUN
ijassa-294	20	38	u.	u.	VERB
ijassa-294	20	39	while	while	SCONJ
ijassa-294	20	40	traditionally	traditionally	ADV
ijassa-294	20	41	g(x	g(x	ADJ
ijassa-294	20	42	,	,	PUNCT
ijassa-294	20	43	u	u	NOUN
ijassa-294	20	44	)	)	PUNCT
ijassa-294	20	45	is	be	AUX
ijassa-294	20	46	assumed	assume	VERB
ijassa-294	20	47	to	to	PART
ijassa-294	20	48	be	be	AUX
ijassa-294	20	49	declining	decline	VERB
ijassa-294	20	50	to	to	PART
ijassa-294	20	51	reflect	reflect	VERB
ijassa-294	20	52	the	the	DET
ijassa-294	20	53	crowding	crowd	VERB
ijassa-294	20	54	effect	effect	NOUN
ijassa-294	20	55	of	of	ADP
ijassa-294	20	56	the	the	DET
ijassa-294	20	57	increasing	increase	VERB
ijassa-294	20	58	population	population	NOUN
ijassa-294	20	59	,	,	PUNCT
ijassa-294	20	60	allee	allee	PROPN
ijassa-294	20	61	suggested	suggest	VERB
ijassa-294	20	62	that	that	SCONJ
ijassa-294	20	63	physiological	physiological	ADJ
ijassa-294	20	64	and	and	CCONJ
ijassa-294	20	65	demographic	demographic	ADJ
ijassa-294	20	66	precesses	precesse	NOUN
ijassa-294	20	67	often	often	ADV
ijassa-294	20	68	possess	possess	VERB
ijassa-294	20	69	an	an	DET
ijassa-294	20	70	optimal	optimal	ADJ
ijassa-294	20	71	density	density	NOUN
ijassa-294	20	72	,	,	PUNCT
ijassa-294	20	73	with	with	ADP
ijassa-294	20	74	the	the	DET
ijassa-294	20	75	response	response	NOUN
ijassa-294	20	76	decreasing	decrease	VERB
ijassa-294	20	77	as	as	ADP
ijassa-294	20	78	either	either	CCONJ
ijassa-294	20	79	higher	high	ADJ
ijassa-294	20	80	or	or	CCONJ
ijassa-294	20	81	lower	low	ADJ
ijassa-294	20	82	densities	density	NOUN
ijassa-294	20	83	.	.	PUNCT
ijassa-294	21	1	such	such	ADJ
ijassa-294	21	2	growth	growth	NOUN
ijassa-294	21	3	pattern	pattern	NOUN
ijassa-294	21	4	is	be	AUX
ijassa-294	21	5	called	call	VERB
ijassa-294	21	6	an	an	DET
ijassa-294	21	7	allee	allee	ADJ
ijassa-294	21	8	effect	effect	NOUN
ijassa-294	21	9	.	.	PUNCT
ijassa-294	22	1	if	if	SCONJ
ijassa-294	22	2	the	the	DET
ijassa-294	22	3	growth	growth	NOUN
ijassa-294	22	4	rate	rate	NOUN
ijassa-294	22	5	per	per	ADP
ijassa-294	22	6	capita	capita	NOUN
ijassa-294	22	7	is	be	AUX
ijassa-294	22	8	negative	negative	ADJ
ijassa-294	22	9	when	when	SCONJ
ijassa-294	22	10	u	u	NOUN
ijassa-294	22	11	is	be	AUX
ijassa-294	22	12	small	small	ADJ
ijassa-294	22	13	,	,	PUNCT
ijassa-294	22	14	we	we	PRON
ijassa-294	22	15	call	call	VERB
ijassa-294	22	16	it	it	PRON
ijassa-294	22	17	a	a	DET
ijassa-294	22	18	strong	strong	ADJ
ijassa-294	22	19	allee	allee	NOUN
ijassa-294	22	20	effect	effect	NOUN
ijassa-294	22	21	;	;	PUNCT
ijassa-294	22	22	if	if	SCONJ
ijassa-294	22	23	the	the	DET
ijassa-294	22	24	growth	growth	NOUN
ijassa-294	22	25	rate	rate	NOUN
ijassa-294	22	26	per	per	ADP
ijassa-294	22	27	capita	capita	NOUN
ijassa-294	22	28	is	be	AUX
ijassa-294	22	29	small	small	ADJ
ijassa-294	22	30	than	than	ADP
ijassa-294	22	31	the	the	DET
ijassa-294	22	32	maximum	maximum	ADJ
ijassa-294	22	33	but	but	CCONJ
ijassa-294	22	34	still	still	ADV
ijassa-294	22	35	positive	positive	ADJ
ijassa-294	22	36	for	for	ADP
ijassa-294	22	37	small	small	ADJ
ijassa-294	22	38	u	u	NOUN
ijassa-294	22	39	,	,	PUNCT
ijassa-294	22	40	we	we	PRON
ijassa-294	22	41	call	call	VERB
ijassa-294	22	42	it	it	PRON
ijassa-294	22	43	a	a	DET
ijassa-294	22	44	weak	weak	ADJ
ijassa-294	22	45	allee	allee	ADJ
ijassa-294	22	46	effect	effect	NOUN
ijassa-294	22	47	(	(	PUNCT
ijassa-294	22	48	for	for	ADP
ijassa-294	22	49	detail	detail	NOUN
ijassa-294	22	50	,	,	PUNCT
ijassa-294	22	51	see	see	VERB
ijassa-294	22	52	[	[	X
ijassa-294	22	53	16	16	NUM
ijassa-294	22	54	]	]	PUNCT
ijassa-294	22	55	or	or	CCONJ
ijassa-294	22	56	[	[	X
ijassa-294	22	57	17	17	NUM
ijassa-294	22	58	]	]	NUM
ijassa-294	22	59	)	)	PUNCT
ijassa-294	22	60	.	.	PUNCT
ijassa-294	23	1	under	under	ADP
ijassa-294	23	2	the	the	DET
ijassa-294	23	3	special	special	ADJ
ijassa-294	23	4	case	case	NOUN
ijassa-294	23	5	of	of	ADP
ijassa-294	23	6	equation	equation	NOUN
ijassa-294	23	7	(	(	PUNCT
ijassa-294	23	8	3	3	NUM
ijassa-294	23	9	)	)	PUNCT
ijassa-294	23	10	with	with	ADP
ijassa-294	23	11	a	a	DET
ijassa-294	23	12	=	=	SYM
ijassa-294	23	13	1	1	NUM
ijassa-294	23	14	,	,	PUNCT
ijassa-294	23	15	b	b	X
ijassa-294	23	16	=	=	SYM
ijassa-294	23	17	0	0	PROPN
ijassa-294	23	18	and	and	CCONJ
ijassa-294	23	19	f(x	f(x	PROPN
ijassa-294	23	20	,	,	PUNCT
ijassa-294	23	21	u	u	NOUN
ijassa-294	23	22	)	)	PUNCT
ijassa-294	23	23	satisfies	satisfy	VERB
ijassa-294	23	24	inhomogeneous	inhomogeneous	ADJ
ijassa-294	23	25	strong	strong	ADJ
ijassa-294	23	26	allee	allee	ADJ
ijassa-294	23	27	effect	effect	NOUN
ijassa-294	23	28	growth	growth	NOUN
ijassa-294	23	29	pattern	pattern	NOUN
ijassa-294	23	30	,	,	PUNCT
ijassa-294	23	31	liu	liu	PROPN
ijassa-294	23	32	,	,	PUNCT
ijassa-294	23	33	wang	wang	PROPN
ijassa-294	23	34	and	and	CCONJ
ijassa-294	23	35	shi[16	shi[16	PROPN
ijassa-294	23	36	]	]	PUNCT
ijassa-294	23	37	prove	prove	VERB
ijassa-294	23	38	that	that	SCONJ
ijassa-294	23	39	the	the	DET
ijassa-294	23	40	equation	equation	NOUN
ijassa-294	23	41	{	{	PUNCT
ijassa-294	23	42	−∆u	−∆u	NOUN
ijassa-294	23	43	=	=	SYM
ijassa-294	23	44	λf(x	λf(x	PROPN
ijassa-294	23	45	,	,	PUNCT
ijassa-294	23	46	u	u	NOUN
ijassa-294	23	47	)	)	PUNCT
ijassa-294	23	48	in	in	ADP
ijassa-294	23	49	ω	ω	PROPN
ijassa-294	23	50	,	,	PUNCT
ijassa-294	23	51	u	u	NOUN
ijassa-294	23	52	=	=	NOUN
ijassa-294	23	53	0	0	NUM
ijassa-294	23	54	on	on	ADP
ijassa-294	23	55	∂ω	∂ω	PROPN
ijassa-294	23	56	(	(	PUNCT
ijassa-294	23	57	4	4	NUM
ijassa-294	23	58	)	)	PUNCT
ijassa-294	23	59	has	have	VERB
ijassa-294	23	60	at	at	ADV
ijassa-294	23	61	least	least	ADV
ijassa-294	23	62	two	two	NUM
ijassa-294	23	63	positive	positive	ADJ
ijassa-294	23	64	solutions	solution	NOUN
ijassa-294	23	65	for	for	ADP
ijassa-294	23	66	large	large	ADJ
ijassa-294	23	67	λ	λ	PROPN
ijassa-294	23	68	if	if	SCONJ
ijassa-294	23	69	∫	∫	PROPN
ijassa-294	23	70	c(x	c(x	NOUN
ijassa-294	23	71	)	)	PUNCT
ijassa-294	23	72	0	0	PUNCT
ijassa-294	24	1	f(x	f(x	PROPN
ijassa-294	24	2	,	,	PUNCT
ijassa-294	24	3	s	s	X
ijassa-294	24	4	)	)	PUNCT
ijassa-294	24	5	ds	ds	VERB
ijassa-294	24	6	>	>	X
ijassa-294	24	7	0	0	PUNCT
ijassa-294	25	1	for	for	ADP
ijassa-294	25	2	x	x	PRON
ijassa-294	25	3	in	in	ADP
ijassa-294	25	4	an	an	DET
ijassa-294	25	5	open	open	ADJ
ijassa-294	25	6	subset	subset	NOUN
ijassa-294	25	7	of	of	ADP
ijassa-294	25	8	ω	ω	PROPN
ijassa-294	25	9	,	,	PUNCT
ijassa-294	25	10	where	where	SCONJ
ijassa-294	25	11	c(x	c(x	NOUN
ijassa-294	25	12	)	)	PUNCT
ijassa-294	25	13	∈	∈	PROPN
ijassa-294	25	14	c1(ω	c1(ω	NOUN
ijassa-294	25	15	)	)	PUNCT
ijassa-294	25	16	such	such	ADJ
ijassa-294	25	17	that	that	SCONJ
ijassa-294	25	18	f(x	f(x	PROPN
ijassa-294	25	19	,	,	PUNCT
ijassa-294	25	20	c(x	c(x	NOUN
ijassa-294	25	21	)	)	PUNCT
ijassa-294	25	22	)	)	PUNCT
ijassa-294	26	1	=	=	PUNCT
ijassa-294	26	2	0(see	0(see	VERB
ijassa-294	26	3	the	the	DET
ijassa-294	26	4	assumption	assumption	NOUN
ijassa-294	26	5	of	of	ADP
ijassa-294	26	6	(	(	PUNCT
ijassa-294	26	7	f2	f2	PROPN
ijassa-294	26	8	)	)	PUNCT
ijassa-294	26	9	)	)	PUNCT
ijassa-294	26	10	.	.	PUNCT
ijassa-294	27	1	they	they	PRON
ijassa-294	27	2	also	also	ADV
ijassa-294	27	3	prove	prove	VERB
ijassa-294	27	4	some	some	DET
ijassa-294	27	5	nonexistence	nonexistence	NOUN
ijassa-294	27	6	results	result	NOUN
ijassa-294	27	7	.	.	PUNCT
ijassa-294	28	1	in	in	ADP
ijassa-294	28	2	particular	particular	ADJ
ijassa-294	28	3	,	,	PUNCT
ijassa-294	28	4	they	they	PRON
ijassa-294	28	5	conjecture	conjecture	VERB
ijassa-294	28	6	that	that	SCONJ
ijassa-294	28	7	the	the	DET
ijassa-294	28	8	nonexistence	nonexistence	NOUN
ijassa-294	28	9	holds	hold	VERB
ijassa-294	28	10	if∫	if∫	ADJ
ijassa-294	28	11	c(x	c(x	NOUN
ijassa-294	28	12	)	)	PUNCT
ijassa-294	28	13	0	0	PUNCT
ijassa-294	29	1	f(x	f(x	PROPN
ijassa-294	29	2	,	,	PUNCT
ijassa-294	29	3	s	s	X
ijassa-294	29	4	)	)	PUNCT
ijassa-294	29	5	ds	ds	ADJ
ijassa-294	29	6	≤	≤	NOUN
ijassa-294	29	7	0	0	NUM
ijassa-294	29	8	for	for	ADP
ijassa-294	29	9	any	any	DET
ijassa-294	29	10	x	x	SYM
ijassa-294	29	11	∈	∈	PROPN
ijassa-294	29	12	ω	ω	NOUN
ijassa-294	29	13	(	(	PUNCT
ijassa-294	29	14	see	see	INTJ
ijassa-294	29	15	remark	remark	NOUN
ijassa-294	29	16	1.7	1.7	NUM
ijassa-294	29	17	of	of	ADP
ijassa-294	29	18	[	[	X
ijassa-294	29	19	16	16	NUM
ijassa-294	29	20	]	]	SYM
ijassa-294	29	21	)	)	PUNCT
ijassa-294	29	22	.	.	PUNCT
ijassa-294	30	1	motivated	motivate	VERB
ijassa-294	30	2	by	by	ADP
ijassa-294	30	3	above	above	ADV
ijassa-294	30	4	,	,	PUNCT
ijassa-294	30	5	we	we	PRON
ijassa-294	30	6	generalize	generalize	VERB
ijassa-294	30	7	existence	existence	NOUN
ijassa-294	30	8	and	and	CCONJ
ijassa-294	30	9	nonexistence	nonexistence	NOUN
ijassa-294	30	10	results	result	VERB
ijassa-294	30	11	for	for	ADP
ijassa-294	30	12	the	the	DET
ijassa-294	30	13	semilinear	semilinear	PROPN
ijassa-294	30	14	elliptic	elliptic	ADJ
ijassa-294	30	15	equation	equation	NOUN
ijassa-294	30	16	(	(	PUNCT
ijassa-294	30	17	4	4	NUM
ijassa-294	30	18	)	)	PUNCT
ijassa-294	30	19	to	to	ADP
ijassa-294	30	20	the	the	DET
ijassa-294	30	21	case	case	NOUN
ijassa-294	30	22	of	of	ADP
ijassa-294	30	23	nonlocal	nonlocal	ADJ
ijassa-294	30	24	semilinear	semilinear	ADJ
ijassa-294	30	25	elliptic	elliptic	ADJ
ijassa-294	30	26	equation	equation	NOUN
ijassa-294	30	27	(	(	PUNCT
ijassa-294	30	28	1	1	NUM
ijassa-294	30	29	)	)	PUNCT
ijassa-294	30	30	.	.	PUNCT
ijassa-294	31	1	more	more	ADV
ijassa-294	31	2	precisely	precisely	ADV
ijassa-294	31	3	,	,	PUNCT
ijassa-294	31	4	if	if	SCONJ
ijassa-294	31	5	f(x	f(x	PROPN
ijassa-294	31	6	,	,	PUNCT
ijassa-294	31	7	u	u	NOUN
ijassa-294	31	8	)	)	PUNCT
ijassa-294	31	9	satisfies	satisfy	VERB
ijassa-294	31	10	inhomogeneous	inhomogeneous	ADJ
ijassa-294	31	11	strong	strong	ADJ
ijassa-294	31	12	allee	allee	ADJ
ijassa-294	31	13	effect	effect	NOUN
ijassa-294	31	14	growth	growth	NOUN
ijassa-294	31	15	pattern	pattern	NOUN
ijassa-294	31	16	and	and	CCONJ
ijassa-294	31	17	the	the	DET
ijassa-294	31	18	nonlocal	nonlocal	ADJ
ijassa-294	31	19	coefficient	coefficient	NOUN
ijassa-294	31	20	m(t	m(t	NOUN
ijassa-294	31	21	)	)	PUNCT
ijassa-294	31	22	satisfies	satisfy	VERB
ijassa-294	31	23	some	some	DET
ijassa-294	31	24	suitable	suitable	ADJ
ijassa-294	31	25	conditions	condition	NOUN
ijassa-294	31	26	,	,	PUNCT
ijassa-294	31	27	we	we	PRON
ijassa-294	31	28	establish	establish	VERB
ijassa-294	31	29	the	the	DET
ijassa-294	31	30	existence	existence	NOUN
ijassa-294	31	31	of	of	ADP
ijassa-294	31	32	at	at	ADV
ijassa-294	31	33	least	least	ADV
ijassa-294	31	34	two	two	NUM
ijassa-294	31	35	positive	positive	ADJ
ijassa-294	31	36	solutions	solution	NOUN
ijassa-294	31	37	for	for	ADP
ijassa-294	31	38	the	the	DET
ijassa-294	31	39	nonlocal	nonlocal	ADJ
ijassa-294	31	40	problem	problem	NOUN
ijassa-294	31	41	(	(	PUNCT
ijassa-294	31	42	1	1	X
ijassa-294	31	43	)	)	PUNCT
ijassa-294	31	44	withλ	withλ	NOUN
ijassa-294	31	45	large	large	ADJ
ijassa-294	31	46	enough	enough	ADV
ijassa-294	31	47	.	.	PUNCT
ijassa-294	32	1	we	we	PRON
ijassa-294	32	2	also	also	ADV
ijassa-294	32	3	prove	prove	VERB
ijassa-294	32	4	some	some	DET
ijassa-294	32	5	nonexistence	nonexistence	NOUN
ijassa-294	32	6	results	result	VERB
ijassa-294	32	7	for	for	ADP
ijassa-294	32	8	the	the	DET
ijassa-294	32	9	nonlocal	nonlocal	ADJ
ijassa-294	32	10	problem	problem	NOUN
ijassa-294	32	11	(	(	PUNCT
ijassa-294	32	12	1	1	NUM
ijassa-294	32	13	)	)	PUNCT
ijassa-294	32	14	.	.	PUNCT
ijassa-294	33	1	in	in	ADP
ijassa-294	33	2	particular	particular	ADJ
ijassa-294	33	3	,	,	PUNCT
ijassa-294	33	4	we	we	PRON
ijassa-294	33	5	shall	shall	AUX
ijassa-294	33	6	give	give	VERB
ijassa-294	33	7	a	a	DET
ijassa-294	33	8	positive	positive	ADJ
ijassa-294	33	9	answer	answer	NOUN
ijassa-294	33	10	to	to	ADP
ijassa-294	33	11	the	the	DET
ijassa-294	33	12	conjecture	conjecture	NOUN
ijassa-294	33	13	by	by	ADP
ijassa-294	33	14	liu	liu	PROPN
ijassa-294	33	15	,	,	PUNCT
ijassa-294	33	16	wang	wang	PROPN
ijassa-294	33	17	and	and	CCONJ
ijassa-294	33	18	shi	shi	PROPN
ijassa-294	33	19	.	.	PUNCT
ijassa-294	34	1	to	to	ADP
ijassa-294	34	2	the	the	DET
ijassa-294	34	3	best	good	ADJ
ijassa-294	34	4	of	of	ADP
ijassa-294	34	5	our	our	PRON
ijassa-294	34	6	knowledge	knowledge	NOUN
ijassa-294	34	7	,	,	PUNCT
ijassa-294	34	8	this	this	PRON
ijassa-294	34	9	is	be	AUX
ijassa-294	34	10	the	the	DET
ijassa-294	34	11	first	first	ADJ
ijassa-294	34	12	paper	paper	NOUN
ijassa-294	34	13	that	that	PRON
ijassa-294	34	14	discusses	discuss	VERB
ijassa-294	34	15	the	the	DET
ijassa-294	34	16	nonlocal	nonlocal	ADJ
ijassa-294	34	17	semilinear	semilinear	ADJ
ijassa-294	34	18	elliptic	elliptic	ADJ
ijassa-294	34	19	equation	equation	NOUN
ijassa-294	34	20	with	with	ADP
ijassa-294	34	21	inhomogeneous	inhomogeneous	ADJ
ijassa-294	34	22	strong	strong	ADJ
ijassa-294	34	23	allee	allee	ADJ
ijassa-294	34	24	effect	effect	NOUN
ijassa-294	34	25	via	via	ADP
ijassa-294	34	26	variational	variational	ADJ
ijassa-294	34	27	method	method	NOUN
ijassa-294	34	28	.	.	PUNCT
ijassa-294	35	1	we	we	PRON
ijassa-294	35	2	point	point	VERB
ijassa-294	35	3	out	out	ADP
ijassa-294	35	4	the	the	DET
ijassa-294	35	5	nonlocal	nonlocal	ADJ
ijassa-294	35	6	coefficient	coefficient	NOUN
ijassa-294	35	7	m(t	m(t	NOUN
ijassa-294	35	8	)	)	PUNCT
ijassa-294	35	9	raises	raise	VERB
ijassa-294	35	10	some	some	PRON
ijassa-294	35	11	of	of	ADP
ijassa-294	35	12	the	the	DET
ijassa-294	35	13	essential	essential	ADJ
ijassa-294	35	14	difficulties	difficulty	NOUN
ijassa-294	35	15	.	.	PUNCT
ijassa-294	36	1	for	for	ADP
ijassa-294	36	2	example	example	NOUN
ijassa-294	36	3	,	,	PUNCT
ijassa-294	36	4	the	the	DET
ijassa-294	36	5	way	way	NOUN
ijassa-294	36	6	of	of	ADP
ijassa-294	36	7	proving	prove	VERB
ijassa-294	36	8	the	the	DET
ijassa-294	36	9	geometry	geometry	NOUN
ijassa-294	36	10	condition	condition	NOUN
ijassa-294	36	11	of	of	ADP
ijassa-294	36	12	mountain	mountain	NOUN
ijassa-294	36	13	pass	pass	NOUN
ijassa-294	36	14	theorem	theorem	NOUN
ijassa-294	36	15	in	in	ADP
ijassa-294	36	16	[	[	X
ijassa-294	36	17	16	16	NUM
ijassa-294	36	18	]	]	PUNCT
ijassa-294	36	19	can	can	AUX
ijassa-294	36	20	not	not	PART
ijassa-294	36	21	be	be	AUX
ijassa-294	36	22	used	use	VERB
ijassa-294	36	23	here	here	ADV
ijassa-294	36	24	because	because	SCONJ
ijassa-294	36	25	the	the	DET
ijassa-294	36	26	functional	functional	NOUN
ijassa-294	36	27	of	of	ADP
ijassa-294	36	28	(	(	PUNCT
ijassa-294	36	29	1	1	NUM
ijassa-294	36	30	)	)	PUNCT
ijassa-294	36	31	is	be	AUX
ijassa-294	36	32	notc2	notc2	NOUN
ijassa-294	36	33	function	function	NOUN
ijassa-294	36	34	under	under	ADP
ijassa-294	36	35	our	our	PRON
ijassa-294	36	36	assumptions	assumption	NOUN
ijassa-294	36	37	.	.	PUNCT
ijassa-294	37	1	in	in	ADP
ijassa-294	37	2	order	order	NOUN
ijassa-294	37	3	to	to	PART
ijassa-294	37	4	overcome	overcome	VERB
ijassa-294	37	5	this	this	DET
ijassa-294	37	6	difficulty	difficulty	NOUN
ijassa-294	37	7	,	,	PUNCT
ijassa-294	37	8	we	we	PRON
ijassa-294	37	9	divided	divide	VERB
ijassa-294	37	10	ω	ω	PROPN
ijassa-294	37	11	into	into	ADP
ijassa-294	37	12	b1	b1	NOUN
ijassa-294	37	13	and	and	CCONJ
ijassa-294	37	14	b2	b2	NOUN
ijassa-294	37	15	by	by	ADP
ijassa-294	37	16	comparing	compare	VERB
ijassa-294	37	17	the	the	DET
ijassa-294	37	18	value	value	NOUN
ijassa-294	37	19	of	of	ADP
ijassa-294	37	20	c(x	c(x	NOUN
ijassa-294	37	21	)	)	PUNCT
ijassa-294	37	22	with	with	ADP
ijassa-294	37	23	b	b	NOUN
ijassa-294	37	24	,	,	PUNCT
ijassa-294	37	25	then	then	ADV
ijassa-294	37	26	use	use	VERB
ijassa-294	37	27	poincaré	poincaré	ADJ
ijassa-294	37	28	inequality	inequality	NOUN
ijassa-294	37	29	to	to	PART
ijassa-294	37	30	prove	prove	VERB
ijassa-294	37	31	it(see	it(see	PROPN
ijassa-294	37	32	lemma	lemma	PROPN
ijassa-294	37	33	3.3	3.3	NUM
ijassa-294	37	34	)	)	PUNCT
ijassa-294	37	35	.	.	PUNCT
ijassa-294	38	1	this	this	DET
ijassa-294	38	2	paper	paper	NOUN
ijassa-294	38	3	is	be	AUX
ijassa-294	38	4	organized	organize	VERB
ijassa-294	38	5	as	as	SCONJ
ijassa-294	38	6	follows	follow	VERB
ijassa-294	38	7	.	.	PUNCT
ijassa-294	39	1	in	in	ADP
ijassa-294	39	2	section	section	NOUN
ijassa-294	39	3	2	2	NUM
ijassa-294	39	4	,	,	PUNCT
ijassa-294	39	5	we	we	PRON
ijassa-294	39	6	present	present	VERB
ijassa-294	39	7	our	our	PRON
ijassa-294	39	8	main	main	ADJ
ijassa-294	39	9	resuts	resut	NOUN
ijassa-294	39	10	and	and	CCONJ
ijassa-294	39	11	some	some	DET
ijassa-294	39	12	necessary	necessary	ADJ
ijassa-294	39	13	preliminary	preliminary	ADJ
ijassa-294	39	14	lemmas	lemma	NOUN
ijassa-294	39	15	.	.	PUNCT
ijassa-294	40	1	in	in	ADP
ijassa-294	40	2	sections	section	NOUN
ijassa-294	40	3	3	3	NUM
ijassa-294	40	4	,	,	PUNCT
ijassa-294	40	5	we	we	PRON
ijassa-294	40	6	use	use	VERB
ijassa-294	40	7	variational	variational	ADJ
ijassa-294	40	8	method	method	NOUN
ijassa-294	40	9	and	and	CCONJ
ijassa-294	40	10	sub	sub	NOUN
ijassa-294	40	11	-	-	NOUN
ijassa-294	40	12	supersolution	supersolution	NOUN
ijassa-294	40	13	method	method	NOUN
ijassa-294	40	14	to	to	PART
ijassa-294	40	15	prove	prove	VERB
ijassa-294	40	16	the	the	DET
ijassa-294	40	17	main	main	ADJ
ijassa-294	40	18	results	result	NOUN
ijassa-294	40	19	.	.	PUNCT
ijassa-294	41	1	in	in	ADP
ijassa-294	41	2	section	section	NOUN
ijassa-294	41	3	4	4	NUM
ijassa-294	41	4	,	,	PUNCT
ijassa-294	41	5	we	we	PRON
ijassa-294	41	6	prove	prove	VERB
ijassa-294	41	7	the	the	DET
ijassa-294	41	8	conjecture	conjecture	NOUN
ijassa-294	41	9	of	of	ADP
ijassa-294	41	10	liu	liu	PROPN
ijassa-294	41	11	,	,	PUNCT
ijassa-294	41	12	wang	wang	PROPN
ijassa-294	41	13	and	and	CCONJ
ijassa-294	41	14	shi	shi	PROPN
ijassa-294	41	15	’s	’s	PART
ijassa-294	41	16	and	and	CCONJ
ijassa-294	41	17	give	give	VERB
ijassa-294	41	18	some	some	DET
ijassa-294	41	19	examples	example	NOUN
ijassa-294	41	20	which	which	PRON
ijassa-294	41	21	satisfy	satisfy	VERB
ijassa-294	41	22	our	our	PRON
ijassa-294	41	23	hypotheses	hypothesis	NOUN
ijassa-294	41	24	.	.	PUNCT
ijassa-294	42	1	2	2	X
ijassa-294	42	2	.	.	X
ijassa-294	42	3	main	main	ADJ
ijassa-294	42	4	resuts	resut	NOUN
ijassa-294	42	5	and	and	CCONJ
ijassa-294	42	6	preliminaries	preliminary	NOUN
ijassa-294	42	7	in	in	ADP
ijassa-294	42	8	this	this	DET
ijassa-294	42	9	section	section	NOUN
ijassa-294	42	10	,	,	PUNCT
ijassa-294	42	11	we	we	PRON
ijassa-294	42	12	give	give	VERB
ijassa-294	42	13	our	our	PRON
ijassa-294	42	14	main	main	ADJ
ijassa-294	42	15	results	result	NOUN
ijassa-294	42	16	and	and	CCONJ
ijassa-294	42	17	some	some	DET
ijassa-294	42	18	necessary	necessary	ADJ
ijassa-294	42	19	preliminary	preliminary	ADJ
ijassa-294	42	20	lemmas	lemma	NOUN
ijassa-294	42	21	which	which	PRON
ijassa-294	42	22	will	will	AUX
ijassa-294	42	23	be	be	AUX
ijassa-294	42	24	used	use	VERB
ijassa-294	42	25	in	in	ADP
ijassa-294	42	26	the	the	DET
ijassa-294	42	27	following	following	ADJ
ijassa-294	42	28	proof	proof	NOUN
ijassa-294	42	29	.	.	PUNCT
ijassa-294	43	1	for	for	ADP
ijassa-294	43	2	simplicity	simplicity	NOUN
ijassa-294	43	3	we	we	PRON
ijassa-294	43	4	write	write	VERB
ijassa-294	43	5	x	x	PUNCT
ijassa-294	43	6	=	=	PRON
ijassa-294	43	7	h1	h1	NOUN
ijassa-294	43	8	0	0	NUM
ijassa-294	43	9	(	(	PUNCT
ijassa-294	43	10	ω	ω	NOUN
ijassa-294	43	11	)	)	PUNCT
ijassa-294	43	12	with	with	ADP
ijassa-294	43	13	the	the	DET
ijassa-294	43	14	norm	norm	NOUN
ijassa-294	44	1	‖u‖	‖u‖	PROPN
ijassa-294	44	2	=	=	PROPN
ijassa-294	44	3	84	84	NUM
ijassa-294	44	4	ma	ma	NOUN
ijassa-294	44	5	:	:	PUNCT
ijassa-294	44	6	existence	existence	NOUN
ijassa-294	44	7	and	and	CCONJ
ijassa-294	44	8	nonexistence	nonexistence	NOUN
ijassa-294	44	9	of	of	ADP
ijassa-294	44	10	positive	positive	ADJ
ijassa-294	44	11	solutions	solution	NOUN
ijassa-294	44	12	for	for	ADP
ijassa-294	44	13	a	a	DET
ijassa-294	44	14	kirchhoff	kirchhoff	NOUN
ijassa-294	44	15	-	-	PUNCT
ijassa-294	44	16	type	type	NOUN
ijassa-294	44	17	.	.	PUNCT
ijassa-294	44	18	.	.	PUNCT
ijassa-294	44	19	.	.	PUNCT
ijassa-294	44	20	.	.	PUNCT
ijassa-294	44	21	.	.	PUNCT
ijassa-294	45	1	.(∫	.(∫	PUNCT
ijassa-294	46	1	1	1	NUM
ijassa-294	46	2	0	0	NUM
ijassa-294	46	3	|∇u|	|∇u|	ADJ
ijassa-294	46	4	2	2	NUM
ijassa-294	46	5	dx	dx	PROPN
ijassa-294	46	6	)	)	PUNCT
ijassa-294	46	7	1	1	NUM
ijassa-294	46	8	2	2	NUM
ijassa-294	46	9	.	.	PUNCT
ijassa-294	47	1	hereafter	hereafter	ADV
ijassa-294	47	2	,	,	PUNCT
ijassa-294	47	3	f(x	f(x	PROPN
ijassa-294	47	4	,	,	PUNCT
ijassa-294	47	5	t	t	PROPN
ijassa-294	47	6	)	)	PUNCT
ijassa-294	47	7	and	and	CCONJ
ijassa-294	47	8	m(t	m(t	NOUN
ijassa-294	47	9	)	)	PUNCT
ijassa-294	47	10	are	be	AUX
ijassa-294	47	11	always	always	ADV
ijassa-294	47	12	supposed	suppose	VERB
ijassa-294	47	13	to	to	PART
ijassa-294	47	14	verify	verify	VERB
ijassa-294	47	15	the	the	DET
ijassa-294	47	16	following	follow	VERB
ijassa-294	47	17	assumptions	assumption	NOUN
ijassa-294	47	18	:	:	PUNCT
ijassa-294	47	19	(	(	PUNCT
ijassa-294	47	20	f1	f1	NOUN
ijassa-294	47	21	)	)	PUNCT
ijassa-294	47	22	f(x	f(x	PROPN
ijassa-294	47	23	,	,	PUNCT
ijassa-294	47	24	u	u	NOUN
ijassa-294	47	25	)	)	PUNCT
ijassa-294	47	26	∈	∈	PROPN
ijassa-294	47	27	c(ω×	c(ω×	NOUN
ijassa-294	47	28	r+	r+	PROPN
ijassa-294	47	29	)	)	PUNCT
ijassa-294	47	30	and	and	CCONJ
ijassa-294	47	31	f(x	f(x	PROPN
ijassa-294	47	32	,	,	PUNCT
ijassa-294	47	33	·	·	PUNCT
ijassa-294	47	34	)	)	PUNCT
ijassa-294	48	1	∈	∈	PROPN
ijassa-294	48	2	c1(r+	c1(r+	PROPN
ijassa-294	48	3	)	)	PUNCT
ijassa-294	48	4	for	for	ADP
ijassa-294	48	5	any	any	DET
ijassa-294	48	6	x	x	SYM
ijassa-294	48	7	∈	∈	PROPN
ijassa-294	48	8	ω	ω	PROPN
ijassa-294	48	9	;	;	PUNCT
ijassa-294	48	10	(	(	PUNCT
ijassa-294	48	11	f2	f2	X
ijassa-294	48	12	)	)	PUNCT
ijassa-294	48	13	there	there	PRON
ijassa-294	48	14	exist	exist	VERB
ijassa-294	48	15	b(x	b(x	NOUN
ijassa-294	48	16	)	)	PUNCT
ijassa-294	48	17	∈	∈	PROPN
ijassa-294	48	18	c(ω	c(ω	PROPN
ijassa-294	48	19	)	)	PUNCT
ijassa-294	48	20	,	,	PUNCT
ijassa-294	48	21	c(x	c(x	NOUN
ijassa-294	48	22	)	)	PUNCT
ijassa-294	48	23	∈	∈	PROPN
ijassa-294	48	24	c1(ω	c1(ω	NOUN
ijassa-294	48	25	)	)	PUNCT
ijassa-294	49	1	such	such	ADJ
ijassa-294	49	2	that	that	SCONJ
ijassa-294	49	3	0	0	NUM
ijassa-294	49	4	<	<	X
ijassa-294	49	5	b(x	b(x	NOUN
ijassa-294	49	6	)	)	PUNCT
ijassa-294	49	7	<	<	X
ijassa-294	49	8	c(x	c(x	NOUN
ijassa-294	49	9	)	)	PUNCT
ijassa-294	49	10	and	and	CCONJ
ijassa-294	49	11	f(x	f(x	PROPN
ijassa-294	49	12	,	,	PUNCT
ijassa-294	49	13	0	0	NUM
ijassa-294	49	14	)	)	PUNCT
ijassa-294	49	15	=	=	SYM
ijassa-294	49	16	f(x	f(x	PROPN
ijassa-294	49	17	,	,	PUNCT
ijassa-294	49	18	b(x	b(x	NOUN
ijassa-294	49	19	)	)	PUNCT
ijassa-294	49	20	)	)	PUNCT
ijassa-294	50	1	=	=	SYM
ijassa-294	50	2	f(x	f(x	PROPN
ijassa-294	50	3	,	,	PUNCT
ijassa-294	50	4	c(x	c(x	NOUN
ijassa-294	50	5	)	)	PUNCT
ijassa-294	50	6	)	)	PUNCT
ijassa-294	51	1	=	=	SYM
ijassa-294	51	2	0	0	NUM
ijassa-294	52	1	for	for	ADP
ijassa-294	52	2	any	any	DET
ijassa-294	52	3	x	x	SYM
ijassa-294	52	4	∈	∈	PROPN
ijassa-294	52	5	ω	ω	PROPN
ijassa-294	52	6	;	;	PUNCT
ijassa-294	52	7	(	(	PUNCT
ijassa-294	52	8	f3	f3	ADJ
ijassa-294	52	9	)	)	PUNCT
ijassa-294	52	10	for	for	ADP
ijassa-294	52	11	almost	almost	ADV
ijassa-294	52	12	all	all	PRON
ijassa-294	52	13	x	x	SYM
ijassa-294	52	14	∈	∈	PROPN
ijassa-294	52	15	ω	ω	PROPN
ijassa-294	52	16	,	,	PUNCT
ijassa-294	52	17	f(x	f(x	PROPN
ijassa-294	52	18	,	,	PUNCT
ijassa-294	52	19	s	s	PART
ijassa-294	52	20	)	)	PUNCT
ijassa-294	52	21	<	<	X
ijassa-294	52	22	0	0	NUM
ijassa-294	52	23	for	for	ADP
ijassa-294	52	24	any	any	DET
ijassa-294	52	25	s	s	X
ijassa-294	52	26	∈	∈	NOUN
ijassa-294	52	27	(	(	PUNCT
ijassa-294	52	28	0	0	NUM
ijassa-294	52	29	,	,	PUNCT
ijassa-294	52	30	b(x	b(x	NOUN
ijassa-294	52	31	)	)	PUNCT
ijassa-294	52	32	)	)	PUNCT
ijassa-294	52	33	∪	∪	X
ijassa-294	52	34	(	(	PUNCT
ijassa-294	52	35	c(x),+∞	c(x),+∞	X
ijassa-294	52	36	)	)	PUNCT
ijassa-294	52	37	and	and	CCONJ
ijassa-294	52	38	f(x	f(x	PROPN
ijassa-294	52	39	,	,	PUNCT
ijassa-294	52	40	s	s	PROPN
ijassa-294	52	41	)	)	PUNCT
ijassa-294	52	42	>	>	X
ijassa-294	52	43	0	0	PUNCT
ijassa-294	53	1	for	for	ADP
ijassa-294	53	2	any	any	DET
ijassa-294	53	3	s	s	X
ijassa-294	53	4	∈	∈	NOUN
ijassa-294	53	5	(	(	PUNCT
ijassa-294	53	6	b(x	b(x	NOUN
ijassa-294	53	7	)	)	PUNCT
ijassa-294	53	8	,	,	PUNCT
ijassa-294	53	9	c(x	c(x	NOUN
ijassa-294	53	10	)	)	PUNCT
ijassa-294	53	11	)	)	PUNCT
ijassa-294	53	12	.	.	PUNCT
ijassa-294	54	1	remark	remark	VERB
ijassa-294	54	2	2.1	2.1	NUM
ijassa-294	54	3	.	.	PUNCT
ijassa-294	55	1	note	note	VERB
ijassa-294	55	2	that	that	SCONJ
ijassa-294	55	3	the	the	DET
ijassa-294	55	4	weak	weak	ADJ
ijassa-294	55	5	maximum	maximum	ADJ
ijassa-294	55	6	principle	principle	NOUN
ijassa-294	55	7	(	(	PUNCT
ijassa-294	55	8	theorem	theorem	VERB
ijassa-294	55	9	8.1	8.1	NUM
ijassa-294	55	10	of	of	ADP
ijassa-294	55	11	[	[	X
ijassa-294	55	12	18	18	NUM
ijassa-294	55	13	]	]	PUNCT
ijassa-294	55	14	)	)	PUNCT
ijassa-294	55	15	and	and	CCONJ
ijassa-294	55	16	strong	strong	ADJ
ijassa-294	55	17	maximum	maximum	ADJ
ijassa-294	55	18	principle	principle	NOUN
ijassa-294	55	19	(	(	PUNCT
ijassa-294	55	20	theorem	theorem	VERB
ijassa-294	55	21	8.1	8.1	NUM
ijassa-294	55	22	of	of	ADP
ijassa-294	55	23	[	[	X
ijassa-294	55	24	18	18	NUM
ijassa-294	55	25	]	]	PUNCT
ijassa-294	55	26	)	)	PUNCT
ijassa-294	55	27	also	also	ADV
ijassa-294	55	28	hold	hold	VERB
ijassa-294	55	29	for	for	ADP
ijassa-294	55	30	the	the	DET
ijassa-294	55	31	nonlocal	nonlocal	ADJ
ijassa-294	55	32	problem	problem	NOUN
ijassa-294	55	33	(	(	PUNCT
ijassa-294	55	34	1	1	NUM
ijassa-294	55	35	)	)	PUNCT
ijassa-294	55	36	because	because	SCONJ
ijassa-294	55	37	m(t	m(t	NOUN
ijassa-294	55	38	)	)	PUNCT
ijassa-294	55	39	satisfies	satisfy	VERB
ijassa-294	55	40	the	the	DET
ijassa-294	55	41	assumption	assumption	NOUN
ijassa-294	55	42	(	(	PUNCT
ijassa-294	55	43	m	m	PROPN
ijassa-294	55	44	)	)	PUNCT
ijassa-294	55	45	.	.	PUNCT
ijassa-294	56	1	(	(	PUNCT
ijassa-294	56	2	m	m	NOUN
ijassa-294	56	3	)	)	PUNCT
ijassa-294	56	4	∃m0	∃m0	PROPN
ijassa-294	56	5	>	>	X
ijassa-294	56	6	0	0	NUM
ijassa-294	57	1	such	such	ADJ
ijassa-294	57	2	that	that	SCONJ
ijassa-294	57	3	m(t	m(t	NOUN
ijassa-294	57	4	)	)	PUNCT
ijassa-294	57	5	≥	≥	PROPN
ijassa-294	57	6	m0	m0	NOUN
ijassa-294	57	7	.	.	PUNCT
ijassa-294	58	1	definition	definition	NOUN
ijassa-294	58	2	2.1	2.1	NUM
ijassa-294	58	3	.	.	PUNCT
ijassa-294	59	1	we	we	PRON
ijassa-294	59	2	say	say	VERB
ijassa-294	59	3	that	that	SCONJ
ijassa-294	59	4	u	u	PRON
ijassa-294	59	5	∈	∈	PROPN
ijassa-294	59	6	x	x	X
ijassa-294	59	7	is	be	AUX
ijassa-294	59	8	a	a	DET
ijassa-294	59	9	weak	weak	ADJ
ijassa-294	59	10	solution	solution	NOUN
ijassa-294	59	11	of	of	ADP
ijassa-294	59	12	(	(	PUNCT
ijassa-294	59	13	1	1	NUM
ijassa-294	59	14	)	)	PUNCT
ijassa-294	59	15	,	,	PUNCT
ijassa-294	59	16	if	if	SCONJ
ijassa-294	59	17	m	m	PROPN
ijassa-294	59	18	(	(	PUNCT
ijassa-294	59	19	∫	∫	PROPN
ijassa-294	59	20	ω	ω	PROPN
ijassa-294	59	21	1	1	NUM
ijassa-294	59	22	2	2	NUM
ijassa-294	59	23	|∇u|2	|∇u|2	NOUN
ijassa-294	59	24	dx	dx	PROPN
ijassa-294	59	25	)	)	PUNCT
ijassa-294	59	26	∫	∫	PROPN
ijassa-294	60	1	ω	ω	NUM
ijassa-294	60	2	∇u∇ϕdx	∇u∇ϕdx	NOUN
ijassa-294	61	1	=	=	SYM
ijassa-294	61	2	λ	λ	PROPN
ijassa-294	61	3	∫	∫	PROPN
ijassa-294	61	4	ω	ω	PROPN
ijassa-294	61	5	f(x	f(x	PROPN
ijassa-294	61	6	,	,	PUNCT
ijassa-294	61	7	u)ϕdx	u)ϕdx	PROPN
ijassa-294	61	8	for	for	ADP
ijassa-294	61	9	any	any	PRON
ijassa-294	61	10	ϕ	ϕ	PROPN
ijassa-294	61	11	∈	∈	PROPN
ijassa-294	61	12	x.	x.	NOUN
ijassa-294	61	13	define	define	VERB
ijassa-294	61	14	φ(u	φ(u	NOUN
ijassa-294	61	15	)	)	PUNCT
ijassa-294	61	16	=	=	SYM
ijassa-294	61	17	m̂	m̂	PROPN
ijassa-294	62	1	(	(	PUNCT
ijassa-294	62	2	∫	∫	PROPN
ijassa-294	62	3	ω	ω	NUM
ijassa-294	62	4	1	1	NUM
ijassa-294	62	5	2	2	NUM
ijassa-294	62	6	|∇u|2	|∇u|2	NOUN
ijassa-294	62	7	dx	dx	PROPN
ijassa-294	62	8	)	)	PUNCT
ijassa-294	62	9	,	,	PUNCT
ijassa-294	62	10	ψ(u	ψ(u	PROPN
ijassa-294	62	11	)	)	PUNCT
ijassa-294	62	12	=	=	PUNCT
ijassa-294	63	1	∫	∫	PROPN
ijassa-294	64	1	ω	ω	NUM
ijassa-294	64	2	f	f	PROPN
ijassa-294	64	3	(	(	PUNCT
ijassa-294	64	4	x	x	NOUN
ijassa-294	64	5	,	,	PUNCT
ijassa-294	64	6	u	u	NOUN
ijassa-294	64	7	)	)	PUNCT
ijassa-294	64	8	dx	dx	PROPN
ijassa-294	64	9	,	,	PUNCT
ijassa-294	64	10	where	where	SCONJ
ijassa-294	64	11	m̂(t	m̂(t	VERB
ijassa-294	64	12	)	)	PUNCT
ijassa-294	64	13	=	=	SYM
ijassa-294	65	1	∫	∫	PROPN
ijassa-294	65	2	t	t	PROPN
ijassa-294	65	3	0	0	NUM
ijassa-294	65	4	m(s	m(s	PROPN
ijassa-294	65	5	)	)	PUNCT
ijassa-294	65	6	ds	ds	PROPN
ijassa-294	65	7	,	,	PUNCT
ijassa-294	65	8	f	f	PROPN
ijassa-294	65	9	(	(	PUNCT
ijassa-294	65	10	x	x	NOUN
ijassa-294	65	11	,	,	PUNCT
ijassa-294	65	12	u	u	NOUN
ijassa-294	65	13	)	)	PUNCT
ijassa-294	65	14	=	=	SYM
ijassa-294	66	1	∫	∫	PROPN
ijassa-294	66	2	u	u	NOUN
ijassa-294	66	3	0	0	PROPN
ijassa-294	66	4	f(x	f(x	PROPN
ijassa-294	66	5	,	,	PUNCT
ijassa-294	66	6	t	t	PROPN
ijassa-294	66	7	)	)	PUNCT
ijassa-294	66	8	dt	dt	PROPN
ijassa-294	66	9	.	.	PUNCT
ijassa-294	67	1	we	we	PRON
ijassa-294	67	2	redefine	redefine	VERB
ijassa-294	67	3	f(x	f(x	PROPN
ijassa-294	67	4	,	,	PUNCT
ijassa-294	67	5	u	u	NOUN
ijassa-294	67	6	)	)	PUNCT
ijassa-294	67	7	,	,	PUNCT
ijassa-294	67	8	such	such	ADJ
ijassa-294	67	9	that	that	SCONJ
ijassa-294	67	10	f(x	f(x	PROPN
ijassa-294	67	11	,	,	PUNCT
ijassa-294	67	12	u	u	NOUN
ijassa-294	67	13	)	)	PUNCT
ijassa-294	67	14	≡	≡	PROPN
ijassa-294	67	15	0	0	PUNCT
ijassa-294	67	16	when	when	SCONJ
ijassa-294	67	17	u	u	PROPN
ijassa-294	67	18	∈	∈	PROPN
ijassa-294	67	19	(	(	PUNCT
ijassa-294	67	20	−∞	−∞	NOUN
ijassa-294	67	21	,	,	PUNCT
ijassa-294	67	22	0	0	NUM
ijassa-294	67	23	)	)	PUNCT
ijassa-294	67	24	∪	∪	NOUN
ijassa-294	67	25	(	(	PUNCT
ijassa-294	67	26	c(x),∞	c(x),∞	PROPN
ijassa-294	67	27	)	)	PUNCT
ijassa-294	67	28	,	,	PUNCT
ijassa-294	67	29	but	but	CCONJ
ijassa-294	67	30	it	it	PRON
ijassa-294	67	31	does	do	AUX
ijassa-294	67	32	not	not	PART
ijassa-294	67	33	change	change	VERB
ijassa-294	67	34	the	the	DET
ijassa-294	67	35	solution	solution	NOUN
ijassa-294	67	36	set	set	VERB
ijassa-294	67	37	of	of	ADP
ijassa-294	67	38	(	(	PUNCT
ijassa-294	67	39	1	1	NUM
ijassa-294	67	40	)	)	PUNCT
ijassa-294	67	41	by	by	ADP
ijassa-294	67	42	the	the	DET
ijassa-294	67	43	weak	weak	ADJ
ijassa-294	67	44	maximum	maximum	ADJ
ijassa-294	67	45	principle	principle	NOUN
ijassa-294	67	46	,	,	PUNCT
ijassa-294	67	47	since	since	SCONJ
ijassa-294	67	48	all	all	DET
ijassa-294	67	49	the	the	DET
ijassa-294	67	50	solution	solution	NOUN
ijassa-294	67	51	of	of	ADP
ijassa-294	67	52	(	(	PUNCT
ijassa-294	67	53	1	1	X
ijassa-294	67	54	)	)	PUNCT
ijassa-294	67	55	satisfies	satisfie	NOUN
ijassa-294	67	56	0	0	NUM
ijassa-294	67	57	≤	≤	NUM
ijassa-294	67	58	u(x	u(x	NOUN
ijassa-294	67	59	)	)	PUNCT
ijassa-294	67	60	≤	≤	NUM
ijassa-294	67	61	c(x	c(x	NOUN
ijassa-294	67	62	)	)	PUNCT
ijassa-294	67	63	.	.	PUNCT
ijassa-294	68	1	then	then	ADV
ijassa-294	68	2	the	the	DET
ijassa-294	68	3	energy	energy	NOUN
ijassa-294	68	4	functional	functional	ADJ
ijassa-294	68	5	iλ(u	iλ(u	NOUN
ijassa-294	68	6	)	)	PUNCT
ijassa-294	68	7	=	=	SYM
ijassa-294	68	8	φ(u	φ(u	NOUN
ijassa-294	68	9	)	)	PUNCT
ijassa-294	68	10	−	−	NOUN
ijassa-294	68	11	λψ(u	λψ(u	NUM
ijassa-294	68	12	)	)	PUNCT
ijassa-294	68	13	:	:	PUNCT
ijassa-294	69	1	x	x	X
ijassa-294	69	2	→	→	SYM
ijassa-294	69	3	r	r	NOUN
ijassa-294	69	4	associated	associate	VERB
ijassa-294	69	5	with	with	ADP
ijassa-294	69	6	problem	problem	NOUN
ijassa-294	69	7	(	(	PUNCT
ijassa-294	69	8	1	1	X
ijassa-294	69	9	)	)	PUNCT
ijassa-294	69	10	is	be	AUX
ijassa-294	69	11	well	well	ADV
ijassa-294	69	12	defined	define	VERB
ijassa-294	69	13	.	.	PUNCT
ijassa-294	70	1	then	then	ADV
ijassa-294	70	2	it	it	PRON
ijassa-294	70	3	is	be	AUX
ijassa-294	70	4	easy	easy	ADJ
ijassa-294	70	5	to	to	PART
ijassa-294	70	6	see	see	VERB
ijassa-294	70	7	that	that	SCONJ
ijassa-294	70	8	iλ	iλ	PROPN
ijassa-294	70	9	∈	∈	PROPN
ijassa-294	70	10	c1	c1	NOUN
ijassa-294	70	11	(	(	PUNCT
ijassa-294	70	12	x	x	NOUN
ijassa-294	70	13	,	,	PUNCT
ijassa-294	70	14	r	r	NOUN
ijassa-294	70	15	)	)	PUNCT
ijassa-294	70	16	is	be	AUX
ijassa-294	70	17	weakly	weakly	ADV
ijassa-294	70	18	lower	low	ADJ
ijassa-294	70	19	semi	semi	ADJ
ijassa-294	70	20	-	-	ADJ
ijassa-294	70	21	continuous	continuous	ADJ
ijassa-294	70	22	and	and	CCONJ
ijassa-294	70	23	u	u	NOUN
ijassa-294	70	24	∈	∈	PROPN
ijassa-294	70	25	x	x	PUNCT
ijassa-294	70	26	is	be	AUX
ijassa-294	70	27	a	a	DET
ijassa-294	70	28	weak	weak	ADJ
ijassa-294	70	29	solution	solution	NOUN
ijassa-294	70	30	of	of	ADP
ijassa-294	70	31	(	(	PUNCT
ijassa-294	70	32	1	1	X
ijassa-294	70	33	)	)	PUNCT
ijassa-294	70	34	if	if	SCONJ
ijassa-294	71	1	and	and	CCONJ
ijassa-294	71	2	only	only	ADV
ijassa-294	71	3	if	if	SCONJ
ijassa-294	71	4	u	u	NOUN
ijassa-294	71	5	is	be	AUX
ijassa-294	71	6	a	a	DET
ijassa-294	71	7	critical	critical	ADJ
ijassa-294	71	8	point	point	NOUN
ijassa-294	71	9	of	of	ADP
ijassa-294	71	10	iλ	iλ	NOUN
ijassa-294	71	11	.	.	PUNCT
ijassa-294	72	1	from	from	ADP
ijassa-294	72	2	the	the	DET
ijassa-294	72	3	regularity	regularity	NOUN
ijassa-294	72	4	assumptions	assumption	NOUN
ijassa-294	72	5	on	on	ADP
ijassa-294	72	6	f(x	f(x	PROPN
ijassa-294	72	7	,	,	PUNCT
ijassa-294	72	8	u	u	NOUN
ijassa-294	72	9	)	)	PUNCT
ijassa-294	72	10	,	,	PUNCT
ijassa-294	72	11	any	any	DET
ijassa-294	72	12	critical	critical	ADJ
ijassa-294	72	13	point	point	NOUN
ijassa-294	72	14	u	u	PROPN
ijassa-294	72	15	of	of	ADP
ijassa-294	72	16	iλ	iλ	PROPN
ijassa-294	72	17	(	(	PUNCT
ijassa-294	72	18	·	·	PUNCT
ijassa-294	72	19	)	)	PUNCT
ijassa-294	72	20	is	be	AUX
ijassa-294	72	21	a	a	DET
ijassa-294	72	22	classical	classical	ADJ
ijassa-294	72	23	solution	solution	NOUN
ijassa-294	72	24	of	of	ADP
ijassa-294	72	25	(	(	PUNCT
ijassa-294	72	26	1	1	NUM
ijassa-294	72	27	)	)	PUNCT
ijassa-294	72	28	(	(	PUNCT
ijassa-294	72	29	see	see	VERB
ijassa-294	72	30	[	[	X
ijassa-294	72	31	19	19	NUM
ijassa-294	72	32	,	,	PUNCT
ijassa-294	72	33	20	20	NUM
ijassa-294	72	34	]	]	NUM
ijassa-294	72	35	)	)	PUNCT
ijassa-294	72	36	,	,	PUNCT
ijassa-294	72	37	and	and	CCONJ
ijassa-294	72	38	from	from	ADP
ijassa-294	72	39	the	the	DET
ijassa-294	72	40	strong	strong	ADJ
ijassa-294	72	41	maximum	maximum	ADJ
ijassa-294	72	42	principle	principle	NOUN
ijassa-294	72	43	and	and	CCONJ
ijassa-294	72	44	the	the	DET
ijassa-294	72	45	definition	definition	NOUN
ijassa-294	72	46	of	of	ADP
ijassa-294	72	47	modified	modify	VERB
ijassa-294	72	48	f(x	f(x	PROPN
ijassa-294	72	49	,	,	PUNCT
ijassa-294	72	50	u	u	NOUN
ijassa-294	72	51	)	)	PUNCT
ijassa-294	72	52	above	above	ADV
ijassa-294	72	53	,	,	PUNCT
ijassa-294	72	54	u	u	NOUN
ijassa-294	72	55	is	be	AUX
ijassa-294	72	56	either	either	PRON
ijassa-294	72	57	zero	zero	NUM
ijassa-294	72	58	or	or	CCONJ
ijassa-294	72	59	satisfies	satisfie	NOUN
ijassa-294	72	60	0	0	PUNCT
ijassa-294	72	61	<	<	X
ijassa-294	72	62	u(x	u(x	PROPN
ijassa-294	72	63	)	)	PUNCT
ijassa-294	72	64	<	<	X
ijassa-294	72	65	c(x	c(x	NOUN
ijassa-294	72	66	)	)	PUNCT
ijassa-294	72	67	for	for	ADP
ijassa-294	72	68	any	any	DET
ijassa-294	72	69	x	x	SYM
ijassa-294	72	70	∈	∈	PROPN
ijassa-294	72	71	ω	ω	PROPN
ijassa-294	72	72	.	.	PUNCT
ijassa-294	73	1	moreover	moreover	ADV
ijassa-294	73	2	,	,	PUNCT
ijassa-294	73	3	we	we	PRON
ijassa-294	73	4	have	have	VERB
ijassa-294	73	5	i	i	PRON
ijassa-294	74	1	′λ(u)v	′λ(u)v	PROPN
ijassa-294	75	1	=	=	SYM
ijassa-294	75	2	m	m	PROPN
ijassa-294	75	3	(	(	PUNCT
ijassa-294	75	4	∫	∫	PROPN
ijassa-294	75	5	ω	ω	NUM
ijassa-294	75	6	1	1	NUM
ijassa-294	75	7	2	2	NUM
ijassa-294	75	8	|∇u|2	|∇u|2	NOUN
ijassa-294	75	9	dx	dx	PROPN
ijassa-294	75	10	)	)	PUNCT
ijassa-294	75	11	∫	∫	PROPN
ijassa-294	76	1	ω	ω	NUM
ijassa-294	76	2	∇u∇v	∇u∇v	X
ijassa-294	76	3	dx−	dx−	NUM
ijassa-294	77	1	λ	λ	PROPN
ijassa-294	77	2	∫	∫	PROPN
ijassa-294	77	3	ω	ω	PROPN
ijassa-294	77	4	f(x	f(x	PROPN
ijassa-294	77	5	,	,	PUNCT
ijassa-294	77	6	u)v	u)v	X
ijassa-294	77	7	dx	dx	PROPN
ijassa-294	78	1	=	=	SYM
ijassa-294	78	2	φ′(u)v	φ′(u)v	PROPN
ijassa-294	78	3	−	−	NUM
ijassa-294	78	4	λψ′(u	λψ′(u	NOUN
ijassa-294	78	5	)	)	PUNCT
ijassa-294	78	6	,	,	PUNCT
ijassa-294	78	7	for	for	ADP
ijassa-294	78	8	any	any	DET
ijassa-294	78	9	v	v	NOUN
ijassa-294	78	10	∈	∈	NOUN
ijassa-294	78	11	x.	x.	NOUN
ijassa-294	78	12	from	from	ADP
ijassa-294	78	13	(	(	PUNCT
ijassa-294	78	14	m	m	PROPN
ijassa-294	78	15	)	)	PUNCT
ijassa-294	78	16	and	and	CCONJ
ijassa-294	78	17	lemma	lemma	PROPN
ijassa-294	78	18	4.1	4.1	NUM
ijassa-294	78	19	of	of	ADP
ijassa-294	78	20	[	[	X
ijassa-294	78	21	21	21	NUM
ijassa-294	78	22	]	]	PUNCT
ijassa-294	78	23	we	we	PRON
ijassa-294	78	24	can	can	AUX
ijassa-294	78	25	easily	easily	ADV
ijassa-294	78	26	see	see	VERB
ijassa-294	78	27	that	that	SCONJ
ijassa-294	78	28	φ′	φ′	NUM
ijassa-294	78	29	is	be	AUX
ijassa-294	78	30	of	of	ADP
ijassa-294	78	31	(	(	PUNCT
ijassa-294	78	32	s+	s+	NOUN
ijassa-294	78	33	)	)	PUNCT
ijassa-294	78	34	type	type	NOUN
ijassa-294	78	35	,	,	PUNCT
ijassa-294	78	36	i.e.	i.e.	X
ijassa-294	78	37	if	if	SCONJ
ijassa-294	78	38	un	un	PROPN
ijassa-294	78	39	⇀	⇀	PROPN
ijassa-294	78	40	u	u	PROPN
ijassa-294	78	41	in	in	ADP
ijassa-294	78	42	x	x	X
ijassa-294	78	43	and	and	CCONJ
ijassa-294	78	44	lim	lim	PROPN
ijassa-294	78	45	n→+∞	n→+∞	PROPN
ijassa-294	78	46	(	(	PUNCT
ijassa-294	78	47	φ′(un)−	φ′(un)−	NOUN
ijassa-294	78	48	φ′(u	φ′(u	PROPN
ijassa-294	78	49	)	)	PUNCT
ijassa-294	78	50	,	,	PUNCT
ijassa-294	78	51	un	un	PROPN
ijassa-294	78	52	−	−	PROPN
ijassa-294	78	53	u	u	PROPN
ijassa-294	78	54	)	)	PUNCT
ijassa-294	78	55	≤	≤	NOUN
ijassa-294	78	56	0	0	NUM
ijassa-294	78	57	,	,	PUNCT
ijassa-294	78	58	then	then	ADV
ijassa-294	78	59	un	un	PROPN
ijassa-294	78	60	→	→	SYM
ijassa-294	78	61	u	u	PROPN
ijassa-294	78	62	in	in	ADP
ijassa-294	78	63	x	x	X
ijassa-294	78	64	.	.	PUNCT
ijassa-294	79	1	it	it	PRON
ijassa-294	79	2	is	be	AUX
ijassa-294	79	3	clear	clear	ADJ
ijassa-294	79	4	that	that	SCONJ
ijassa-294	79	5	ψ′	ψ′	PROPN
ijassa-294	79	6	is	be	AUX
ijassa-294	79	7	weak	weak	ADJ
ijassa-294	79	8	-	-	PUNCT
ijassa-294	79	9	strong	strong	ADJ
ijassa-294	79	10	continuous	continuous	ADJ
ijassa-294	79	11	(	(	PUNCT
ijassa-294	79	12	or	or	CCONJ
ijassa-294	79	13	see	see	VERB
ijassa-294	79	14	lemma	lemma	PROPN
ijassa-294	79	15	1.2	1.2	NUM
ijassa-294	79	16	of	of	ADP
ijassa-294	79	17	[	[	X
ijassa-294	79	18	1	1	NUM
ijassa-294	79	19	]	]	NUM
ijassa-294	79	20	)	)	PUNCT
ijassa-294	79	21	.	.	PUNCT
ijassa-294	80	1	so	so	ADV
ijassa-294	80	2	i	i	PRON
ijassa-294	80	3	′λ	′λ	PROPN
ijassa-294	80	4	is	be	AUX
ijassa-294	80	5	of	of	ADP
ijassa-294	80	6	(	(	PUNCT
ijassa-294	80	7	s+	s+	NOUN
ijassa-294	80	8	)	)	PUNCT
ijassa-294	80	9	type	type	NOUN
ijassa-294	80	10	.	.	PUNCT
ijassa-294	81	1	advances	advance	NOUN
ijassa-294	81	2	in	in	ADP
ijassa-294	81	3	systems	system	NOUN
ijassa-294	81	4	science	science	NOUN
ijassa-294	81	5	and	and	CCONJ
ijassa-294	81	6	applications	application	NOUN
ijassa-294	81	7	(	(	PUNCT
ijassa-294	81	8	2011	2011	NUM
ijassa-294	81	9	)	)	PUNCT
ijassa-294	81	10	,	,	PUNCT
ijassa-294	81	11	vol	vol	NOUN
ijassa-294	81	12	.	.	PROPN
ijassa-294	82	1	11	11	NUM
ijassa-294	82	2	,	,	PUNCT
ijassa-294	82	3	no	no	INTJ
ijassa-294	82	4	.	.	NOUN
ijassa-294	82	5	1	1	NUM
ijassa-294	82	6	-	-	SYM
ijassa-294	82	7	2	2	NUM
ijassa-294	82	8	85	85	NUM
ijassa-294	82	9	our	our	PRON
ijassa-294	82	10	main	main	ADJ
ijassa-294	82	11	existence	existence	NOUN
ijassa-294	82	12	result	result	NOUN
ijassa-294	82	13	is	be	AUX
ijassa-294	82	14	as	as	SCONJ
ijassa-294	82	15	follows	follow	VERB
ijassa-294	82	16	:	:	PUNCT
ijassa-294	82	17	theorem	theorem	NOUN
ijassa-294	82	18	2.1	2.1	NUM
ijassa-294	82	19	.	.	PUNCT
ijassa-294	83	1	if	if	SCONJ
ijassa-294	83	2	m(t	m(t	NOUN
ijassa-294	83	3	)	)	PUNCT
ijassa-294	83	4	satisfies	satisfie	NOUN
ijassa-294	83	5	(	(	PUNCT
ijassa-294	83	6	m	m	PROPN
ijassa-294	83	7	)	)	PUNCT
ijassa-294	83	8	and	and	CCONJ
ijassa-294	83	9	f(x	f(x	PROPN
ijassa-294	83	10	,	,	PUNCT
ijassa-294	83	11	u	u	NOUN
ijassa-294	83	12	)	)	PUNCT
ijassa-294	83	13	satisfies	satisfie	NOUN
ijassa-294	83	14	(	(	PUNCT
ijassa-294	83	15	f1)–(f3	f1)–(f3	NOUN
ijassa-294	83	16	)	)	PUNCT
ijassa-294	83	17	,	,	PUNCT
ijassa-294	83	18	and	and	CCONJ
ijassa-294	83	19	ω1	ω1	PROPN
ijassa-294	83	20	is	be	AUX
ijassa-294	83	21	an	an	DET
ijassa-294	83	22	open	open	ADJ
ijassa-294	83	23	subset	subset	NOUN
ijassa-294	83	24	of	of	ADP
ijassa-294	83	25	ω	ω	NUM
ijassa-294	83	26	such	such	ADJ
ijassa-294	83	27	that	that	DET
ijassa-294	83	28	∫	∫	PROPN
ijassa-294	83	29	c(x	c(x	NOUN
ijassa-294	83	30	)	)	PUNCT
ijassa-294	83	31	0	0	PUNCT
ijassa-294	84	1	f(x	f(x	PROPN
ijassa-294	84	2	,	,	PUNCT
ijassa-294	84	3	s	s	X
ijassa-294	84	4	)	)	PUNCT
ijassa-294	84	5	ds	ds	X
ijassa-294	84	6	>	>	X
ijassa-294	84	7	0	0	PUNCT
ijassa-294	85	1	(	(	PUNCT
ijassa-294	85	2	5	5	NUM
ijassa-294	85	3	)	)	PUNCT
ijassa-294	85	4	for	for	ADP
ijassa-294	85	5	x	x	PROPN
ijassa-294	85	6	∈	∈	PROPN
ijassa-294	85	7	ω1	ω1	PROPN
ijassa-294	85	8	,	,	PUNCT
ijassa-294	85	9	then	then	ADV
ijassa-294	85	10	for	for	ADP
ijassa-294	85	11	λ	λ	PROPN
ijassa-294	85	12	large	large	ADJ
ijassa-294	85	13	enough	enough	ADV
ijassa-294	85	14	,	,	PUNCT
ijassa-294	85	15	(	(	PUNCT
ijassa-294	85	16	1	1	X
ijassa-294	85	17	)	)	PUNCT
ijassa-294	85	18	has	have	VERB
ijassa-294	85	19	at	at	ADV
ijassa-294	85	20	least	least	ADV
ijassa-294	85	21	two	two	NUM
ijassa-294	85	22	positive	positive	ADJ
ijassa-294	85	23	solutions	solution	NOUN
ijassa-294	85	24	,	,	PUNCT
ijassa-294	85	25	and	and	CCONJ
ijassa-294	85	26	(	(	PUNCT
ijassa-294	85	27	1	1	X
ijassa-294	85	28	)	)	PUNCT
ijassa-294	85	29	has	have	VERB
ijassa-294	85	30	no	no	DET
ijassa-294	85	31	solution	solution	NOUN
ijassa-294	85	32	for	for	ADP
ijassa-294	85	33	small	small	ADJ
ijassa-294	85	34	λ	λ	NOUN
ijassa-294	85	35	.	.	PUNCT
ijassa-294	86	1	in	in	ADP
ijassa-294	86	2	order	order	NOUN
ijassa-294	86	3	to	to	PART
ijassa-294	86	4	prove	prove	VERB
ijassa-294	86	5	our	our	PRON
ijassa-294	86	6	main	main	ADJ
ijassa-294	86	7	existence	existence	NOUN
ijassa-294	86	8	result	result	NOUN
ijassa-294	86	9	we	we	PRON
ijassa-294	86	10	need	need	VERB
ijassa-294	86	11	the	the	DET
ijassa-294	86	12	following	follow	VERB
ijassa-294	86	13	lemma	lemma	PROPN
ijassa-294	86	14	:	:	PUNCT
ijassa-294	86	15	lemma	lemma	PROPN
ijassa-294	86	16	2.1	2.1	NUM
ijassa-294	86	17	(	(	PUNCT
ijassa-294	86	18	see	see	VERB
ijassa-294	86	19	[	[	X
ijassa-294	86	20	1	1	NUM
ijassa-294	86	21	]	]	NUM
ijassa-294	86	22	.	.	PUNCT
ijassa-294	86	23	)	)	PUNCT
ijassa-294	86	24	suppose	suppose	VERB
ijassa-294	86	25	that	that	SCONJ
ijassa-294	86	26	f	f	PROPN
ijassa-294	86	27	satisfies	satisfie	NOUN
ijassa-294	86	28	(	(	PUNCT
ijassa-294	86	29	f1)–(f3	f1)–(f3	NOUN
ijassa-294	86	30	)	)	PUNCT
ijassa-294	86	31	.	.	PUNCT
ijassa-294	87	1	if	if	SCONJ
ijassa-294	87	2	u(x	u(x	NOUN
ijassa-294	87	3	)	)	PUNCT
ijassa-294	87	4	is	be	AUX
ijassa-294	87	5	an	an	DET
ijassa-294	87	6	integrable	integrable	ADJ
ijassa-294	87	7	function	function	NOUN
ijassa-294	87	8	in	in	ADP
ijassa-294	87	9	ω	ω	PROPN
ijassa-294	87	10	,	,	PUNCT
ijassa-294	87	11	and	and	CCONJ
ijassa-294	87	12	there	there	PRON
ijassa-294	87	13	is	be	VERB
ijassa-294	87	14	a	a	DET
ijassa-294	87	15	measurable	measurable	ADJ
ijassa-294	87	16	subset	subset	NOUN
ijassa-294	87	17	ω0	ω0	ADV
ijassa-294	87	18	of	of	ADP
ijassa-294	87	19	ω	ω	NUM
ijassa-294	87	20	with	with	ADP
ijassa-294	87	21	positive	positive	ADJ
ijassa-294	87	22	measure	measure	NOUN
ijassa-294	87	23	,	,	PUNCT
ijassa-294	87	24	such	such	ADJ
ijassa-294	87	25	that∫	that∫	NOUN
ijassa-294	87	26	c(x	c(x	NOUN
ijassa-294	87	27	)	)	PUNCT
ijassa-294	87	28	0	0	PUNCT
ijassa-294	88	1	f(x	f(x	PROPN
ijassa-294	88	2	,	,	PUNCT
ijassa-294	88	3	s	s	X
ijassa-294	88	4	)	)	PUNCT
ijassa-294	88	5	ds	ds	VERB
ijassa-294	88	6	>	>	X
ijassa-294	88	7	0	0	PUNCT
ijassa-294	89	1	in	in	ADP
ijassa-294	89	2	ω0	ω0	PROPN
ijassa-294	89	3	and	and	CCONJ
ijassa-294	89	4	∫	∫	PROPN
ijassa-294	89	5	c(x	c(x	PROPN
ijassa-294	89	6	)	)	PUNCT
ijassa-294	89	7	0	0	PUNCT
ijassa-294	90	1	f(x	f(x	PROPN
ijassa-294	90	2	,	,	PUNCT
ijassa-294	90	3	s	s	X
ijassa-294	90	4	)	)	PUNCT
ijassa-294	90	5	ds	ds	ADJ
ijassa-294	90	6	≤	≤	NOUN
ijassa-294	90	7	0	0	NUM
ijassa-294	90	8	in	in	ADP
ijassa-294	90	9	ω	ω	PROPN
ijassa-294	90	10	\	\	PROPN
ijassa-294	90	11	ω0	ω0	NOUN
ijassa-294	90	12	,	,	PUNCT
ijassa-294	90	13	then	then	ADV
ijassa-294	90	14	∫	∫	PROPN
ijassa-294	90	15	u(x	u(x	PROPN
ijassa-294	90	16	)	)	PUNCT
ijassa-294	90	17	0	0	PUNCT
ijassa-294	91	1	f(x	f(x	PROPN
ijassa-294	91	2	,	,	PUNCT
ijassa-294	91	3	s	s	X
ijassa-294	91	4	)	)	PUNCT
ijassa-294	91	5	ds	ds	ADJ
ijassa-294	91	6	≤	≤	NUM
ijassa-294	91	7	∫	∫	PROPN
ijassa-294	91	8	c(x	c(x	NOUN
ijassa-294	91	9	)	)	PUNCT
ijassa-294	91	10	0	0	PUNCT
ijassa-294	92	1	f(x	f(x	PROPN
ijassa-294	92	2	,	,	PUNCT
ijassa-294	92	3	s	s	X
ijassa-294	92	4	)	)	PUNCT
ijassa-294	92	5	ds	ds	NOUN
ijassa-294	92	6	in	in	ADP
ijassa-294	92	7	ω0	ω0	PROPN
ijassa-294	92	8	and	and	CCONJ
ijassa-294	92	9	∫	∫	PROPN
ijassa-294	92	10	u(x	u(x	PROPN
ijassa-294	92	11	)	)	PUNCT
ijassa-294	92	12	0	0	PUNCT
ijassa-294	93	1	f(x	f(x	PROPN
ijassa-294	93	2	,	,	PUNCT
ijassa-294	93	3	s	s	X
ijassa-294	93	4	)	)	PUNCT
ijassa-294	93	5	ds	ds	ADJ
ijassa-294	93	6	≤	≤	NOUN
ijassa-294	93	7	0	0	NUM
ijassa-294	93	8	in	in	ADP
ijassa-294	93	9	ω	ω	PROPN
ijassa-294	93	10	\	\	PROPN
ijassa-294	93	11	ω0	ω0	NOUN
ijassa-294	93	12	,	,	PUNCT
ijassa-294	93	13	now	now	ADV
ijassa-294	93	14	we	we	PRON
ijassa-294	93	15	turn	turn	VERB
ijassa-294	93	16	to	to	ADP
ijassa-294	93	17	the	the	DET
ijassa-294	93	18	nonexistence	nonexistence	NOUN
ijassa-294	93	19	of	of	ADP
ijassa-294	93	20	the	the	DET
ijassa-294	93	21	positive	positive	ADJ
ijassa-294	93	22	solutions	solution	NOUN
ijassa-294	93	23	of	of	ADP
ijassa-294	93	24	(	(	PUNCT
ijassa-294	93	25	1	1	NUM
ijassa-294	93	26	)	)	PUNCT
ijassa-294	93	27	when	when	SCONJ
ijassa-294	93	28	(	(	PUNCT
ijassa-294	93	29	5	5	X
ijassa-294	93	30	)	)	PUNCT
ijassa-294	93	31	does	do	AUX
ijassa-294	93	32	not	not	PART
ijassa-294	93	33	hold	hold	VERB
ijassa-294	93	34	for	for	ADP
ijassa-294	93	35	any	any	DET
ijassa-294	93	36	x	x	SYM
ijassa-294	93	37	∈	∈	PROPN
ijassa-294	93	38	ω	ω	NOUN
ijassa-294	93	39	.	.	PUNCT
ijassa-294	94	1	we	we	PRON
ijassa-294	94	2	define	define	VERB
ijassa-294	94	3	c	c	NOUN
ijassa-294	94	4	=	=	SYM
ijassa-294	94	5	maxx∈ω	maxx∈ω	NOUN
ijassa-294	94	6	c(x	c(x	NOUN
ijassa-294	94	7	)	)	PUNCT
ijassa-294	94	8	,	,	PUNCT
ijassa-294	94	9	f(u	f(u	PROPN
ijassa-294	94	10	)	)	PUNCT
ijassa-294	94	11	=	=	PUNCT
ijassa-294	95	1	maxx∈ω	maxx∈ω	PROPN
ijassa-294	95	2	f(x	f(x	PROPN
ijassa-294	95	3	,	,	PUNCT
ijassa-294	95	4	u	u	NOUN
ijassa-294	95	5	)	)	PUNCT
ijassa-294	95	6	.	.	PUNCT
ijassa-294	96	1	our	our	PRON
ijassa-294	96	2	main	main	ADJ
ijassa-294	96	3	nonexistence	nonexistence	NOUN
ijassa-294	96	4	result	result	NOUN
ijassa-294	96	5	is	be	AUX
ijassa-294	96	6	theorem	theorem	VERB
ijassa-294	96	7	2.2	2.2	NUM
ijassa-294	96	8	.	.	PUNCT
ijassa-294	97	1	if	if	SCONJ
ijassa-294	97	2	∫	∫	PROPN
ijassa-294	97	3	c	c	PROPN
ijassa-294	97	4	0	0	NUM
ijassa-294	97	5	f(u	f(u	PROPN
ijassa-294	97	6	)	)	PUNCT
ijassa-294	97	7	du	du	PROPN
ijassa-294	97	8	≤	≤	PROPN
ijassa-294	97	9	0	0	NUM
ijassa-294	97	10	,	,	PUNCT
ijassa-294	97	11	then	then	ADV
ijassa-294	97	12	(	(	PUNCT
ijassa-294	97	13	1	1	X
ijassa-294	97	14	)	)	PUNCT
ijassa-294	97	15	has	have	VERB
ijassa-294	97	16	no	no	DET
ijassa-294	97	17	positive	positive	ADJ
ijassa-294	97	18	solution	solution	NOUN
ijassa-294	97	19	for	for	ADP
ijassa-294	97	20	any	any	DET
ijassa-294	97	21	λ	λ	PROPN
ijassa-294	97	22	>	>	X
ijassa-294	97	23	0	0	NUM
ijassa-294	97	24	.	.	PUNCT
ijassa-294	98	1	in	in	ADP
ijassa-294	98	2	order	order	NOUN
ijassa-294	98	3	to	to	PART
ijassa-294	98	4	prove	prove	VERB
ijassa-294	98	5	our	our	PRON
ijassa-294	98	6	main	main	ADJ
ijassa-294	98	7	nonexistence	nonexistence	NOUN
ijassa-294	98	8	result	result	NOUN
ijassa-294	98	9	,	,	PUNCT
ijassa-294	98	10	we	we	PRON
ijassa-294	98	11	recall	recall	VERB
ijassa-294	98	12	a	a	DET
ijassa-294	98	13	theorem	theorem	NOUN
ijassa-294	98	14	in	in	ADP
ijassa-294	98	15	[	[	X
ijassa-294	98	16	22	22	NUM
ijassa-294	98	17	]	]	PUNCT
ijassa-294	98	18	for	for	ADP
ijassa-294	98	19	(	(	PUNCT
ijassa-294	98	20	1	1	NUM
ijassa-294	98	21	)	)	PUNCT
ijassa-294	98	22	with	with	ADP
ijassa-294	98	23	the	the	DET
ijassa-294	98	24	special	special	ADJ
ijassa-294	98	25	case	case	NOUN
ijassa-294	98	26	of	of	ADP
ijassa-294	98	27	m(t	m(t	NOUN
ijassa-294	98	28	)	)	PUNCT
ijassa-294	98	29	≡	≡	PROPN
ijassa-294	98	30	1	1	NUM
ijassa-294	98	31	and	and	CCONJ
ijassa-294	98	32	f(x	f(x	PROPN
ijassa-294	98	33	,	,	PUNCT
ijassa-294	98	34	u	u	NOUN
ijassa-294	98	35	)	)	PUNCT
ijassa-294	98	36	≡	≡	PROPN
ijassa-294	98	37	f(u	f(u	PROPN
ijassa-294	98	38	)	)	PUNCT
ijassa-294	98	39	.	.	PUNCT
ijassa-294	99	1	in	in	ADP
ijassa-294	99	2	fact	fact	NOUN
ijassa-294	99	3	,	,	PUNCT
ijassa-294	99	4	the	the	DET
ijassa-294	99	5	theorem	theorem	NOUN
ijassa-294	99	6	also	also	ADV
ijassa-294	99	7	holds	hold	VERB
ijassa-294	99	8	for	for	ADP
ijassa-294	99	9	the	the	DET
ijassa-294	99	10	nonlocal	nonlocal	ADJ
ijassa-294	99	11	problem	problem	NOUN
ijassa-294	99	12	(	(	PUNCT
ijassa-294	99	13	1	1	NUM
ijassa-294	99	14	)	)	PUNCT
ijassa-294	99	15	with	with	ADP
ijassa-294	99	16	f(x	f(x	PROPN
ijassa-294	99	17	,	,	PUNCT
ijassa-294	99	18	u	u	NOUN
ijassa-294	99	19	)	)	PUNCT
ijassa-294	99	20	≡	≡	PROPN
ijassa-294	99	21	f(u	f(u	PROPN
ijassa-294	99	22	)	)	PUNCT
ijassa-294	99	23	.	.	PUNCT
ijassa-294	100	1	because	because	SCONJ
ijassa-294	100	2	the	the	DET
ijassa-294	100	3	proof	proof	NOUN
ijassa-294	100	4	is	be	AUX
ijassa-294	100	5	similar	similar	ADJ
ijassa-294	100	6	to	to	ADP
ijassa-294	100	7	the	the	DET
ijassa-294	100	8	proof	proof	NOUN
ijassa-294	100	9	of[22	of[22	PROPN
ijassa-294	100	10	]	]	PUNCT
ijassa-294	100	11	,	,	PUNCT
ijassa-294	100	12	we	we	PRON
ijassa-294	100	13	omit	omit	VERB
ijassa-294	100	14	it	it	PRON
ijassa-294	100	15	here	here	ADV
ijassa-294	100	16	(	(	PUNCT
ijassa-294	100	17	for	for	ADP
ijassa-294	100	18	detail	detail	NOUN
ijassa-294	100	19	,	,	PUNCT
ijassa-294	100	20	see	see	VERB
ijassa-294	100	21	the	the	DET
ijassa-294	100	22	proof	proof	NOUN
ijassa-294	100	23	of	of	ADP
ijassa-294	100	24	theorem	theorem	NOUN
ijassa-294	100	25	1	1	NUM
ijassa-294	100	26	in	in	ADP
ijassa-294	100	27	[	[	PUNCT
ijassa-294	100	28	22	22	NUM
ijassa-294	100	29	]	]	PUNCT
ijassa-294	100	30	)	)	PUNCT
ijassa-294	100	31	.	.	PUNCT
ijassa-294	101	1	let	let	VERB
ijassa-294	101	2	us	we	PRON
ijassa-294	101	3	assume	assume	VERB
ijassa-294	101	4	that	that	SCONJ
ijassa-294	101	5	f	f	X
ijassa-294	101	6	:	:	PUNCT
ijassa-294	101	7	r→	r→	PROPN
ijassa-294	101	8	r	r	NOUN
ijassa-294	101	9	is	be	AUX
ijassa-294	101	10	a	a	DET
ijassa-294	101	11	c1	c1	NOUN
ijassa-294	101	12	function	function	NOUN
ijassa-294	101	13	and	and	CCONJ
ijassa-294	101	14	let	let	VERB
ijassa-294	101	15	the	the	DET
ijassa-294	101	16	following	follow	VERB
ijassa-294	101	17	conditions	condition	NOUN
ijassa-294	101	18	hold	hold	VERB
ijassa-294	101	19	:	:	PUNCT
ijassa-294	101	20	there	there	PRON
ijassa-294	101	21	exist	exist	VERB
ijassa-294	101	22	0	0	NUM
ijassa-294	101	23	≤	≤	NUM
ijassa-294	101	24	s0	s0	NOUN
ijassa-294	101	25	<	<	X
ijassa-294	101	26	s1	s1	PROPN
ijassa-294	101	27	<	<	X
ijassa-294	101	28	s2	s2	PROPN
ijassa-294	101	29	,	,	PUNCT
ijassa-294	101	30	such	such	ADJ
ijassa-294	101	31	that	that	NUM
ijassa-294	101	32	f(si	f(si	PROPN
ijassa-294	101	33	)	)	PUNCT
ijassa-294	102	1	=	=	SYM
ijassa-294	103	1	0	0	NUM
ijassa-294	103	2	,	,	PUNCT
ijassa-294	103	3	i	i	PRON
ijassa-294	103	4	=	=	NOUN
ijassa-294	103	5	1	1	NUM
ijassa-294	103	6	,	,	PUNCT
ijassa-294	103	7	2	2	NUM
ijassa-294	103	8	,	,	PUNCT
ijassa-294	103	9	f(s0	f(s0	NOUN
ijassa-294	103	10	)	)	PUNCT
ijassa-294	103	11	≤	≤	NOUN
ijassa-294	103	12	0	0	NUM
ijassa-294	103	13	,	,	PUNCT
ijassa-294	103	14	f(s	f(s	ADV
ijassa-294	103	15	)	)	PUNCT
ijassa-294	103	16	<	<	X
ijassa-294	103	17	0	0	PROPN
ijassa-294	103	18	,	,	PUNCT
ijassa-294	103	19	s0	s0	PROPN
ijassa-294	103	20	<	<	X
ijassa-294	103	21	s	s	X
ijassa-294	103	22	<	<	X
ijassa-294	103	23	s1	s1	NOUN
ijassa-294	103	24	,	,	PUNCT
ijassa-294	103	25	f(s	f(s	ADV
ijassa-294	103	26	)	)	PUNCT
ijassa-294	103	27	>	>	X
ijassa-294	103	28	0	0	NUM
ijassa-294	103	29	,	,	PUNCT
ijassa-294	103	30	s1	s1	PROPN
ijassa-294	103	31	<	<	X
ijassa-294	103	32	s	s	X
ijassa-294	103	33	<	<	X
ijassa-294	103	34	s2	s2	NOUN
ijassa-294	103	35	(	(	PUNCT
ijassa-294	103	36	6	6	NUM
ijassa-294	103	37	)	)	PUNCT
ijassa-294	103	38	and	and	CCONJ
ijassa-294	103	39	let	let	VERB
ijassa-294	103	40	∫	∫	PROPN
ijassa-294	103	41	s2	s2	VERB
ijassa-294	103	42	s0	s0	PROPN
ijassa-294	103	43	f(s	f(s	ADV
ijassa-294	103	44	)	)	PUNCT
ijassa-294	103	45	ds	ds	ADJ
ijassa-294	103	46	≤	≤	NUM
ijassa-294	103	47	0	0	NUM
ijassa-294	103	48	.	.	PUNCT
ijassa-294	104	1	(	(	PUNCT
ijassa-294	104	2	7	7	X
ijassa-294	104	3	)	)	PUNCT
ijassa-294	104	4	we	we	PRON
ijassa-294	104	5	have	have	VERB
ijassa-294	104	6	the	the	DET
ijassa-294	104	7	following	follow	VERB
ijassa-294	104	8	lemma	lemma	PROPN
ijassa-294	104	9	.	.	PUNCT
ijassa-294	105	1	lemma	lemma	PROPN
ijassa-294	105	2	2.2	2.2	NUM
ijassa-294	105	3	.	.	PUNCT
ijassa-294	106	1	assume	assume	VERB
ijassa-294	106	2	that	that	SCONJ
ijassa-294	106	3	f	f	PROPN
ijassa-294	106	4	satisfies	satisfie	NOUN
ijassa-294	106	5	(	(	PUNCT
ijassa-294	106	6	6	6	NUM
ijassa-294	106	7	)	)	PUNCT
ijassa-294	106	8	and	and	CCONJ
ijassa-294	106	9	(	(	PUNCT
ijassa-294	106	10	7	7	NUM
ijassa-294	106	11	)	)	PUNCT
ijassa-294	106	12	.	.	PUNCT
ijassa-294	107	1	let	let	VERB
ijassa-294	107	2	ω	ω	PRON
ijassa-294	107	3	be	be	AUX
ijassa-294	107	4	a	a	DET
ijassa-294	107	5	bounded	bounded	ADJ
ijassa-294	107	6	domain	domain	NOUN
ijassa-294	107	7	with	with	ADP
ijassa-294	107	8	smooth	smooth	ADJ
ijassa-294	107	9	boundary	boundary	NOUN
ijassa-294	107	10	.	.	PUNCT
ijassa-294	108	1	if	if	SCONJ
ijassa-294	108	2	(	(	PUNCT
ijassa-294	108	3	1	1	X
ijassa-294	108	4	)	)	PUNCT
ijassa-294	108	5	with	with	ADP
ijassa-294	108	6	f(x	f(x	PROPN
ijassa-294	108	7	,	,	PUNCT
ijassa-294	108	8	u	u	NOUN
ijassa-294	108	9	)	)	PUNCT
ijassa-294	108	10	≡	≡	PROPN
ijassa-294	108	11	f(u	f(u	PROPN
ijassa-294	108	12	)	)	PUNCT
ijassa-294	108	13	has	have	VERB
ijassa-294	108	14	a	a	DET
ijassa-294	108	15	positive	positive	ADJ
ijassa-294	108	16	solution	solution	NOUN
ijassa-294	108	17	u	u	NOUN
ijassa-294	108	18	,	,	PUNCT
ijassa-294	108	19	then	then	ADV
ijassa-294	108	20	u	u	NOUN
ijassa-294	108	21	can	can	AUX
ijassa-294	108	22	not	not	PART
ijassa-294	108	23	satisfy	satisfy	VERB
ijassa-294	108	24	{	{	PUNCT
ijassa-294	108	25	umax	umax	ADJ
ijassa-294	108	26	=	=	SYM
ijassa-294	108	27	maxx∈ω	maxx∈ω	NOUN
ijassa-294	108	28	u(x	u(x	NOUN
ijassa-294	108	29	)	)	PUNCT
ijassa-294	108	30	∈	∈	PROPN
ijassa-294	108	31	(	(	PUNCT
ijassa-294	108	32	s1	s1	NOUN
ijassa-294	108	33	,	,	PUNCT
ijassa-294	108	34	s2	s2	PROPN
ijassa-294	108	35	)	)	PUNCT
ijassa-294	108	36	,	,	PUNCT
ijassa-294	108	37	u(x	u(x	PROPN
ijassa-294	108	38	)	)	PUNCT
ijassa-294	108	39	>	>	X
ijassa-294	108	40	0	0	NUM
ijassa-294	108	41	,	,	PUNCT
ijassa-294	108	42	x	x	X
ijassa-294	108	43	∈	∈	PROPN
ijassa-294	108	44	ω	ω	PROPN
ijassa-294	108	45	.	.	PUNCT
ijassa-294	109	1	(	(	PUNCT
ijassa-294	109	2	8)	8)	NUM
ijassa-294	109	3	86	86	NUM
ijassa-294	109	4	ma	ma	NOUN
ijassa-294	109	5	:	:	PUNCT
ijassa-294	109	6	existence	existence	NOUN
ijassa-294	109	7	and	and	CCONJ
ijassa-294	109	8	nonexistence	nonexistence	NOUN
ijassa-294	109	9	of	of	ADP
ijassa-294	109	10	positive	positive	ADJ
ijassa-294	109	11	solutions	solution	NOUN
ijassa-294	109	12	for	for	ADP
ijassa-294	109	13	a	a	DET
ijassa-294	109	14	kirchhoff	kirchhoff	NOUN
ijassa-294	109	15	-	-	PUNCT
ijassa-294	109	16	type	type	NOUN
ijassa-294	109	17	.	.	PUNCT
ijassa-294	109	18	.	.	PUNCT
ijassa-294	109	19	.	.	PUNCT
ijassa-294	109	20	.	.	PUNCT
ijassa-294	109	21	.	.	PUNCT
ijassa-294	110	1	.	.	PUNCT
ijassa-294	111	1	remark	remark	VERB
ijassa-294	111	2	2.2	2.2	NUM
ijassa-294	111	3	.	.	PUNCT
ijassa-294	112	1	note	note	VERB
ijassa-294	112	2	that	that	SCONJ
ijassa-294	112	3	our	our	PRON
ijassa-294	112	4	assumptions	assumption	NOUN
ijassa-294	112	5	(	(	PUNCT
ijassa-294	112	6	f1)–(f3	f1)–(f3	NOUN
ijassa-294	112	7	)	)	PUNCT
ijassa-294	112	8	are	be	AUX
ijassa-294	112	9	weaker	weak	ADJ
ijassa-294	112	10	than	than	ADP
ijassa-294	112	11	(	(	PUNCT
ijassa-294	112	12	f1)–(f4	f1)–(f4	ADJ
ijassa-294	112	13	)	)	PUNCT
ijassa-294	112	14	of[1	of[1	NOUN
ijassa-294	112	15	]	]	PUNCT
ijassa-294	112	16	even	even	ADV
ijassa-294	112	17	in	in	ADP
ijassa-294	112	18	the	the	DET
ijassa-294	112	19	case	case	NOUN
ijassa-294	112	20	ofm(t	ofm(t	PROPN
ijassa-294	112	21	)	)	PUNCT
ijassa-294	112	22	≡	≡	PROPN
ijassa-294	112	23	1	1	X
ijassa-294	112	24	.	.	PUNCT
ijassa-294	113	1	in	in	ADP
ijassa-294	113	2	fact	fact	NOUN
ijassa-294	113	3	,	,	PUNCT
ijassa-294	113	4	from	from	ADP
ijassa-294	113	5	(	(	PUNCT
ijassa-294	113	6	f1)–(f3	f1)–(f3	NOUN
ijassa-294	113	7	)	)	PUNCT
ijassa-294	113	8	,	,	PUNCT
ijassa-294	113	9	we	we	PRON
ijassa-294	113	10	can	can	AUX
ijassa-294	113	11	easily	easily	ADV
ijassa-294	113	12	see	see	VERB
ijassa-294	113	13	that	that	SCONJ
ijassa-294	113	14	there	there	PRON
ijassa-294	113	15	exist	exist	VERB
ijassa-294	113	16	a	a	DET
ijassa-294	113	17	positive	positive	ADJ
ijassa-294	113	18	constant	constant	ADJ
ijassa-294	113	19	β	β	NOUN
ijassa-294	113	20	such	such	ADJ
ijassa-294	113	21	that	that	SCONJ
ijassa-294	113	22	f(x	f(x	PROPN
ijassa-294	113	23	,	,	PUNCT
ijassa-294	113	24	s	s	NOUN
ijassa-294	113	25	)	)	PUNCT
ijassa-294	113	26	≤	≤	NUM
ijassa-294	113	27	βs	βs	PUNCT
ijassa-294	113	28	for	for	ADP
ijassa-294	113	29	any	any	DET
ijassa-294	113	30	s	s	X
ijassa-294	113	31	≥	≥	NOUN
ijassa-294	113	32	0	0	NUM
ijassa-294	113	33	and	and	CCONJ
ijassa-294	113	34	a.e	a.e	PROPN
ijassa-294	113	35	.	.	PROPN
ijassa-294	113	36	x	x	SYM
ijassa-294	113	37	∈	∈	PROPN
ijassa-294	113	38	ω	ω	PROPN
ijassa-294	113	39	,	,	PUNCT
ijassa-294	113	40	i.e.	i.e.	X
ijassa-294	113	41	,	,	PUNCT
ijassa-294	113	42	the	the	DET
ijassa-294	113	43	condition	condition	NOUN
ijassa-294	113	44	(	(	PUNCT
ijassa-294	113	45	f4	f4	PROPN
ijassa-294	113	46	)	)	PUNCT
ijassa-294	113	47	of	of	ADP
ijassa-294	113	48	[	[	X
ijassa-294	113	49	1	1	NUM
ijassa-294	113	50	]	]	PUNCT
ijassa-294	113	51	.	.	PUNCT
ijassa-294	114	1	we	we	PRON
ijassa-294	114	2	do	do	AUX
ijassa-294	114	3	not	not	PART
ijassa-294	114	4	need	need	VERB
ijassa-294	114	5	the	the	DET
ijassa-294	114	6	conditions	condition	NOUN
ijassa-294	114	7	of	of	ADP
ijassa-294	114	8	b(x	b(x	NOUN
ijassa-294	114	9	)	)	PUNCT
ijassa-294	114	10	∈	∈	PROPN
ijassa-294	114	11	c1,α(ω)(0	c1,α(ω)(0	NOUN
ijassa-294	114	12	<	<	X
ijassa-294	114	13	α	α	X
ijassa-294	114	14	<	<	X
ijassa-294	114	15	1	1	NUM
ijassa-294	114	16	)	)	PUNCT
ijassa-294	114	17	and	and	CCONJ
ijassa-294	114	18	f	f	X
ijassa-294	114	19	(	(	PUNCT
ijassa-294	114	20	·	·	PUNCT
ijassa-294	114	21	,	,	PUNCT
ijassa-294	114	22	u	u	NOUN
ijassa-294	114	23	)	)	PUNCT
ijassa-294	114	24	∈	∈	PROPN
ijassa-294	114	25	c1,α(ω	c1,α(ω	NOUN
ijassa-294	114	26	)	)	PUNCT
ijassa-294	114	27	for	for	ADP
ijassa-294	114	28	any	any	DET
ijassa-294	114	29	u	u	NOUN
ijassa-294	114	30	≥	≥	NOUN
ijassa-294	114	31	0	0	NUM
ijassa-294	114	32	because	because	SCONJ
ijassa-294	114	33	we	we	PRON
ijassa-294	114	34	do	do	AUX
ijassa-294	114	35	not	not	PART
ijassa-294	114	36	need	need	VERB
ijassa-294	114	37	energy	energy	NOUN
ijassa-294	114	38	functional	functional	ADJ
ijassa-294	114	39	of	of	ADP
ijassa-294	114	40	(	(	PUNCT
ijassa-294	114	41	1	1	NUM
ijassa-294	114	42	)	)	PUNCT
ijassa-294	114	43	is	be	AUX
ijassa-294	114	44	ac2	ac2	PROPN
ijassa-294	114	45	function	function	NOUN
ijassa-294	114	46	in	in	ADP
ijassa-294	114	47	x	x	PUNCT
ijassa-294	114	48	in	in	ADP
ijassa-294	114	49	our	our	PRON
ijassa-294	114	50	proof	proof	NOUN
ijassa-294	114	51	.	.	PUNCT
ijassa-294	115	1	remark	remark	VERB
ijassa-294	115	2	2.3	2.3	NUM
ijassa-294	115	3	.	.	PUNCT
ijassa-294	116	1	the	the	DET
ijassa-294	116	2	condition	condition	NOUN
ijassa-294	116	3	of	of	ADP
ijassa-294	116	4	f(x	f(x	PROPN
ijassa-294	116	5	,	,	PUNCT
ijassa-294	116	6	·	·	PUNCT
ijassa-294	116	7	)	)	PUNCT
ijassa-294	116	8	∈	∈	PROPN
ijassa-294	116	9	c1(r+	c1(r+	PROPN
ijassa-294	116	10	)	)	PUNCT
ijassa-294	116	11	for	for	ADP
ijassa-294	116	12	any	any	DET
ijassa-294	116	13	x	x	SYM
ijassa-294	116	14	∈	∈	PROPN
ijassa-294	116	15	ω	ω	NOUN
ijassa-294	116	16	can	can	AUX
ijassa-294	116	17	be	be	AUX
ijassa-294	116	18	relaxed	relax	VERB
ijassa-294	116	19	to	to	ADP
ijassa-294	116	20	f(x	f(x	PROPN
ijassa-294	116	21	,	,	PUNCT
ijassa-294	116	22	·	·	PUNCT
ijassa-294	116	23	)	)	PUNCT
ijassa-294	117	1	is	be	AUX
ijassa-294	117	2	locally	locally	ADV
ijassa-294	117	3	lipschitz	lipschitz	ADJ
ijassa-294	117	4	in	in	ADP
ijassa-294	117	5	r+	r+	NOUN
ijassa-294	117	6	for	for	ADP
ijassa-294	117	7	any	any	DET
ijassa-294	117	8	x	x	SYM
ijassa-294	117	9	∈	∈	PROPN
ijassa-294	117	10	ω	ω	NOUN
ijassa-294	117	11	.	.	PUNCT
ijassa-294	118	1	in	in	ADP
ijassa-294	118	2	fact	fact	NOUN
ijassa-294	118	3	,	,	PUNCT
ijassa-294	118	4	lemma	lemma	PROPN
ijassa-294	118	5	2.2	2.2	NUM
ijassa-294	118	6	also	also	ADV
ijassa-294	118	7	holds	hold	VERB
ijassa-294	118	8	when	when	SCONJ
ijassa-294	118	9	f	f	NOUN
ijassa-294	118	10	:	:	PUNCT
ijassa-294	118	11	r	r	NOUN
ijassa-294	118	12	→	→	SYM
ijassa-294	118	13	r	r	NOUN
ijassa-294	118	14	is	be	AUX
ijassa-294	118	15	a	a	DET
ijassa-294	118	16	locally	locally	ADV
ijassa-294	118	17	lipschitz	lipschitz	NOUN
ijassa-294	118	18	function	function	NOUN
ijassa-294	118	19	because	because	SCONJ
ijassa-294	118	20	the	the	DET
ijassa-294	118	21	symmetry	symmetry	NOUN
ijassa-294	118	22	results	result	VERB
ijassa-294	118	23	of	of	ADP
ijassa-294	118	24	[	[	X
ijassa-294	118	25	23	23	NUM
ijassa-294	118	26	]	]	PUNCT
ijassa-294	118	27	holds	hold	VERB
ijassa-294	118	28	under	under	ADP
ijassa-294	118	29	this	this	DET
ijassa-294	118	30	weaker	weak	ADJ
ijassa-294	118	31	condition	condition	NOUN
ijassa-294	118	32	.	.	PUNCT
ijassa-294	119	1	3	3	X
ijassa-294	119	2	.	.	X
ijassa-294	119	3	proof	proof	NOUN
ijassa-294	119	4	of	of	ADP
ijassa-294	119	5	theorem	theorem	ADJ
ijassa-294	119	6	2.1	2.1	NUM
ijassa-294	119	7	and	and	CCONJ
ijassa-294	119	8	2.2	2.2	NUM
ijassa-294	119	9	in	in	ADP
ijassa-294	119	10	this	this	DET
ijassa-294	119	11	section	section	NOUN
ijassa-294	119	12	we	we	PRON
ijassa-294	119	13	will	will	AUX
ijassa-294	119	14	prove	prove	VERB
ijassa-294	119	15	theorem	theorem	VERB
ijassa-294	119	16	2.1	2.1	NUM
ijassa-294	119	17	and	and	CCONJ
ijassa-294	119	18	2.2	2.2	NUM
ijassa-294	119	19	.	.	PUNCT
ijassa-294	120	1	lemma	lemma	PROPN
ijassa-294	120	2	3.1	3.1	NUM
ijassa-294	120	3	.	.	PUNCT
ijassa-294	121	1	if	if	SCONJ
ijassa-294	121	2	m(t	m(t	NOUN
ijassa-294	121	3	)	)	PUNCT
ijassa-294	121	4	satisfies	satisfie	NOUN
ijassa-294	121	5	(	(	PUNCT
ijassa-294	121	6	m	m	NOUN
ijassa-294	121	7	)	)	PUNCT
ijassa-294	121	8	,	,	PUNCT
ijassa-294	121	9	and	and	CCONJ
ijassa-294	121	10	f(x	f(x	PROPN
ijassa-294	121	11	,	,	PUNCT
ijassa-294	121	12	u	u	NOUN
ijassa-294	121	13	)	)	PUNCT
ijassa-294	121	14	satisfies	satisfie	NOUN
ijassa-294	121	15	(	(	PUNCT
ijassa-294	121	16	f1)–(f3	f1)–(f3	NOUN
ijassa-294	121	17	)	)	PUNCT
ijassa-294	121	18	and	and	CCONJ
ijassa-294	121	19	(	(	PUNCT
ijassa-294	121	20	5	5	NUM
ijassa-294	121	21	)	)	PUNCT
ijassa-294	121	22	,	,	PUNCT
ijassa-294	121	23	then	then	ADV
ijassa-294	121	24	for	for	ADP
ijassa-294	121	25	λ	λ	PROPN
ijassa-294	121	26	large	large	ADJ
ijassa-294	121	27	enough	enough	ADV
ijassa-294	121	28	,	,	PUNCT
ijassa-294	121	29	iλ	iλ	X
ijassa-294	121	30	(	(	PUNCT
ijassa-294	121	31	·	·	PUNCT
ijassa-294	121	32	)	)	PUNCT
ijassa-294	121	33	has	have	VERB
ijassa-294	121	34	a	a	DET
ijassa-294	121	35	global	global	ADJ
ijassa-294	121	36	minimum	minimum	NOUN
ijassa-294	121	37	point	point	NOUN
ijassa-294	121	38	u1	u1	NOUN
ijassa-294	121	39	such	such	ADJ
ijassa-294	121	40	that	that	DET
ijassa-294	121	41	iλ(u1	iλ(u1	NOUN
ijassa-294	121	42	)	)	PUNCT
ijassa-294	121	43	<	<	X
ijassa-294	121	44	0	0	X
ijassa-294	121	45	.	.	PUNCT
ijassa-294	121	46	proof	proof	NOUN
ijassa-294	121	47	.	.	PUNCT
ijassa-294	122	1	since	since	SCONJ
ijassa-294	122	2	∫	∫	PROPN
ijassa-294	122	3	c(x	c(x	PROPN
ijassa-294	122	4	)	)	PUNCT
ijassa-294	122	5	0	0	PUNCT
ijassa-294	123	1	f(x	f(x	PROPN
ijassa-294	123	2	,	,	PUNCT
ijassa-294	123	3	s	s	X
ijassa-294	123	4	)	)	PUNCT
ijassa-294	123	5	ds	ds	VERB
ijassa-294	123	6	>	>	X
ijassa-294	123	7	0	0	PUNCT
ijassa-294	124	1	in	in	ADP
ijassa-294	124	2	ω1	ω1	PROPN
ijassa-294	124	3	,	,	PUNCT
ijassa-294	124	4	then	then	ADV
ijassa-294	124	5	there	there	PRON
ijassa-294	124	6	exists	exist	VERB
ijassa-294	124	7	a	a	DET
ijassa-294	124	8	measurable	measurable	ADJ
ijassa-294	124	9	set	set	NOUN
ijassa-294	124	10	ω0	ω0	PROPN
ijassa-294	124	11	⊂	⊂	PROPN
ijassa-294	124	12	ω	ω	PROPN
ijassa-294	124	13	with	with	ADP
ijassa-294	124	14	positive	positive	ADJ
ijassa-294	124	15	measure	measure	NOUN
ijassa-294	124	16	,	,	PUNCT
ijassa-294	124	17	such	such	ADJ
ijassa-294	124	18	that	that	DET
ijassa-294	124	19	∫	∫	PROPN
ijassa-294	124	20	c(x	c(x	NOUN
ijassa-294	124	21	)	)	PUNCT
ijassa-294	124	22	0	0	PUNCT
ijassa-294	125	1	f(x	f(x	PROPN
ijassa-294	125	2	,	,	PUNCT
ijassa-294	125	3	s	s	X
ijassa-294	125	4	)	)	PUNCT
ijassa-294	125	5	ds	ds	VERB
ijassa-294	125	6	>	>	X
ijassa-294	125	7	0	0	PUNCT
ijassa-294	125	8	in	in	ADP
ijassa-294	125	9	ω0	ω0	NOUN
ijassa-294	125	10	,	,	PUNCT
ijassa-294	125	11	and	and	CCONJ
ijassa-294	125	12	∫	∫	PROPN
ijassa-294	125	13	c(x	c(x	NOUN
ijassa-294	125	14	)	)	PUNCT
ijassa-294	125	15	0	0	PUNCT
ijassa-294	126	1	f(x	f(x	PROPN
ijassa-294	126	2	,	,	PUNCT
ijassa-294	126	3	s	s	X
ijassa-294	126	4	)	)	PUNCT
ijassa-294	126	5	ds	ds	ADJ
ijassa-294	126	6	≤	≤	NOUN
ijassa-294	126	7	0	0	NUM
ijassa-294	126	8	in	in	ADP
ijassa-294	126	9	ω	ω	PROPN
ijassa-294	126	10	\	\	PROPN
ijassa-294	126	11	ω0	ω0	NOUN
ijassa-294	126	12	.	.	PUNCT
ijassa-294	127	1	from	from	ADP
ijassa-294	127	2	(	(	PUNCT
ijassa-294	127	3	m	m	PROPN
ijassa-294	127	4	)	)	PUNCT
ijassa-294	127	5	and	and	CCONJ
ijassa-294	127	6	the	the	DET
ijassa-294	127	7	definition	definition	NOUN
ijassa-294	127	8	of	of	ADP
ijassa-294	127	9	m̂(t	m̂(t	NOUN
ijassa-294	127	10	)	)	PUNCT
ijassa-294	127	11	,	,	PUNCT
ijassa-294	127	12	we	we	PRON
ijassa-294	127	13	have	have	VERB
ijassa-294	127	14	m̂(t	m̂(t	NOUN
ijassa-294	127	15	)	)	PUNCT
ijassa-294	127	16	≥	≥	NOUN
ijassa-294	127	17	m0	m0	NOUN
ijassa-294	127	18	t.	t.	PROPN
ijassa-294	127	19	in	in	ADP
ijassa-294	127	20	view	view	NOUN
ijassa-294	127	21	of	of	ADP
ijassa-294	127	22	lemma	lemma	PROPN
ijassa-294	127	23	2.1	2.1	NUM
ijassa-294	127	24	,	,	PUNCT
ijassa-294	127	25	we	we	PRON
ijassa-294	127	26	have	have	VERB
ijassa-294	127	27	iλ(u	iλ(u	NUM
ijassa-294	127	28	)	)	PUNCT
ijassa-294	128	1	=	=	SYM
ijassa-294	128	2	m̂	m̂	PROPN
ijassa-294	128	3	(	(	PUNCT
ijassa-294	128	4	∫	∫	PROPN
ijassa-294	128	5	ω	ω	NUM
ijassa-294	128	6	1	1	NUM
ijassa-294	128	7	2	2	NUM
ijassa-294	128	8	|∇u|2	|∇u|2	NOUN
ijassa-294	128	9	dx	dx	PROPN
ijassa-294	128	10	)	)	PUNCT
ijassa-294	128	11	−	−	PUNCT
ijassa-294	129	1	λ	λ	INTJ
ijassa-294	129	2	∫	∫	PROPN
ijassa-294	129	3	ω	ω	NUM
ijassa-294	129	4	f	f	PROPN
ijassa-294	129	5	(	(	PUNCT
ijassa-294	129	6	x	x	NOUN
ijassa-294	129	7	,	,	PUNCT
ijassa-294	129	8	u	u	NOUN
ijassa-294	129	9	)	)	PUNCT
ijassa-294	129	10	dx	dx	PROPN
ijassa-294	129	11	≥	≥	PROPN
ijassa-294	129	12	m0	m0	PROPN
ijassa-294	129	13	∫	∫	PROPN
ijassa-294	129	14	ω	ω	PROPN
ijassa-294	129	15	1	1	NUM
ijassa-294	129	16	2	2	NUM
ijassa-294	129	17	|∇u|2	|∇u|2	NOUN
ijassa-294	129	18	dx−	dx−	SYM
ijassa-294	129	19	λ	λ	PROPN
ijassa-294	129	20	∫	∫	PROPN
ijassa-294	129	21	ω	ω	PROPN
ijassa-294	129	22	(	(	PUNCT
ijassa-294	129	23	∫	∫	PROPN
ijassa-294	129	24	u(x	u(x	PROPN
ijassa-294	129	25	)	)	PUNCT
ijassa-294	129	26	0	0	PUNCT
ijassa-294	130	1	f(x	f(x	PROPN
ijassa-294	130	2	,	,	PUNCT
ijassa-294	130	3	s	s	X
ijassa-294	130	4	)	)	PUNCT
ijassa-294	130	5	ds	ds	ADJ
ijassa-294	130	6	)	)	PUNCT
ijassa-294	130	7	dx	dx	PROPN
ijassa-294	130	8	≥	≥	PROPN
ijassa-294	131	1	m0	m0	PROPN
ijassa-294	131	2	∫	∫	PROPN
ijassa-294	131	3	ω	ω	PROPN
ijassa-294	131	4	1	1	NUM
ijassa-294	131	5	2	2	NUM
ijassa-294	131	6	|∇u|2	|∇u|2	NOUN
ijassa-294	131	7	dx−	dx−	NUM
ijassa-294	131	8	λ	λ	PROPN
ijassa-294	131	9	∫	∫	PROPN
ijassa-294	131	10	ω0	ω0	PROPN
ijassa-294	131	11	(	(	PUNCT
ijassa-294	131	12	∫	∫	PROPN
ijassa-294	131	13	u(x	u(x	PROPN
ijassa-294	131	14	)	)	PUNCT
ijassa-294	131	15	0	0	PUNCT
ijassa-294	132	1	f(x	f(x	PROPN
ijassa-294	132	2	,	,	PUNCT
ijassa-294	132	3	s	s	X
ijassa-294	132	4	)	)	PUNCT
ijassa-294	132	5	ds	ds	X
ijassa-294	132	6	)	)	PUNCT
ijassa-294	132	7	dx−	dx−	PUNCT
ijassa-294	133	1	λ	λ	PROPN
ijassa-294	133	2	∫	∫	PROPN
ijassa-294	133	3	ω\ω0	ω\ω0	ADV
ijassa-294	133	4	(	(	PUNCT
ijassa-294	133	5	∫	∫	PROPN
ijassa-294	133	6	u(x	u(x	PROPN
ijassa-294	133	7	)	)	PUNCT
ijassa-294	133	8	0	0	PUNCT
ijassa-294	134	1	f(x	f(x	PROPN
ijassa-294	134	2	,	,	PUNCT
ijassa-294	134	3	s	s	X
ijassa-294	134	4	)	)	PUNCT
ijassa-294	134	5	ds	ds	ADJ
ijassa-294	134	6	)	)	PUNCT
ijassa-294	134	7	dx	dx	PROPN
ijassa-294	134	8	≥	≥	PROPN
ijassa-294	135	1	m0	m0	PROPN
ijassa-294	135	2	∫	∫	PROPN
ijassa-294	135	3	ω	ω	PROPN
ijassa-294	135	4	1	1	NUM
ijassa-294	135	5	2	2	NUM
ijassa-294	135	6	|∇u|2	|∇u|2	NOUN
ijassa-294	135	7	dx−	dx−	NUM
ijassa-294	135	8	λ	λ	PROPN
ijassa-294	135	9	∫	∫	PROPN
ijassa-294	135	10	ω0	ω0	PROPN
ijassa-294	135	11	(	(	PUNCT
ijassa-294	135	12	∫	∫	PROPN
ijassa-294	135	13	c(x	c(x	PROPN
ijassa-294	135	14	)	)	PUNCT
ijassa-294	135	15	0	0	PUNCT
ijassa-294	136	1	f(x	f(x	PROPN
ijassa-294	136	2	,	,	PUNCT
ijassa-294	136	3	s	s	X
ijassa-294	136	4	)	)	PUNCT
ijassa-294	136	5	ds	ds	ADJ
ijassa-294	136	6	)	)	PUNCT
ijassa-294	136	7	dx	dx	PROPN
ijassa-294	136	8	≥	≥	PROPN
ijassa-294	137	1	m0	m0	PROPN
ijassa-294	137	2	∫	∫	PROPN
ijassa-294	137	3	ω	ω	PROPN
ijassa-294	137	4	1	1	NUM
ijassa-294	137	5	2	2	NUM
ijassa-294	137	6	|∇u|2	|∇u|2	NOUN
ijassa-294	137	7	dx−	dx−	ADP
ijassa-294	137	8	λ	λ	PROPN
ijassa-294	137	9	∫	∫	PROPN
ijassa-294	137	10	ω0	ω0	PROPN
ijassa-294	137	11	a1	a1	NOUN
ijassa-294	137	12	dx	dx	PROPN
ijassa-294	137	13	=	=	PROPN
ijassa-294	137	14	m0	m0	PROPN
ijassa-294	137	15	2	2	NUM
ijassa-294	137	16	‖u‖2	‖u‖2	ADJ
ijassa-294	137	17	−	−	PROPN
ijassa-294	137	18	λ|ω0|a1	λ|ω0|a1	NUM
ijassa-294	137	19	→	→	SYM
ijassa-294	137	20	+	+	ADJ
ijassa-294	137	21	∞	∞	PROPN
ijassa-294	137	22	,	,	PUNCT
ijassa-294	137	23	as	as	ADP
ijassa-294	137	24	‖u‖	‖u‖	PROPN
ijassa-294	137	25	→	→	SYM
ijassa-294	137	26	+	+	PROPN
ijassa-294	137	27	∞	∞	PROPN
ijassa-294	137	28	,	,	PUNCT
ijassa-294	137	29	(	(	PUNCT
ijassa-294	137	30	9	9	X
ijassa-294	137	31	)	)	PUNCT
ijassa-294	137	32	where	where	SCONJ
ijassa-294	137	33	a1	a1	NOUN
ijassa-294	137	34	=	=	PROPN
ijassa-294	137	35	maxx∈ω0	maxx∈ω0	PROPN
ijassa-294	137	36	|f	|f	PROPN
ijassa-294	137	37	(	(	PUNCT
ijassa-294	137	38	x	x	NOUN
ijassa-294	137	39	,	,	PUNCT
ijassa-294	137	40	c(x))|	c(x))|	PROPN
ijassa-294	137	41	.	.	PUNCT
ijassa-294	138	1	since	since	SCONJ
ijassa-294	138	2	iλ	iλ	NOUN
ijassa-294	138	3	is	be	AUX
ijassa-294	138	4	weakly	weakly	ADV
ijassa-294	138	5	lower	low	ADJ
ijassa-294	138	6	semi	semi	ADJ
ijassa-294	138	7	-	-	ADJ
ijassa-294	138	8	continuous	continuous	ADJ
ijassa-294	138	9	,	,	PUNCT
ijassa-294	138	10	iλ	iλ	PROPN
ijassa-294	138	11	has	have	VERB
ijassa-294	138	12	a	a	DET
ijassa-294	138	13	minimum	minimum	ADJ
ijassa-294	138	14	point	point	NOUN
ijassa-294	138	15	u1	u1	NOUN
ijassa-294	138	16	in	in	ADP
ijassa-294	138	17	x	x	X
ijassa-294	138	18	.	.	PUNCT
ijassa-294	139	1	next	next	ADV
ijassa-294	139	2	we	we	PRON
ijassa-294	139	3	shall	shall	AUX
ijassa-294	139	4	prove	prove	VERB
ijassa-294	139	5	iλ(u1	iλ(u1	NOUN
ijassa-294	139	6	)	)	PUNCT
ijassa-294	139	7	<	<	X
ijassa-294	139	8	0	0	NUM
ijassa-294	139	9	,	,	PUNCT
ijassa-294	139	10	thus	thus	ADV
ijassa-294	139	11	u1	u1	NOUN
ijassa-294	139	12	is	be	AUX
ijassa-294	139	13	a	a	DET
ijassa-294	139	14	positive	positive	ADJ
ijassa-294	139	15	solution	solution	NOUN
ijassa-294	139	16	of	of	ADP
ijassa-294	139	17	(	(	PUNCT
ijassa-294	139	18	1	1	NUM
ijassa-294	139	19	)	)	PUNCT
ijassa-294	139	20	.	.	PUNCT
ijassa-294	140	1	in	in	ADP
ijassa-294	140	2	fact	fact	NOUN
ijassa-294	140	3	,	,	PUNCT
ijassa-294	140	4	we	we	PRON
ijassa-294	140	5	only	only	ADV
ijassa-294	140	6	need	need	VERB
ijassa-294	140	7	to	to	PART
ijassa-294	140	8	verify	verify	VERB
ijassa-294	140	9	that	that	SCONJ
ijassa-294	140	10	when	when	SCONJ
ijassa-294	140	11	λ	λ	PROPN
ijassa-294	140	12	is	be	AUX
ijassa-294	140	13	large	large	ADJ
ijassa-294	140	14	there	there	ADV
ijassa-294	140	15	exists	exist	VERB
ijassa-294	140	16	a	a	DET
ijassa-294	140	17	u0	u0	ADJ
ijassa-294	140	18	∈	∈	PROPN
ijassa-294	140	19	x	x	X
ijassa-294	140	20	,	,	PUNCT
ijassa-294	140	21	such	such	ADJ
ijassa-294	140	22	that	that	SCONJ
ijassa-294	140	23	iλ(u0	iλ(u0	NOUN
ijassa-294	140	24	)	)	PUNCT
ijassa-294	140	25	<	<	X
ijassa-294	140	26	0	0	PUNCT
ijassa-294	141	1	=	=	SYM
ijassa-294	141	2	iλ(0	iλ(0	NOUN
ijassa-294	141	3	)	)	PUNCT
ijassa-294	141	4	.	.	PUNCT
ijassa-294	142	1	we	we	PRON
ijassa-294	142	2	define	define	VERB
ijassa-294	142	3	u0(x	u0(x	PRON
ijassa-294	142	4	)	)	PUNCT
ijassa-294	142	5	=	=	SYM
ijassa-294	142	6	0	0	NUM
ijassa-294	143	1	in	in	ADP
ijassa-294	143	2	ω	ω	NUM
ijassa-294	143	3	\	\	PROPN
ijassa-294	143	4	ω1ε	ω1ε	PROPN
ijassa-294	143	5	,	,	PUNCT
ijassa-294	143	6	and	and	CCONJ
ijassa-294	143	7	u0(x	u0(x	PRON
ijassa-294	143	8	)	)	PUNCT
ijassa-294	143	9	=	=	SYM
ijassa-294	143	10	c(x	c(x	NOUN
ijassa-294	143	11	)	)	PUNCT
ijassa-294	143	12	in	in	ADP
ijassa-294	143	13	ω1	ω1	PROPN
ijassa-294	143	14	and	and	CCONJ
ijassa-294	143	15	properly	properly	ADV
ijassa-294	143	16	in	in	ADP
ijassa-294	143	17	ω1ε	ω1ε	NOUN
ijassa-294	143	18	\	\	NOUN
ijassa-294	143	19	ω1	ω1	PROPN
ijassa-294	143	20	such	such	ADJ
ijassa-294	143	21	that	that	DET
ijassa-294	143	22	u0	u0	PROPN
ijassa-294	143	23	∈	∈	PROPN
ijassa-294	143	24	x	x	X
ijassa-294	143	25	,	,	PUNCT
ijassa-294	143	26	where	where	SCONJ
ijassa-294	143	27	ω1ε	ω1ε	ADV
ijassa-294	143	28	=	=	SYM
ijassa-294	143	29	{	{	PUNCT
ijassa-294	143	30	x	x	PUNCT
ijassa-294	143	31	∈	∈	PROPN
ijassa-294	143	32	ω	ω	NOUN
ijassa-294	143	33	:	:	PUNCT
ijassa-294	143	34	dist(x	dist(x	INTJ
ijassa-294	143	35	,	,	PUNCT
ijassa-294	143	36	ω1	ω1	PROPN
ijassa-294	143	37	)	)	PUNCT
ijassa-294	143	38	≤	≤	NUM
ijassa-294	143	39	ε	ε	PROPN
ijassa-294	143	40	}	}	PUNCT
ijassa-294	143	41	.	.	PUNCT
ijassa-294	144	1	using	use	VERB
ijassa-294	144	2	the	the	DET
ijassa-294	144	3	similar	similar	ADJ
ijassa-294	144	4	method	method	NOUN
ijassa-294	144	5	with[1	with[1	ADV
ijassa-294	144	6	]	]	PUNCT
ijassa-294	144	7	,	,	PUNCT
ijassa-294	144	8	we	we	PRON
ijassa-294	144	9	have	have	VERB
ijassa-294	144	10	iλ(u0	iλ(u0	NOUN
ijassa-294	144	11	)	)	PUNCT
ijassa-294	144	12	≤	≤	NOUN
ijassa-294	144	13	m̂	m̂	PROPN
ijassa-294	145	1	(	(	PUNCT
ijassa-294	145	2	∫	∫	PROPN
ijassa-294	145	3	ω	ω	NUM
ijassa-294	145	4	1	1	NUM
ijassa-294	145	5	2	2	NUM
ijassa-294	145	6	|∇u0|2	|∇u0|2	NOUN
ijassa-294	145	7	dx	dx	NOUN
ijassa-294	145	8	)	)	PUNCT
ijassa-294	146	1	−	−	PROPN
ijassa-294	147	1	λ	λ	INTJ
ijassa-294	147	2	∫	∫	PROPN
ijassa-294	147	3	ω1	ω1	PROPN
ijassa-294	147	4	f	f	PROPN
ijassa-294	147	5	(	(	PUNCT
ijassa-294	147	6	x	x	NOUN
ijassa-294	147	7	,	,	PUNCT
ijassa-294	147	8	c(x	c(x	NOUN
ijassa-294	147	9	)	)	PUNCT
ijassa-294	147	10	)	)	PUNCT
ijassa-294	147	11	dx−	dx−	X
ijassa-294	148	1	λ	λ	X
ijassa-294	149	1	[	[	X
ijassa-294	149	2	−a1	−a1	PROPN
ijassa-294	149	3	(	(	PUNCT
ijassa-294	149	4	|ω1ε|	|ω1ε|	NOUN
ijassa-294	149	5	−	−	PROPN
ijassa-294	149	6	|ω1|	|ω1|	NOUN
ijassa-294	149	7	)	)	PUNCT
ijassa-294	149	8	]	]	PUNCT
ijassa-294	150	1	dx	dx	PROPN
ijassa-294	150	2	.	.	PUNCT
ijassa-294	151	1	(	(	PUNCT
ijassa-294	151	2	10	10	NUM
ijassa-294	151	3	)	)	PUNCT
ijassa-294	151	4	advances	advance	NOUN
ijassa-294	151	5	in	in	ADP
ijassa-294	151	6	systems	system	NOUN
ijassa-294	151	7	science	science	NOUN
ijassa-294	151	8	and	and	CCONJ
ijassa-294	151	9	applications	application	NOUN
ijassa-294	151	10	(	(	PUNCT
ijassa-294	151	11	2011	2011	NUM
ijassa-294	151	12	)	)	PUNCT
ijassa-294	151	13	,	,	PUNCT
ijassa-294	151	14	vol	vol	NOUN
ijassa-294	151	15	.	.	PROPN
ijassa-294	151	16	11	11	NUM
ijassa-294	151	17	,	,	PUNCT
ijassa-294	151	18	no	no	INTJ
ijassa-294	151	19	.	.	NOUN
ijassa-294	151	20	1	1	NUM
ijassa-294	151	21	-	-	SYM
ijassa-294	151	22	2	2	NUM
ijassa-294	151	23	87	87	NUM
ijassa-294	151	24	since	since	SCONJ
ijassa-294	151	25	∫	∫	PROPN
ijassa-294	151	26	c(cx	c(cx	PART
ijassa-294	151	27	)	)	PUNCT
ijassa-294	151	28	0	0	PUNCT
ijassa-294	152	1	f(x	f(x	PROPN
ijassa-294	152	2	,	,	PUNCT
ijassa-294	152	3	s	s	X
ijassa-294	152	4	)	)	PUNCT
ijassa-294	152	5	ds	ds	NOUN
ijassa-294	152	6	>	>	X
ijassa-294	152	7	0	0	PUNCT
ijassa-294	153	1	when	when	SCONJ
ijassa-294	153	2	x	x	PROPN
ijassa-294	153	3	∈	∈	PROPN
ijassa-294	153	4	ω1	ω1	PROPN
ijassa-294	153	5	and	and	CCONJ
ijassa-294	153	6	∫	∫	PROPN
ijassa-294	153	7	c(x	c(x	PROPN
ijassa-294	153	8	)	)	PUNCT
ijassa-294	153	9	0	0	PUNCT
ijassa-294	154	1	f(x	f(x	PROPN
ijassa-294	154	2	,	,	PUNCT
ijassa-294	154	3	s	s	X
ijassa-294	154	4	)	)	PUNCT
ijassa-294	154	5	ds	ds	NOUN
ijassa-294	154	6	is	be	AUX
ijassa-294	154	7	continuous	continuous	ADJ
ijassa-294	154	8	,	,	PUNCT
ijassa-294	154	9	then	then	ADV
ijassa-294	154	10	there	there	PRON
ijassa-294	154	11	must	must	AUX
ijassa-294	154	12	exists	exist	VERB
ijassa-294	154	13	an	an	DET
ijassa-294	154	14	open	open	ADJ
ijassa-294	154	15	subset	subset	NOUN
ijassa-294	154	16	ω2	ω2	ADJ
ijassa-294	154	17	with	with	ADP
ijassa-294	154	18	ω2	ω2	PROPN
ijassa-294	154	19	⊂	⊂	PROPN
ijassa-294	154	20	ω1	ω1	PROPN
ijassa-294	154	21	and	and	CCONJ
ijassa-294	154	22	δ	δ	PROPN
ijassa-294	154	23	>	>	X
ijassa-294	154	24	0	0	PROPN
ijassa-294	154	25	,	,	PUNCT
ijassa-294	154	26	such	such	ADJ
ijassa-294	154	27	that	that	DET
ijassa-294	154	28	|ω2|	|ω2|	VERB
ijassa-294	154	29	>	>	X
ijassa-294	154	30	0	0	NUM
ijassa-294	154	31	and	and	CCONJ
ijassa-294	154	32	∫	∫	PROPN
ijassa-294	154	33	c(x	c(x	PROPN
ijassa-294	154	34	)	)	PUNCT
ijassa-294	154	35	0	0	PUNCT
ijassa-294	155	1	f(x	f(x	PROPN
ijassa-294	155	2	,	,	PUNCT
ijassa-294	155	3	s	s	X
ijassa-294	155	4	)	)	PUNCT
ijassa-294	155	5	ds	ds	ADJ
ijassa-294	155	6	≥	≥	NOUN
ijassa-294	155	7	δ	δ	PROPN
ijassa-294	155	8	for	for	ADP
ijassa-294	155	9	x	x	PROPN
ijassa-294	155	10	∈	∈	PROPN
ijassa-294	155	11	ω2	ω2	PROPN
ijassa-294	155	12	.	.	PUNCT
ijassa-294	156	1	choose	choose	VERB
ijassa-294	156	2	ε	ε	PROPN
ijassa-294	156	3	small	small	ADJ
ijassa-294	156	4	enough	enough	ADV
ijassa-294	156	5	,	,	PUNCT
ijassa-294	156	6	such	such	ADJ
ijassa-294	156	7	that	that	SCONJ
ijassa-294	156	8	δ|ω2|	δ|ω2|	NOUN
ijassa-294	156	9	+	+	CCONJ
ijassa-294	156	10	a(|ω1|	a(|ω1|	NOUN
ijassa-294	156	11	−	−	PROPN
ijassa-294	156	12	|ω1ε|	|ω1ε|	NOUN
ijassa-294	156	13	)	)	PUNCT
ijassa-294	156	14	>	>	X
ijassa-294	157	1	0	0	X
ijassa-294	157	2	.	.	PUNCT
ijassa-294	157	3	again	again	ADV
ijassa-294	157	4	using	use	VERB
ijassa-294	157	5	the	the	DET
ijassa-294	157	6	similar	similar	ADJ
ijassa-294	157	7	method	method	NOUN
ijassa-294	157	8	with	with	ADP
ijassa-294	157	9	[	[	X
ijassa-294	157	10	1	1	NUM
ijassa-294	157	11	]	]	PUNCT
ijassa-294	157	12	,	,	PUNCT
ijassa-294	157	13	we	we	PRON
ijassa-294	157	14	have	have	VERB
ijassa-294	157	15	iλ(u0	iλ(u0	NOUN
ijassa-294	157	16	)	)	PUNCT
ijassa-294	157	17	≤	≤	NOUN
ijassa-294	157	18	m̂	m̂	PROPN
ijassa-294	158	1	(	(	PUNCT
ijassa-294	158	2	∫	∫	PROPN
ijassa-294	158	3	ω	ω	NUM
ijassa-294	158	4	1	1	NUM
ijassa-294	158	5	2	2	NUM
ijassa-294	158	6	|∇u0|2	|∇u0|2	NOUN
ijassa-294	158	7	dx	dx	NOUN
ijassa-294	158	8	)	)	PUNCT
ijassa-294	159	1	−	−	PROPN
ijassa-294	160	1	λ	λ	X
ijassa-294	160	2	[	[	X
ijassa-294	160	3	δ|ω2|+a1(|ω1|	δ|ω2|+a1(|ω1|	X
ijassa-294	160	4	−	−	PROPN
ijassa-294	160	5	|ω1ε|	|ω1ε|	NOUN
ijassa-294	160	6	)	)	PUNCT
ijassa-294	160	7	]	]	PUNCT
ijassa-294	160	8	.	.	PUNCT
ijassa-294	161	1	therefore	therefore	ADV
ijassa-294	161	2	when	when	SCONJ
ijassa-294	161	3	λ	λ	PROPN
ijassa-294	161	4	large	large	ADJ
ijassa-294	161	5	enough	enough	ADV
ijassa-294	161	6	,	,	PUNCT
ijassa-294	161	7	iλ(u0	iλ(u0	NOUN
ijassa-294	161	8	)	)	PUNCT
ijassa-294	161	9	<	<	X
ijassa-294	161	10	0	0	NUM
ijassa-294	161	11	,	,	PUNCT
ijassa-294	161	12	and	and	CCONJ
ijassa-294	161	13	consequently	consequently	ADV
ijassa-294	161	14	when	when	SCONJ
ijassa-294	161	15	λ	λ	PROPN
ijassa-294	161	16	is	be	AUX
ijassa-294	161	17	large	large	ADJ
ijassa-294	161	18	enough	enough	ADV
ijassa-294	161	19	,	,	PUNCT
ijassa-294	161	20	(	(	PUNCT
ijassa-294	161	21	1	1	X
ijassa-294	161	22	)	)	PUNCT
ijassa-294	161	23	has	have	VERB
ijassa-294	161	24	a	a	DET
ijassa-294	161	25	positive	positive	ADJ
ijassa-294	161	26	solution	solution	NOUN
ijassa-294	161	27	u1(x	u1(x	NOUN
ijassa-294	161	28	)	)	PUNCT
ijassa-294	161	29	satisfying	satisfy	VERB
ijassa-294	161	30	iλ(u1	iλ(u1	NOUN
ijassa-294	161	31	)	)	PUNCT
ijassa-294	162	1	=	=	PUNCT
ijassa-294	162	2	infu∈x	infu∈x	PROPN
ijassa-294	162	3	iλ(u	iλ(u	NUM
ijassa-294	162	4	)	)	PUNCT
ijassa-294	162	5	<	<	X
ijassa-294	162	6	0	0	X
ijassa-294	162	7	.	.	PUNCT
ijassa-294	163	1	next	next	ADV
ijassa-294	163	2	we	we	PRON
ijassa-294	163	3	shall	shall	AUX
ijassa-294	163	4	use	use	VERB
ijassa-294	163	5	mountain	mountain	NOUN
ijassa-294	163	6	pass	pass	NOUN
ijassa-294	163	7	theorem	theorem	VERB
ijassa-294	163	8	to	to	PART
ijassa-294	163	9	prove	prove	VERB
ijassa-294	163	10	that	that	SCONJ
ijassa-294	163	11	(	(	PUNCT
ijassa-294	163	12	1	1	X
ijassa-294	163	13	)	)	PUNCT
ijassa-294	163	14	has	have	VERB
ijassa-294	163	15	another	another	DET
ijassa-294	163	16	positive	positive	ADJ
ijassa-294	163	17	solution	solution	NOUN
ijassa-294	163	18	u2	u2	NOUN
ijassa-294	163	19	.	.	PUNCT
ijassa-294	164	1	first	first	ADV
ijassa-294	164	2	we	we	PRON
ijassa-294	164	3	prove	prove	VERB
ijassa-294	164	4	iλ(u	iλ(u	NOUN
ijassa-294	164	5	)	)	PUNCT
ijassa-294	164	6	satisfies	satisfy	VERB
ijassa-294	164	7	palais	palais	PROPN
ijassa-294	164	8	-	-	PUNCT
ijassa-294	164	9	smale	smale	ADJ
ijassa-294	164	10	condition	condition	NOUN
ijassa-294	164	11	.	.	PUNCT
ijassa-294	165	1	definition	definition	NOUN
ijassa-294	165	2	3.1	3.1	NUM
ijassa-294	165	3	.	.	PUNCT
ijassa-294	166	1	we	we	PRON
ijassa-294	166	2	say	say	VERB
ijassa-294	166	3	that	that	SCONJ
ijassa-294	166	4	iλ	iλ	ADJ
ijassa-294	166	5	satisfies	satisfie	NOUN
ijassa-294	166	6	(	(	PUNCT
ijassa-294	166	7	p.s	p.s	INTJ
ijassa-294	166	8	.	.	PUNCT
ijassa-294	166	9	)	)	PUNCT
ijassa-294	166	10	condition	condition	NOUN
ijassa-294	166	11	in	in	ADP
ijassa-294	166	12	x	x	SYM
ijassa-294	166	13	,	,	PUNCT
ijassa-294	166	14	if	if	SCONJ
ijassa-294	166	15	any	any	DET
ijassa-294	166	16	sequence	sequence	NOUN
ijassa-294	166	17	{	{	PUNCT
ijassa-294	166	18	un	un	PROPN
ijassa-294	166	19	}	}	PUNCT
ijassa-294	166	20	⊂	⊂	X
ijassa-294	166	21	x	x	PUNCT
ijassa-294	166	22	such	such	ADJ
ijassa-294	166	23	that	that	SCONJ
ijassa-294	166	24	{	{	PUNCT
ijassa-294	166	25	iλ(un	iλ(un	PROPN
ijassa-294	166	26	)	)	PUNCT
ijassa-294	166	27	}	}	PUNCT
ijassa-294	166	28	is	be	AUX
ijassa-294	166	29	bounded	bound	VERB
ijassa-294	166	30	and	and	CCONJ
ijassa-294	166	31	i	i	PRON
ijassa-294	166	32	′λ(un	′λ(un	PROPN
ijassa-294	166	33	)	)	PUNCT
ijassa-294	166	34	→	→	SYM
ijassa-294	166	35	0	0	NUM
ijassa-294	166	36	as	as	ADP
ijassa-294	166	37	n	n	PRON
ijassa-294	166	38	→	→	SYM
ijassa-294	166	39	+	+	NOUN
ijassa-294	166	40	∞	∞	PROPN
ijassa-294	166	41	,	,	PUNCT
ijassa-294	166	42	has	have	VERB
ijassa-294	166	43	a	a	DET
ijassa-294	166	44	convergent	convergent	NOUN
ijassa-294	166	45	subsequence	subsequence	NOUN
ijassa-294	166	46	,	,	PUNCT
ijassa-294	166	47	where	where	SCONJ
ijassa-294	166	48	(	(	PUNCT
ijassa-294	166	49	p.s	p.s	NOUN
ijassa-294	166	50	.	.	PUNCT
ijassa-294	166	51	)	)	PUNCT
ijassa-294	166	52	means	mean	VERB
ijassa-294	166	53	palais	palais	PROPN
ijassa-294	166	54	-	-	PUNCT
ijassa-294	166	55	smale	smale	NOUN
ijassa-294	166	56	.	.	PUNCT
ijassa-294	167	1	lemma	lemma	PROPN
ijassa-294	167	2	3.2	3.2	NUM
ijassa-294	167	3	.	.	PUNCT
ijassa-294	168	1	if	if	SCONJ
ijassa-294	168	2	m(t	m(t	NOUN
ijassa-294	168	3	)	)	PUNCT
ijassa-294	168	4	satisfies	satisfie	NOUN
ijassa-294	168	5	(	(	PUNCT
ijassa-294	168	6	m	m	PROPN
ijassa-294	168	7	)	)	PUNCT
ijassa-294	168	8	,	,	PUNCT
ijassa-294	168	9	f	f	PROPN
ijassa-294	168	10	satisfies	satisfie	NOUN
ijassa-294	168	11	(	(	PUNCT
ijassa-294	168	12	f1)–(f3	f1)–(f3	NOUN
ijassa-294	168	13	)	)	PUNCT
ijassa-294	168	14	and	and	CCONJ
ijassa-294	168	15	(	(	PUNCT
ijassa-294	168	16	5	5	NUM
ijassa-294	168	17	)	)	PUNCT
ijassa-294	168	18	,	,	PUNCT
ijassa-294	168	19	then	then	ADV
ijassa-294	168	20	iλ	iλ	VERB
ijassa-294	168	21	satisfies	satisfie	NOUN
ijassa-294	168	22	(	(	PUNCT
ijassa-294	168	23	p.s	p.s	INTJ
ijassa-294	168	24	.	.	PUNCT
ijassa-294	168	25	)	)	PUNCT
ijassa-294	169	1	condition	condition	NOUN
ijassa-294	169	2	.	.	PUNCT
ijassa-294	170	1	proof	proof	NOUN
ijassa-294	170	2	.	.	PUNCT
ijassa-294	171	1	suppose	suppose	VERB
ijassa-294	171	2	that	that	SCONJ
ijassa-294	171	3	{	{	PUNCT
ijassa-294	171	4	un	un	PROPN
ijassa-294	171	5	}	}	PUNCT
ijassa-294	171	6	⊂	⊂	NOUN
ijassa-294	171	7	x	x	X
ijassa-294	171	8	,	,	PUNCT
ijassa-294	171	9	|iλ(un)|	|iλ(un)|	ADV
ijassa-294	171	10	≤	≤	ADJ
ijassa-294	171	11	c0	c0	NOUN
ijassa-294	171	12	and	and	CCONJ
ijassa-294	171	13	i	i	PROPN
ijassa-294	171	14	′λ(un	′λ(un	PROPN
ijassa-294	171	15	)	)	PUNCT
ijassa-294	171	16	→	→	SYM
ijassa-294	171	17	0	0	NUM
ijassa-294	171	18	as	as	ADP
ijassa-294	171	19	n	n	PRON
ijassa-294	171	20	→	→	PUNCT
ijassa-294	171	21	+	+	NOUN
ijassa-294	171	22	∞.	∞.	PROPN
ijassa-294	171	23	in	in	ADP
ijassa-294	171	24	view	view	NOUN
ijassa-294	171	25	of	of	ADP
ijassa-294	171	26	(	(	PUNCT
ijassa-294	171	27	9	9	NUM
ijassa-294	171	28	)	)	PUNCT
ijassa-294	171	29	,	,	PUNCT
ijassa-294	171	30	we	we	PRON
ijassa-294	171	31	have	have	VERB
ijassa-294	171	32	c0	c0	PROPN
ijassa-294	171	33	≥	≥	PROPN
ijassa-294	171	34	iλ(un	iλ(un	PROPN
ijassa-294	171	35	)	)	PUNCT
ijassa-294	171	36	≥	≥	PROPN
ijassa-294	171	37	m0	m0	NOUN
ijassa-294	171	38	2	2	NUM
ijassa-294	171	39	‖un‖2	‖un‖2	PROPN
ijassa-294	171	40	−	−	NOUN
ijassa-294	171	41	λ|ω0|a	λ|ω0|a	X
ijassa-294	171	42	.	.	PUNCT
ijassa-294	172	1	hence	hence	ADV
ijassa-294	172	2	,	,	PUNCT
ijassa-294	172	3	{	{	PUNCT
ijassa-294	172	4	‖un‖	‖un‖	NOUN
ijassa-294	172	5	}	}	PUNCT
ijassa-294	172	6	is	be	AUX
ijassa-294	172	7	bounded	bound	VERB
ijassa-294	172	8	.	.	PUNCT
ijassa-294	173	1	without	without	ADP
ijassa-294	173	2	loss	loss	NOUN
ijassa-294	173	3	of	of	ADP
ijassa-294	173	4	generality	generality	NOUN
ijassa-294	173	5	,	,	PUNCT
ijassa-294	173	6	we	we	PRON
ijassa-294	173	7	assume	assume	VERB
ijassa-294	173	8	that	that	SCONJ
ijassa-294	173	9	un	un	PROPN
ijassa-294	173	10	⇀	⇀	PROPN
ijassa-294	173	11	u	u	PROPN
ijassa-294	173	12	,	,	PUNCT
ijassa-294	173	13	then	then	ADV
ijassa-294	173	14	i	i	PRON
ijassa-294	173	15	′(un)(un−	′(un)(un−	VERB
ijassa-294	173	16	u)→	u)→	NOUN
ijassa-294	173	17	0	0	NUM
ijassa-294	173	18	.	.	PUNCT
ijassa-294	174	1	therefore	therefore	ADV
ijassa-294	174	2	,	,	PUNCT
ijassa-294	174	3	we	we	PRON
ijassa-294	174	4	have	have	VERB
ijassa-294	174	5	un	un	PROPN
ijassa-294	174	6	→	→	SYM
ijassa-294	174	7	u	u	PROPN
ijassa-294	174	8	by	by	ADP
ijassa-294	174	9	the	the	DET
ijassa-294	174	10	(	(	PUNCT
ijassa-294	174	11	s+	s+	NOUN
ijassa-294	174	12	)	)	PUNCT
ijassa-294	174	13	property	property	NOUN
ijassa-294	174	14	of	of	ADP
ijassa-294	174	15	i	i	PRON
ijassa-294	174	16	′λ	′λ	PROPN
ijassa-294	174	17	.	.	PUNCT
ijassa-294	175	1	lemma	lemma	PROPN
ijassa-294	175	2	3.3	3.3	NUM
ijassa-294	175	3	.	.	PUNCT
ijassa-294	176	1	ifm(t	ifm(t	PROPN
ijassa-294	176	2	)	)	PUNCT
ijassa-294	176	3	satisfies	satisfie	NOUN
ijassa-294	176	4	(	(	PUNCT
ijassa-294	176	5	m	m	PROPN
ijassa-294	176	6	)	)	PUNCT
ijassa-294	176	7	,	,	PUNCT
ijassa-294	176	8	f	f	PROPN
ijassa-294	176	9	satisfies	satisfie	NOUN
ijassa-294	176	10	(	(	PUNCT
ijassa-294	176	11	f1)–(f3	f1)–(f3	NOUN
ijassa-294	176	12	)	)	PUNCT
ijassa-294	176	13	,	,	PUNCT
ijassa-294	176	14	then	then	ADV
ijassa-294	176	15	there	there	PRON
ijassa-294	176	16	exist	exist	VERB
ijassa-294	176	17	ρ	ρ	PROPN
ijassa-294	176	18	>	>	X
ijassa-294	176	19	0	0	PROPN
ijassa-294	176	20	and	and	CCONJ
ijassa-294	176	21	γ	γ	X
ijassa-294	176	22	>	>	X
ijassa-294	176	23	0	0	NUM
ijassa-294	176	24	such	such	ADJ
ijassa-294	176	25	that	that	DET
ijassa-294	176	26	iλ(u	iλ(u	NUM
ijassa-294	176	27	)	)	PUNCT
ijassa-294	176	28	≥	≥	PROPN
ijassa-294	176	29	γ	γ	PROPN
ijassa-294	176	30	for	for	ADP
ijassa-294	176	31	every	every	DET
ijassa-294	176	32	u	u	NOUN
ijassa-294	176	33	∈	∈	PROPN
ijassa-294	176	34	x	x	PUNCT
ijassa-294	176	35	with	with	ADP
ijassa-294	176	36	‖u‖	‖u‖	PROPN
ijassa-294	176	37	=	=	SYM
ijassa-294	176	38	ρ	ρ	PROPN
ijassa-294	176	39	.	.	PUNCT
ijassa-294	176	40	proof	proof	NOUN
ijassa-294	176	41	.	.	PUNCT
ijassa-294	177	1	we	we	PRON
ijassa-294	177	2	define	define	VERB
ijassa-294	177	3	b	b	NOUN
ijassa-294	177	4	=	=	SYM
ijassa-294	177	5	minx∈ω	minx∈ω	NOUN
ijassa-294	177	6	.	.	NOUN
ijassa-294	178	1	for	for	ADP
ijassa-294	178	2	any	any	DET
ijassa-294	178	3	u(x	u(x	NOUN
ijassa-294	178	4	)	)	PUNCT
ijassa-294	178	5	∈	∈	PROPN
ijassa-294	178	6	x	x	X
ijassa-294	178	7	,	,	PUNCT
ijassa-294	178	8	we	we	PRON
ijassa-294	178	9	also	also	ADV
ijassa-294	178	10	define	define	VERB
ijassa-294	178	11	b1	b1	NOUN
ijassa-294	178	12	=	=	SYM
ijassa-294	178	13	{	{	PUNCT
ijassa-294	178	14	x	x	PUNCT
ijassa-294	178	15	∈	∈	PROPN
ijassa-294	178	16	ω	ω	NOUN
ijassa-294	178	17	:	:	PUNCT
ijassa-294	178	18	u(x	u(x	PROPN
ijassa-294	178	19	)	)	PUNCT
ijassa-294	178	20	<	<	X
ijassa-294	178	21	b	b	X
ijassa-294	178	22	}	}	PUNCT
ijassa-294	178	23	,	,	PUNCT
ijassa-294	178	24	b2	b2	NOUN
ijassa-294	178	25	=	=	SYM
ijassa-294	178	26	{	{	PUNCT
ijassa-294	178	27	x	x	PUNCT
ijassa-294	178	28	∈	∈	PROPN
ijassa-294	178	29	ω	ω	NOUN
ijassa-294	178	30	:	:	PUNCT
ijassa-294	178	31	u(x	u(x	PROPN
ijassa-294	178	32	)	)	PUNCT
ijassa-294	178	33	≥	≥	NOUN
ijassa-294	178	34	b	b	NOUN
ijassa-294	178	35	}	}	PUNCT
ijassa-294	178	36	.	.	PUNCT
ijassa-294	179	1	it	it	PRON
ijassa-294	179	2	is	be	AUX
ijassa-294	179	3	well	well	ADV
ijassa-294	179	4	known	know	VERB
ijassa-294	179	5	that	that	SCONJ
ijassa-294	179	6	the	the	DET
ijassa-294	179	7	embedding	embedding	NOUN
ijassa-294	179	8	of	of	ADP
ijassa-294	179	9	x	x	X
ijassa-294	179	10	↪	↪	PROPN
ijassa-294	179	11	→	→	SYM
ijassa-294	179	12	lp(ω	lp(ω	NUM
ijassa-294	179	13	)	)	PUNCT
ijassa-294	179	14	is	be	AUX
ijassa-294	179	15	continuous	continuous	ADJ
ijassa-294	179	16	when	when	SCONJ
ijassa-294	179	17	2	2	NUM
ijassa-294	179	18	<	<	X
ijassa-294	179	19	p	p	X
ijassa-294	179	20	≤	≤	NUM
ijassa-294	179	21	2∗	2∗	NUM
ijassa-294	179	22	,	,	PUNCT
ijassa-294	179	23	where	where	SCONJ
ijassa-294	179	24	2∗	2∗	NUM
ijassa-294	179	25	is	be	AUX
ijassa-294	179	26	the	the	DET
ijassa-294	179	27	critical	critical	ADJ
ijassa-294	179	28	exponent	exponent	NOUN
ijassa-294	179	29	.	.	PUNCT
ijassa-294	180	1	from	from	ADP
ijassa-294	180	2	poincaré	poincaré	ADJ
ijassa-294	180	3	inequality	inequality	NOUN
ijassa-294	180	4	,	,	PUNCT
ijassa-294	180	5	we	we	PRON
ijassa-294	180	6	have	have	VERB
ijassa-294	180	7	b|b2|	b|b2|	ADV
ijassa-294	180	8	1	1	NUM
ijassa-294	180	9	p	p	NOUN
ijassa-294	180	10	≤	≤	NUM
ijassa-294	180	11	(	(	PUNCT
ijassa-294	180	12	∫	∫	PROPN
ijassa-294	180	13	b2	b2	PROPN
ijassa-294	180	14	up	up	ADP
ijassa-294	180	15	dx	dx	PROPN
ijassa-294	180	16	)	)	PUNCT
ijassa-294	180	17	1	1	NUM
ijassa-294	180	18	p	p	NOUN
ijassa-294	180	19	≤	≤	PROPN
ijassa-294	180	20	c1	c1	NOUN
ijassa-294	180	21	(	(	PUNCT
ijassa-294	180	22	∫	∫	PROPN
ijassa-294	180	23	b2	b2	PROPN
ijassa-294	180	24	|∇u|2	|∇u|2	NOUN
ijassa-294	180	25	dx	dx	PROPN
ijassa-294	180	26	)	)	PUNCT
ijassa-294	180	27	1	1	NUM
ijassa-294	180	28	2	2	NUM
ijassa-294	180	29	≤	≤	NOUN
ijassa-294	180	30	c1	c1	NOUN
ijassa-294	180	31	(	(	PUNCT
ijassa-294	180	32	∫	∫	PROPN
ijassa-294	180	33	ω	ω	PROPN
ijassa-294	180	34	|∇u|2	|∇u|2	PROPN
ijassa-294	180	35	dx	dx	PROPN
ijassa-294	180	36	)	)	PUNCT
ijassa-294	180	37	1	1	NUM
ijassa-294	180	38	2	2	NUM
ijassa-294	180	39	=	=	SYM
ijassa-294	180	40	c1‖u‖	c1‖u‖	PROPN
ijassa-294	180	41	,	,	PUNCT
ijassa-294	180	42	88	88	NUM
ijassa-294	180	43	ma	ma	NOUN
ijassa-294	180	44	:	:	PUNCT
ijassa-294	180	45	existence	existence	NOUN
ijassa-294	180	46	and	and	CCONJ
ijassa-294	180	47	nonexistence	nonexistence	NOUN
ijassa-294	180	48	of	of	ADP
ijassa-294	180	49	positive	positive	ADJ
ijassa-294	180	50	solutions	solution	NOUN
ijassa-294	180	51	for	for	ADP
ijassa-294	180	52	a	a	DET
ijassa-294	180	53	kirchhoff	kirchhoff	NOUN
ijassa-294	180	54	-	-	PUNCT
ijassa-294	180	55	type	type	NOUN
ijassa-294	180	56	.	.	PUNCT
ijassa-294	180	57	.	.	PUNCT
ijassa-294	180	58	.	.	PUNCT
ijassa-294	180	59	.	.	PUNCT
ijassa-294	180	60	.	.	PUNCT
ijassa-294	180	61	.	.	PUNCT
ijassa-294	181	1	where	where	SCONJ
ijassa-294	181	2	c1	c1	PROPN
ijassa-294	181	3	is	be	AUX
ijassa-294	181	4	the	the	DET
ijassa-294	181	5	embedding	embed	VERB
ijassa-294	181	6	constant	constant	ADJ
ijassa-294	181	7	of	of	ADP
ijassa-294	181	8	x	x	X
ijassa-294	181	9	↪	↪	PROPN
ijassa-294	181	10	→	→	SYM
ijassa-294	181	11	lp(ω	lp(ω	NUM
ijassa-294	181	12	)	)	PUNCT
ijassa-294	181	13	.	.	PUNCT
ijassa-294	182	1	thus	thus	ADV
ijassa-294	182	2	,	,	PUNCT
ijassa-294	182	3	we	we	PRON
ijassa-294	182	4	have	have	VERB
ijassa-294	182	5	iλ(u	iλ(u	NUM
ijassa-294	182	6	)	)	PUNCT
ijassa-294	182	7	=	=	SYM
ijassa-294	182	8	m̂	m̂	PROPN
ijassa-294	182	9	(	(	PUNCT
ijassa-294	182	10	∫	∫	PROPN
ijassa-294	182	11	ω	ω	NUM
ijassa-294	182	12	1	1	NUM
ijassa-294	182	13	2	2	NUM
ijassa-294	182	14	|∇u|2	|∇u|2	NOUN
ijassa-294	182	15	dx	dx	PROPN
ijassa-294	182	16	)	)	PUNCT
ijassa-294	182	17	−	−	PUNCT
ijassa-294	183	1	λ	λ	INTJ
ijassa-294	183	2	∫	∫	PROPN
ijassa-294	183	3	ω	ω	NUM
ijassa-294	183	4	f	f	PROPN
ijassa-294	183	5	(	(	PUNCT
ijassa-294	183	6	x	x	NOUN
ijassa-294	183	7	,	,	PUNCT
ijassa-294	183	8	u	u	NOUN
ijassa-294	183	9	)	)	PUNCT
ijassa-294	183	10	dx	dx	PROPN
ijassa-294	183	11	≥	≥	PROPN
ijassa-294	183	12	m0	m0	PROPN
ijassa-294	183	13	2	2	NUM
ijassa-294	183	14	‖u‖2	‖u‖2	ADJ
ijassa-294	183	15	−	−	PROPN
ijassa-294	184	1	λ	λ	PROPN
ijassa-294	184	2	∫	∫	PROPN
ijassa-294	184	3	b1	b1	PROPN
ijassa-294	184	4	f	f	PROPN
ijassa-294	184	5	(	(	PUNCT
ijassa-294	184	6	x	x	NOUN
ijassa-294	184	7	,	,	PUNCT
ijassa-294	184	8	u	u	NOUN
ijassa-294	184	9	)	)	PUNCT
ijassa-294	184	10	dx−	dx−	NUM
ijassa-294	184	11	λ	λ	PROPN
ijassa-294	184	12	∫	∫	PROPN
ijassa-294	184	13	b2	b2	PROPN
ijassa-294	184	14	f	f	PROPN
ijassa-294	184	15	(	(	PUNCT
ijassa-294	184	16	x	x	NOUN
ijassa-294	184	17	,	,	PUNCT
ijassa-294	184	18	u	u	NOUN
ijassa-294	184	19	)	)	PUNCT
ijassa-294	184	20	dx	dx	PROPN
ijassa-294	184	21	≥	≥	PROPN
ijassa-294	184	22	m0	m0	PROPN
ijassa-294	184	23	2	2	NUM
ijassa-294	184	24	‖u‖2	‖u‖2	ADJ
ijassa-294	184	25	−	−	PROPN
ijassa-294	185	1	λ	λ	PROPN
ijassa-294	185	2	∫	∫	PROPN
ijassa-294	185	3	b2	b2	PROPN
ijassa-294	185	4	f	f	PROPN
ijassa-294	185	5	(	(	PUNCT
ijassa-294	185	6	x	x	NOUN
ijassa-294	185	7	,	,	PUNCT
ijassa-294	185	8	u	u	NOUN
ijassa-294	185	9	)	)	PUNCT
ijassa-294	185	10	dx	dx	PROPN
ijassa-294	185	11	≥	≥	PROPN
ijassa-294	185	12	m0	m0	PROPN
ijassa-294	185	13	2	2	NUM
ijassa-294	185	14	‖u‖2	‖u‖2	ADJ
ijassa-294	185	15	−	−	PROPN
ijassa-294	185	16	λa2|b2|	λa2|b2|	NOUN
ijassa-294	185	17	≥	≥	NOUN
ijassa-294	185	18	m0	m0	PROPN
ijassa-294	185	19	2	2	NUM
ijassa-294	185	20	‖u‖2	‖u‖2	ADJ
ijassa-294	185	21	−	−	PROPN
ijassa-294	186	1	λa2	λa2	NOUN
ijassa-294	186	2	(	(	PUNCT
ijassa-294	186	3	c1	c1	PROPN
ijassa-294	186	4	b	b	PROPN
ijassa-294	186	5	)	)	PUNCT
ijassa-294	186	6	p	p	NOUN
ijassa-294	186	7	‖u‖p	‖u‖p	NOUN
ijassa-294	186	8	=	=	SYM
ijassa-294	186	9	‖u‖2	‖u‖2	PROPN
ijassa-294	186	10	(	(	PUNCT
ijassa-294	186	11	m0	m0	PROPN
ijassa-294	186	12	2	2	NUM
ijassa-294	186	13	−	−	NOUN
ijassa-294	187	1	λa2	λa2	NOUN
ijassa-294	187	2	(	(	PUNCT
ijassa-294	187	3	c1	c1	PROPN
ijassa-294	187	4	b	b	PROPN
ijassa-294	187	5	)	)	PUNCT
ijassa-294	187	6	p	p	NOUN
ijassa-294	187	7	‖u‖p−2	‖u‖p−2	NOUN
ijassa-294	187	8	)	)	PUNCT
ijassa-294	187	9	,	,	PUNCT
ijassa-294	187	10	where	where	SCONJ
ijassa-294	187	11	a2	a2	PROPN
ijassa-294	187	12	=	=	SYM
ijassa-294	187	13	max(x	max(x	PROPN
ijassa-294	187	14	,	,	PUNCT
ijassa-294	187	15	s)∈b2×[b	s)∈b2×[b	PROPN
ijassa-294	187	16	,	,	PUNCT
ijassa-294	187	17	c	c	X
ijassa-294	187	18	]	]	X
ijassa-294	187	19	|f	|f	PROPN
ijassa-294	187	20	(	(	PUNCT
ijassa-294	187	21	x	x	PROPN
ijassa-294	187	22	,	,	PUNCT
ijassa-294	187	23	s)|	s)|	PROPN
ijassa-294	187	24	.	.	PUNCT
ijassa-294	188	1	therefore	therefore	ADV
ijassa-294	188	2	,	,	PUNCT
ijassa-294	188	3	there	there	PRON
ijassa-294	188	4	exist	exist	VERB
ijassa-294	188	5	m0b	m0b	NOUN
ijassa-294	188	6	p	p	NOUN
ijassa-294	188	7	2λa2c	2λa2c	NUM
ijassa-294	188	8	p	p	NOUN
ijassa-294	188	9	1	1	NUM
ijassa-294	188	10	>	>	SYM
ijassa-294	188	11	ρ	ρ	PROPN
ijassa-294	188	12	>	>	X
ijassa-294	188	13	0	0	NUM
ijassa-294	188	14	such	such	ADJ
ijassa-294	188	15	that	that	DET
ijassa-294	188	16	iλ(u	iλ(u	NUM
ijassa-294	188	17	)	)	PUNCT
ijassa-294	188	18	≥	≥	NOUN
ijassa-294	188	19	ρ2	ρ2	NOUN
ijassa-294	188	20	(	(	PUNCT
ijassa-294	188	21	m0	m0	PROPN
ijassa-294	188	22	2	2	NUM
ijassa-294	188	23	−	−	NOUN
ijassa-294	189	1	λa2	λa2	NOUN
ijassa-294	190	1	(	(	PUNCT
ijassa-294	190	2	c1	c1	PROPN
ijassa-294	190	3	b	b	PROPN
ijassa-294	190	4	)	)	PUNCT
ijassa-294	190	5	p	p	PROPN
ijassa-294	190	6	ρp−2	ρp−2	NOUN
ijassa-294	190	7	)	)	PUNCT
ijassa-294	190	8	:	:	PUNCT
ijassa-294	191	1	=	=	PUNCT
ijassa-294	191	2	γ	γ	X
ijassa-294	191	3	>	>	X
ijassa-294	191	4	0	0	NUM
ijassa-294	191	5	for	for	ADP
ijassa-294	191	6	every	every	DET
ijassa-294	191	7	‖u‖	‖u‖	PROPN
ijassa-294	191	8	=	=	SYM
ijassa-294	191	9	ρ	ρ	PROPN
ijassa-294	191	10	and	and	CCONJ
ijassa-294	191	11	fixed	fix	VERB
ijassa-294	191	12	λ	λ	PROPN
ijassa-294	191	13	.	.	PUNCT
ijassa-294	191	14	proof	proof	NOUN
ijassa-294	191	15	of	of	ADP
ijassa-294	191	16	theorem	theorem	ADJ
ijassa-294	191	17	2.1	2.1	NUM
ijassa-294	191	18	concluded	conclude	VERB
ijassa-294	191	19	.	.	PUNCT
ijassa-294	192	1	first	first	ADV
ijassa-294	192	2	let	let	VERB
ijassa-294	192	3	us	we	PRON
ijassa-294	192	4	show	show	VERB
ijassa-294	192	5	that	that	SCONJ
ijassa-294	192	6	iλ	iλ	PROPN
ijassa-294	192	7	satisfies	satisfy	VERB
ijassa-294	192	8	the	the	DET
ijassa-294	192	9	conditions	condition	NOUN
ijassa-294	192	10	of	of	ADP
ijassa-294	192	11	mountain	mountain	NOUN
ijassa-294	192	12	pass	pass	NOUN
ijassa-294	192	13	theorem	theorem	NOUN
ijassa-294	192	14	(	(	PUNCT
ijassa-294	192	15	see	see	INTJ
ijassa-294	192	16	theorem	theorem	VERB
ijassa-294	192	17	2.10	2.10	NUM
ijassa-294	192	18	of	of	ADP
ijassa-294	192	19	[	[	X
ijassa-294	192	20	24	24	NUM
ijassa-294	192	21	]	]	PUNCT
ijassa-294	192	22	)	)	PUNCT
ijassa-294	192	23	.	.	PUNCT
ijassa-294	193	1	by	by	ADP
ijassa-294	193	2	lemma	lemma	PROPN
ijassa-294	193	3	3.2	3.2	NUM
ijassa-294	193	4	,	,	PUNCT
ijassa-294	193	5	iλ	iλ	ADJ
ijassa-294	193	6	satisfies	satisfie	NOUN
ijassa-294	193	7	(	(	PUNCT
ijassa-294	193	8	p.s	p.s	INTJ
ijassa-294	193	9	.	.	PUNCT
ijassa-294	193	10	)	)	PUNCT
ijassa-294	193	11	condition	condition	NOUN
ijassa-294	193	12	in	in	ADP
ijassa-294	193	13	x	x	X
ijassa-294	193	14	.	.	PUNCT
ijassa-294	194	1	by	by	ADP
ijassa-294	194	2	lemma	lemma	PROPN
ijassa-294	194	3	3.3	3.3	NUM
ijassa-294	194	4	,	,	PUNCT
ijassa-294	194	5	for	for	ADP
ijassa-294	194	6	fixed	fixed	ADJ
ijassa-294	194	7	λ	λ	PROPN
ijassa-294	194	8	>	>	X
ijassa-294	194	9	0	0	PROPN
ijassa-294	194	10	,	,	PUNCT
ijassa-294	194	11	there	there	PRON
ijassa-294	194	12	exist	exist	VERB
ijassa-294	194	13	min	min	PROPN
ijassa-294	194	14	{	{	PUNCT
ijassa-294	194	15	‖u0‖	‖u0‖	NOUN
ijassa-294	194	16	,	,	PUNCT
ijassa-294	194	17	m0b	m0b	NOUN
ijassa-294	194	18	p	p	NOUN
ijassa-294	194	19	2λa2c	2λa2c	NUM
ijassa-294	194	20	p	p	NOUN
ijassa-294	194	21	1	1	NUM
ijassa-294	194	22	}	}	PUNCT
ijassa-294	194	23	>	>	PUNCT
ijassa-294	194	24	ρ	ρ	PROPN
ijassa-294	194	25	>	>	X
ijassa-294	194	26	0	0	PROPN
ijassa-294	194	27	,	,	PUNCT
ijassa-294	194	28	γ	γ	X
ijassa-294	194	29	>	>	X
ijassa-294	194	30	0	0	NUM
ijassa-294	194	31	such	such	ADJ
ijassa-294	194	32	that	that	DET
ijassa-294	194	33	iλ(u	iλ(u	NUM
ijassa-294	194	34	)	)	PUNCT
ijassa-294	194	35	≥	≥	PROPN
ijassa-294	194	36	γ	γ	X
ijassa-294	194	37	>	>	X
ijassa-294	194	38	0	0	NUM
ijassa-294	194	39	for	for	ADP
ijassa-294	194	40	every	every	DET
ijassa-294	194	41	‖u‖	‖u‖	PROPN
ijassa-294	194	42	=	=	SYM
ijassa-294	194	43	ρ	ρ	PROPN
ijassa-294	194	44	,	,	PUNCT
ijassa-294	194	45	where	where	SCONJ
ijassa-294	194	46	u0	u0	PROPN
ijassa-294	194	47	comes	come	VERB
ijassa-294	194	48	from	from	ADP
ijassa-294	194	49	(	(	PUNCT
ijassa-294	194	50	10	10	NUM
ijassa-294	194	51	)	)	PUNCT
ijassa-294	194	52	.	.	PUNCT
ijassa-294	195	1	on	on	ADP
ijassa-294	195	2	the	the	DET
ijassa-294	195	3	other	other	ADJ
ijassa-294	195	4	hand	hand	NOUN
ijassa-294	195	5	,	,	PUNCT
ijassa-294	195	6	since	since	SCONJ
ijassa-294	195	7	iλ(0	iλ(0	NOUN
ijassa-294	195	8	)	)	PUNCT
ijassa-294	195	9	=	=	SYM
ijassa-294	195	10	0	0	NUM
ijassa-294	195	11	and	and	CCONJ
ijassa-294	195	12	from	from	ADP
ijassa-294	195	13	the	the	DET
ijassa-294	195	14	proof	proof	NOUN
ijassa-294	195	15	lemma	lemma	PROPN
ijassa-294	195	16	3.1	3.1	NUM
ijassa-294	195	17	,	,	PUNCT
ijassa-294	195	18	there	there	PRON
ijassa-294	195	19	exists	exist	VERB
ijassa-294	195	20	u0	u0	ADJ
ijassa-294	195	21	∈	∈	PROPN
ijassa-294	195	22	x	x	PUNCT
ijassa-294	195	23	such	such	ADJ
ijassa-294	195	24	that	that	SCONJ
ijassa-294	195	25	iλ(u0	iλ(u0	NOUN
ijassa-294	195	26	)	)	PUNCT
ijassa-294	195	27	<	<	X
ijassa-294	195	28	0	0	PUNCT
ijassa-294	195	29	and	and	CCONJ
ijassa-294	195	30	‖u0‖	‖u0‖	PROPN
ijassa-294	195	31	>	>	X
ijassa-294	195	32	ρ	ρ	PROPN
ijassa-294	195	33	.	.	PUNCT
ijassa-294	196	1	so	so	ADV
ijassa-294	196	2	from	from	ADP
ijassa-294	196	3	mountain	mountain	NOUN
ijassa-294	196	4	pass	pass	NOUN
ijassa-294	196	5	theorem	theorem	NOUN
ijassa-294	196	6	,	,	PUNCT
ijassa-294	196	7	iλ	iλ	PROPN
ijassa-294	196	8	has	have	VERB
ijassa-294	196	9	another	another	DET
ijassa-294	196	10	critical	critical	ADJ
ijassa-294	196	11	point	point	NOUN
ijassa-294	196	12	u2	u2	NOUN
ijassa-294	196	13	such	such	ADJ
ijassa-294	196	14	that	that	SCONJ
ijassa-294	196	15	iλ(u2	iλ(u2	PROPN
ijassa-294	196	16	)	)	PUNCT
ijassa-294	196	17	≥	≥	PROPN
ijassa-294	196	18	γ	γ	X
ijassa-294	196	19	>	>	X
ijassa-294	196	20	0	0	PUNCT
ijassa-294	196	21	>	>	X
ijassa-294	196	22	iλ(u1	iλ(u1	NOUN
ijassa-294	196	23	)	)	PUNCT
ijassa-294	196	24	.	.	PUNCT
ijassa-294	197	1	therefore	therefore	ADV
ijassa-294	197	2	,	,	PUNCT
ijassa-294	197	3	u2	u2	PROPN
ijassa-294	197	4	is	be	AUX
ijassa-294	197	5	another	another	DET
ijassa-294	197	6	positive	positive	ADJ
ijassa-294	197	7	solution	solution	NOUN
ijassa-294	197	8	of	of	ADP
ijassa-294	197	9	(	(	PUNCT
ijassa-294	197	10	1	1	NUM
ijassa-294	197	11	)	)	PUNCT
ijassa-294	197	12	.	.	PUNCT
ijassa-294	198	1	finally	finally	ADV
ijassa-294	198	2	we	we	PRON
ijassa-294	198	3	show	show	VERB
ijassa-294	198	4	that	that	SCONJ
ijassa-294	198	5	(	(	PUNCT
ijassa-294	198	6	1	1	X
ijassa-294	198	7	)	)	PUNCT
ijassa-294	198	8	has	have	VERB
ijassa-294	198	9	no	no	DET
ijassa-294	198	10	positive	positive	ADJ
ijassa-294	198	11	solution	solution	NOUN
ijassa-294	198	12	when	when	SCONJ
ijassa-294	198	13	λ	λ	PROPN
ijassa-294	198	14	is	be	AUX
ijassa-294	198	15	small	small	ADJ
ijassa-294	198	16	.	.	PUNCT
ijassa-294	199	1	we	we	PRON
ijassa-294	199	2	assume	assume	VERB
ijassa-294	199	3	(	(	PUNCT
ijassa-294	199	4	1	1	X
ijassa-294	199	5	)	)	PUNCT
ijassa-294	199	6	has	have	VERB
ijassa-294	199	7	a	a	DET
ijassa-294	199	8	positive	positive	ADJ
ijassa-294	199	9	solution	solution	NOUN
ijassa-294	199	10	u	u	NOUN
ijassa-294	199	11	,	,	PUNCT
ijassa-294	199	12	let	let	VERB
ijassa-294	199	13	(	(	PUNCT
ijassa-294	199	14	λ1	λ1	ADJ
ijassa-294	199	15	,	,	PUNCT
ijassa-294	199	16	ϕ1(x	ϕ1(x	NUM
ijassa-294	199	17	)	)	PUNCT
ijassa-294	199	18	)	)	PUNCT
ijassa-294	199	19	be	be	AUX
ijassa-294	199	20	the	the	DET
ijassa-294	199	21	principal	principal	ADJ
ijassa-294	199	22	eigen	eigen	NOUN
ijassa-294	199	23	-	-	PUNCT
ijassa-294	199	24	pair	pair	NOUN
ijassa-294	199	25	of	of	ADP
ijassa-294	199	26	the	the	DET
ijassa-294	199	27	problem	problem	NOUN
ijassa-294	199	28	{	{	PUNCT
ijassa-294	199	29	−∆φ	−∆φ	NOUN
ijassa-294	200	1	=	=	PRON
ijassa-294	200	2	λφ	λφ	ADP
ijassa-294	200	3	in	in	ADP
ijassa-294	200	4	ω	ω	NUM
ijassa-294	200	5	,	,	PUNCT
ijassa-294	200	6	u	u	NOUN
ijassa-294	200	7	=	=	NOUN
ijassa-294	200	8	0	0	NUM
ijassa-294	200	9	on	on	ADP
ijassa-294	200	10	∂ω	∂ω	PROPN
ijassa-294	200	11	,	,	PUNCT
ijassa-294	200	12	(	(	PUNCT
ijassa-294	200	13	11	11	NUM
ijassa-294	200	14	)	)	PUNCT
ijassa-294	200	15	such	such	ADJ
ijassa-294	200	16	that	that	PRON
ijassa-294	200	17	ϕ1(x	ϕ1(x	NOUN
ijassa-294	200	18	)	)	PUNCT
ijassa-294	200	19	>	>	X
ijassa-294	200	20	0	0	PUNCT
ijassa-294	201	1	in	in	ADP
ijassa-294	201	2	ω	ω	NUM
ijassa-294	201	3	.	.	PUNCT
ijassa-294	202	1	we	we	PRON
ijassa-294	202	2	rewrite	rewrite	VERB
ijassa-294	202	3	(	(	PUNCT
ijassa-294	202	4	1	1	NUM
ijassa-294	202	5	)	)	PUNCT
ijassa-294	202	6	as	as	ADP
ijassa-294	202	7	the	the	DET
ijassa-294	202	8	following	follow	VERB
ijassa-294	202	9	form	form	NOUN
ijassa-294	202	10	{	{	PUNCT
ijassa-294	202	11	−∆u	−∆u	NOUN
ijassa-294	202	12	=	=	PUNCT
ijassa-294	202	13	λ	λ	SYM
ijassa-294	202	14	f(x	f(x	PROPN
ijassa-294	202	15	,	,	PUNCT
ijassa-294	202	16	u	u	NOUN
ijassa-294	202	17	)	)	PUNCT
ijassa-294	202	18	m	m	PROPN
ijassa-294	202	19	(	(	PUNCT
ijassa-294	202	20	∫	∫	PROPN
ijassa-294	202	21	ω	ω	PROPN
ijassa-294	202	22	1	1	NUM
ijassa-294	202	23	2	2	NUM
ijassa-294	202	24	|∇u|2	|∇u|2	NOUN
ijassa-294	202	25	dx	dx	PROPN
ijassa-294	202	26	)	)	PUNCT
ijassa-294	202	27	in	in	ADP
ijassa-294	202	28	ω	ω	PROPN
ijassa-294	202	29	,	,	PUNCT
ijassa-294	202	30	u	u	NOUN
ijassa-294	202	31	=	=	NOUN
ijassa-294	202	32	0	0	NUM
ijassa-294	202	33	on	on	ADP
ijassa-294	202	34	∂ω	∂ω	PROPN
ijassa-294	202	35	.	.	PUNCT
ijassa-294	203	1	(	(	PUNCT
ijassa-294	203	2	12	12	NUM
ijassa-294	203	3	)	)	PUNCT
ijassa-294	203	4	multiplying	multiplying	NOUN
ijassa-294	203	5	(	(	PUNCT
ijassa-294	203	6	11	11	NUM
ijassa-294	203	7	)	)	PUNCT
ijassa-294	203	8	by	by	ADP
ijassa-294	203	9	u	u	PROPN
ijassa-294	203	10	,	,	PUNCT
ijassa-294	203	11	multiplying	multiply	VERB
ijassa-294	203	12	(	(	PUNCT
ijassa-294	203	13	12	12	NUM
ijassa-294	203	14	)	)	PUNCT
ijassa-294	203	15	by	by	ADP
ijassa-294	203	16	ϕ1	ϕ1	NOUN
ijassa-294	203	17	,	,	PUNCT
ijassa-294	203	18	subtracting	subtract	VERB
ijassa-294	203	19	and	and	CCONJ
ijassa-294	203	20	integrating	integrate	VERB
ijassa-294	203	21	in	in	ADP
ijassa-294	203	22	ω	ω	PROPN
ijassa-294	203	23	,	,	PUNCT
ijassa-294	203	24	we	we	PRON
ijassa-294	203	25	obtain	obtain	VERB
ijassa-294	203	26	0	0	NUM
ijassa-294	204	1	=	=	SYM
ijassa-294	204	2	∫	∫	PROPN
ijassa-294	204	3	ω	ω	PROPN
ijassa-294	204	4	[	[	PUNCT
ijassa-294	204	5	λ1uϕ1	λ1uϕ1	NOUN
ijassa-294	204	6	−	−	PROPN
ijassa-294	204	7	λϕ1	λϕ1	PROPN
ijassa-294	204	8	f(x	f(x	PROPN
ijassa-294	204	9	,	,	PUNCT
ijassa-294	204	10	u	u	NOUN
ijassa-294	204	11	)	)	PUNCT
ijassa-294	204	12	m	m	PROPN
ijassa-294	204	13	(	(	PUNCT
ijassa-294	204	14	t	t	PROPN
ijassa-294	204	15	)	)	PUNCT
ijassa-294	204	16	]	]	PUNCT
ijassa-294	205	1	dx	dx	PROPN
ijassa-294	206	1	=	=	SYM
ijassa-294	206	2	∫	∫	PROPN
ijassa-294	206	3	ω	ω	PROPN
ijassa-294	206	4	uϕ1	uϕ1	PROPN
ijassa-294	206	5	m	m	PROPN
ijassa-294	206	6	(	(	PUNCT
ijassa-294	206	7	t	t	PROPN
ijassa-294	206	8	)	)	PUNCT
ijassa-294	206	9	[	[	PUNCT
ijassa-294	206	10	m	m	PROPN
ijassa-294	206	11	(	(	PUNCT
ijassa-294	206	12	t	t	NOUN
ijassa-294	206	13	)	)	PUNCT
ijassa-294	206	14	λ1	λ1	PROPN
ijassa-294	206	15	−	−	PROPN
ijassa-294	206	16	λ	λ	PROPN
ijassa-294	206	17	f(x	f(x	PROPN
ijassa-294	206	18	,	,	PUNCT
ijassa-294	206	19	u	u	NOUN
ijassa-294	206	20	)	)	PUNCT
ijassa-294	206	21	u	u	NOUN
ijassa-294	206	22	]	]	X
ijassa-294	206	23	dx	dx	PROPN
ijassa-294	206	24	,	,	PUNCT
ijassa-294	206	25	(	(	PUNCT
ijassa-294	206	26	13	13	NUM
ijassa-294	206	27	)	)	PUNCT
ijassa-294	206	28	where	where	SCONJ
ijassa-294	206	29	t	t	NOUN
ijassa-294	206	30	=	=	SYM
ijassa-294	206	31	∫	∫	PROPN
ijassa-294	206	32	ω	ω	NUM
ijassa-294	206	33	1	1	NUM
ijassa-294	206	34	2	2	NUM
ijassa-294	206	35	|∇u|	|∇u|	ADJ
ijassa-294	206	36	2	2	NUM
ijassa-294	206	37	dx	dx	NOUN
ijassa-294	206	38	.	.	PUNCT
ijassa-294	207	1	if	if	SCONJ
ijassa-294	207	2	λ	λ	X
ijassa-294	207	3	<	<	X
ijassa-294	207	4	m0λ1	m0λ1	PROPN
ijassa-294	207	5	β	β	X
ijassa-294	207	6	,	,	PUNCT
ijassa-294	207	7	then	then	ADV
ijassa-294	207	8	by	by	ADP
ijassa-294	207	9	remark	remark	NOUN
ijassa-294	207	10	2.2	2.2	NUM
ijassa-294	207	11	,	,	PUNCT
ijassa-294	207	12	we	we	PRON
ijassa-294	207	13	have	have	VERB
ijassa-294	207	14	m	m	PROPN
ijassa-294	207	15	(	(	PUNCT
ijassa-294	207	16	t	t	PROPN
ijassa-294	207	17	)	)	PUNCT
ijassa-294	207	18	λ1	λ1	PROPN
ijassa-294	207	19	−	−	PROPN
ijassa-294	207	20	λ	λ	PROPN
ijassa-294	207	21	f(x	f(x	PROPN
ijassa-294	207	22	,	,	PUNCT
ijassa-294	207	23	u	u	NOUN
ijassa-294	207	24	)	)	PUNCT
ijassa-294	207	25	u	u	NOUN
ijassa-294	207	26	≥	≥	NOUN
ijassa-294	207	27	m0λ1	m0λ1	NUM
ijassa-294	207	28	−	−	NOUN
ijassa-294	207	29	λ	λ	PROPN
ijassa-294	207	30	f(x	f(x	PROPN
ijassa-294	207	31	,	,	PUNCT
ijassa-294	207	32	u	u	NOUN
ijassa-294	207	33	)	)	PUNCT
ijassa-294	207	34	u	u	NOUN
ijassa-294	207	35	>	>	X
ijassa-294	207	36	m0λ1	m0λ1	NOUN
ijassa-294	208	1	−	−	NOUN
ijassa-294	208	2	λβ	λβ	ADP
ijassa-294	208	3	>	>	X
ijassa-294	208	4	0	0	X
ijassa-294	208	5	.	.	PUNCT
ijassa-294	209	1	advances	advance	NOUN
ijassa-294	209	2	in	in	ADP
ijassa-294	209	3	systems	system	NOUN
ijassa-294	209	4	science	science	NOUN
ijassa-294	209	5	and	and	CCONJ
ijassa-294	209	6	applications	application	NOUN
ijassa-294	209	7	(	(	PUNCT
ijassa-294	209	8	2011	2011	NUM
ijassa-294	209	9	)	)	PUNCT
ijassa-294	209	10	,	,	PUNCT
ijassa-294	209	11	vol	vol	NOUN
ijassa-294	209	12	.	.	PROPN
ijassa-294	210	1	11	11	NUM
ijassa-294	210	2	,	,	PUNCT
ijassa-294	210	3	no	no	INTJ
ijassa-294	210	4	.	.	NOUN
ijassa-294	210	5	1	1	NUM
ijassa-294	210	6	-	-	SYM
ijassa-294	210	7	2	2	NUM
ijassa-294	210	8	89	89	NUM
ijassa-294	210	9	that	that	PRON
ijassa-294	210	10	is	be	AUX
ijassa-294	210	11	contrary	contrary	ADJ
ijassa-294	210	12	to	to	ADP
ijassa-294	210	13	(	(	PUNCT
ijassa-294	210	14	13	13	NUM
ijassa-294	210	15	)	)	PUNCT
ijassa-294	210	16	.	.	PUNCT
ijassa-294	211	1	so	so	ADV
ijassa-294	211	2	for	for	ADP
ijassa-294	211	3	small	small	ADJ
ijassa-294	211	4	λ	λ	NOUN
ijassa-294	211	5	,	,	PUNCT
ijassa-294	211	6	(	(	PUNCT
ijassa-294	211	7	1	1	X
ijassa-294	211	8	)	)	PUNCT
ijassa-294	211	9	has	have	VERB
ijassa-294	211	10	no	no	DET
ijassa-294	211	11	positive	positive	ADJ
ijassa-294	211	12	solution	solution	NOUN
ijassa-294	211	13	.	.	PUNCT
ijassa-294	212	1	proof	proof	NOUN
ijassa-294	212	2	of	of	ADP
ijassa-294	212	3	theorem	theorem	ADJ
ijassa-294	212	4	2.2	2.2	NUM
ijassa-294	212	5	.	.	PUNCT
ijassa-294	213	1	the	the	DET
ijassa-294	213	2	proof	proof	NOUN
ijassa-294	213	3	is	be	AUX
ijassa-294	213	4	similar	similar	ADJ
ijassa-294	213	5	to	to	ADP
ijassa-294	213	6	the	the	DET
ijassa-294	213	7	proof	proof	NOUN
ijassa-294	213	8	of	of	ADP
ijassa-294	213	9	[	[	X
ijassa-294	213	10	1	1	NUM
ijassa-294	213	11	]	]	PUNCT
ijassa-294	213	12	.	.	PUNCT
ijassa-294	214	1	for	for	ADP
ijassa-294	214	2	the	the	DET
ijassa-294	214	3	sake	sake	NOUN
ijassa-294	214	4	of	of	ADP
ijassa-294	214	5	completeness	completeness	NOUN
ijassa-294	214	6	,	,	PUNCT
ijassa-294	214	7	we	we	PRON
ijassa-294	214	8	include	include	VERB
ijassa-294	214	9	it	it	PRON
ijassa-294	214	10	here	here	ADV
ijassa-294	214	11	.	.	PUNCT
ijassa-294	215	1	if	if	SCONJ
ijassa-294	215	2	there	there	PRON
ijassa-294	215	3	exists	exist	VERB
ijassa-294	215	4	a	a	DET
ijassa-294	215	5	positive	positive	ADJ
ijassa-294	215	6	solution	solution	NOUN
ijassa-294	215	7	(	(	PUNCT
ijassa-294	215	8	λ	λ	NOUN
ijassa-294	215	9	,	,	PUNCT
ijassa-294	215	10	u∗	u∗	PROPN
ijassa-294	215	11	)	)	PUNCT
ijassa-294	215	12	for	for	ADP
ijassa-294	215	13	(	(	PUNCT
ijassa-294	215	14	1	1	NUM
ijassa-294	215	15	)	)	PUNCT
ijassa-294	215	16	,	,	PUNCT
ijassa-294	215	17	then	then	ADV
ijassa-294	215	18	u∗	u∗	ADV
ijassa-294	215	19	is	be	AUX
ijassa-294	215	20	a	a	DET
ijassa-294	215	21	subsolution	subsolution	NOUN
ijassa-294	215	22	of	of	ADP
ijassa-294	215	23	{	{	PUNCT
ijassa-294	215	24	m	m	PROPN
ijassa-294	215	25	(	(	PUNCT
ijassa-294	215	26	∫	∫	PROPN
ijassa-294	215	27	ω	ω	PROPN
ijassa-294	215	28	1	1	NUM
ijassa-294	215	29	2	2	NUM
ijassa-294	215	30	|∇u|	|∇u|	ADJ
ijassa-294	215	31	2	2	NUM
ijassa-294	215	32	dx	dx	PROPN
ijassa-294	215	33	)	)	PUNCT
ijassa-294	215	34	∆u+	∆u+	NOUN
ijassa-294	215	35	λf(u	λf(u	NUM
ijassa-294	215	36	)	)	PUNCT
ijassa-294	216	1	=	=	SYM
ijassa-294	216	2	0	0	NUM
ijassa-294	216	3	in	in	ADP
ijassa-294	216	4	ω	ω	PROPN
ijassa-294	216	5	,	,	PUNCT
ijassa-294	216	6	u	u	NOUN
ijassa-294	216	7	=	=	NOUN
ijassa-294	216	8	0	0	NUM
ijassa-294	216	9	on	on	ADP
ijassa-294	216	10	∂ω	∂ω	PROPN
ijassa-294	216	11	,	,	PUNCT
ijassa-294	216	12	(	(	PUNCT
ijassa-294	216	13	14	14	NUM
ijassa-294	216	14	)	)	PUNCT
ijassa-294	216	15	since	since	SCONJ
ijassa-294	216	16	m	m	PROPN
ijassa-294	216	17	(	(	PUNCT
ijassa-294	216	18	∫	∫	PROPN
ijassa-294	216	19	ω	ω	PROPN
ijassa-294	216	20	1	1	NUM
ijassa-294	216	21	2	2	NUM
ijassa-294	216	22	|∇u∗|	|∇u∗|	PROPN
ijassa-294	216	23	2	2	NUM
ijassa-294	216	24	dx	dx	PROPN
ijassa-294	216	25	)	)	PUNCT
ijassa-294	216	26	∆u∗	∆u∗	VERB
ijassa-294	216	27	+	+	SYM
ijassa-294	216	28	λf(u∗	λf(u∗	NUM
ijassa-294	216	29	)	)	PUNCT
ijassa-294	216	30	≥	≥	NUM
ijassa-294	216	31	m	m	PROPN
ijassa-294	216	32	(	(	PUNCT
ijassa-294	216	33	∫	∫	PROPN
ijassa-294	216	34	ω	ω	PROPN
ijassa-294	216	35	1	1	NUM
ijassa-294	216	36	2	2	NUM
ijassa-294	216	37	|∇u∗|	|∇u∗|	PROPN
ijassa-294	216	38	2	2	NUM
ijassa-294	216	39	dx	dx	PROPN
ijassa-294	216	40	)	)	PUNCT
ijassa-294	216	41	∆u∗	∆u∗	PROPN
ijassa-294	216	42	+	+	SYM
ijassa-294	216	43	λf(x	λf(x	NUM
ijassa-294	216	44	,	,	PUNCT
ijassa-294	216	45	u∗	u∗	PROPN
ijassa-294	216	46	)	)	PUNCT
ijassa-294	216	47	.	.	PUNCT
ijassa-294	217	1	and	and	CCONJ
ijassa-294	217	2	c	c	PROPN
ijassa-294	217	3	is	be	AUX
ijassa-294	217	4	supersolution	supersolution	NOUN
ijassa-294	217	5	of	of	ADP
ijassa-294	217	6	(	(	PUNCT
ijassa-294	217	7	13	13	NUM
ijassa-294	217	8	)	)	PUNCT
ijassa-294	217	9	.	.	PUNCT
ijassa-294	218	1	so	so	ADV
ijassa-294	218	2	by	by	ADP
ijassa-294	218	3	the	the	DET
ijassa-294	218	4	standard	standard	ADJ
ijassa-294	218	5	comparison	comparison	NOUN
ijassa-294	218	6	arguments	argument	NOUN
ijassa-294	218	7	,	,	PUNCT
ijassa-294	218	8	(	(	PUNCT
ijassa-294	218	9	13	13	NUM
ijassa-294	218	10	)	)	PUNCT
ijassa-294	218	11	has	have	VERB
ijassa-294	218	12	a	a	DET
ijassa-294	218	13	positive	positive	ADJ
ijassa-294	218	14	solution	solution	NOUN
ijassa-294	218	15	u	u	PRON
ijassa-294	218	16	such	such	ADJ
ijassa-294	218	17	that	that	DET
ijassa-294	218	18	u∗	u∗	PROPN
ijassa-294	218	19	≤	≤	NUM
ijassa-294	218	20	u	u	PROPN
ijassa-294	218	21	≤	≤	ADJ
ijassa-294	218	22	c.	c.	NOUN
ijassa-294	219	1	but	but	CCONJ
ijassa-294	219	2	if	if	SCONJ
ijassa-294	219	3	we	we	PRON
ijassa-294	219	4	let	let	VERB
ijassa-294	219	5	s0	s0	PROPN
ijassa-294	219	6	=	=	SYM
ijassa-294	219	7	0	0	NUM
ijassa-294	219	8	,	,	PUNCT
ijassa-294	219	9	s1	s1	PROPN
ijassa-294	219	10	=	=	SYM
ijassa-294	219	11	b	b	PROPN
ijassa-294	219	12	and	and	CCONJ
ijassa-294	219	13	s2	s2	PROPN
ijassa-294	220	1	=	=	SYM
ijassa-294	220	2	c	c	X
ijassa-294	220	3	,	,	PUNCT
ijassa-294	220	4	f	f	PROPN
ijassa-294	220	5	satisfies	satisfie	NOUN
ijassa-294	220	6	(	(	PUNCT
ijassa-294	220	7	6	6	NUM
ijassa-294	220	8	)	)	PUNCT
ijassa-294	220	9	and	and	CCONJ
ijassa-294	220	10	(	(	PUNCT
ijassa-294	220	11	7	7	NUM
ijassa-294	220	12	)	)	PUNCT
ijassa-294	220	13	,	,	PUNCT
ijassa-294	220	14	then	then	ADV
ijassa-294	220	15	by	by	ADP
ijassa-294	220	16	lemma	lemma	PROPN
ijassa-294	220	17	2.2	2.2	NUM
ijassa-294	220	18	,	,	PUNCT
ijassa-294	220	19	(	(	PUNCT
ijassa-294	220	20	13	13	NUM
ijassa-294	220	21	)	)	PUNCT
ijassa-294	220	22	has	have	VERB
ijassa-294	220	23	no	no	DET
ijassa-294	220	24	positive	positive	ADJ
ijassa-294	220	25	solution	solution	NOUN
ijassa-294	220	26	.	.	PUNCT
ijassa-294	221	1	this	this	PRON
ijassa-294	221	2	is	be	AUX
ijassa-294	221	3	a	a	DET
ijassa-294	221	4	contradiction	contradiction	NOUN
ijassa-294	221	5	.	.	PUNCT
ijassa-294	222	1	so	so	ADV
ijassa-294	222	2	(	(	PUNCT
ijassa-294	222	3	1	1	X
ijassa-294	222	4	)	)	PUNCT
ijassa-294	222	5	has	have	VERB
ijassa-294	222	6	no	no	DET
ijassa-294	222	7	positive	positive	ADJ
ijassa-294	222	8	solution	solution	NOUN
ijassa-294	222	9	if	if	SCONJ
ijassa-294	222	10	∫	∫	PROPN
ijassa-294	222	11	c	c	PROPN
ijassa-294	222	12	0	0	NUM
ijassa-294	222	13	f(u	f(u	PROPN
ijassa-294	222	14	)	)	PUNCT
ijassa-294	222	15	du	du	PROPN
ijassa-294	222	16	≤	≤	NUM
ijassa-294	222	17	0	0	NUM
ijassa-294	222	18	.	.	PUNCT
ijassa-294	223	1	4	4	NUM
ijassa-294	223	2	.	.	X
ijassa-294	223	3	proof	proof	NOUN
ijassa-294	223	4	of	of	ADP
ijassa-294	223	5	a	a	DET
ijassa-294	223	6	conjecture	conjecture	NOUN
ijassa-294	223	7	and	and	CCONJ
ijassa-294	223	8	some	some	DET
ijassa-294	223	9	examples	example	NOUN
ijassa-294	223	10	in	in	ADP
ijassa-294	223	11	this	this	DET
ijassa-294	223	12	section	section	NOUN
ijassa-294	223	13	we	we	PRON
ijassa-294	223	14	will	will	AUX
ijassa-294	223	15	prove	prove	VERB
ijassa-294	223	16	the	the	DET
ijassa-294	223	17	conjecture	conjecture	NOUN
ijassa-294	223	18	of	of	ADP
ijassa-294	223	19	liu	liu	PROPN
ijassa-294	223	20	,	,	PUNCT
ijassa-294	223	21	wang	wang	PROPN
ijassa-294	223	22	and	and	CCONJ
ijassa-294	223	23	shi	shi	PROPN
ijassa-294	223	24	’s	’s	PART
ijassa-294	223	25	and	and	CCONJ
ijassa-294	223	26	give	give	VERB
ijassa-294	223	27	some	some	DET
ijassa-294	223	28	typical	typical	ADJ
ijassa-294	223	29	consequences	consequence	NOUN
ijassa-294	223	30	of	of	ADP
ijassa-294	223	31	theorem	theorem	ADJ
ijassa-294	223	32	2.1	2.1	NUM
ijassa-294	223	33	to	to	PART
ijassa-294	223	34	theorem	theorem	VERB
ijassa-294	223	35	2.2	2.2	NUM
ijassa-294	223	36	.	.	PUNCT
ijassa-294	224	1	in	in	ADP
ijassa-294	224	2	[	[	X
ijassa-294	224	3	1	1	NUM
ijassa-294	224	4	]	]	PUNCT
ijassa-294	224	5	,	,	PUNCT
ijassa-294	224	6	liu	liu	PROPN
ijassa-294	224	7	,	,	PUNCT
ijassa-294	224	8	wang	wang	PROPN
ijassa-294	224	9	and	and	CCONJ
ijassa-294	224	10	shi	shi	PROPN
ijassa-294	224	11	conjecture	conjecture	VERB
ijassa-294	224	12	that	that	SCONJ
ijassa-294	224	13	the	the	DET
ijassa-294	224	14	nonexistence	nonexistence	NOUN
ijassa-294	224	15	holds	hold	VERB
ijassa-294	224	16	with	with	ADP
ijassa-294	224	17	a	a	DET
ijassa-294	224	18	weaker	weak	ADJ
ijassa-294	224	19	condition:∫	condition:∫	NOUN
ijassa-294	224	20	c(x	c(x	NOUN
ijassa-294	224	21	)	)	PUNCT
ijassa-294	224	22	0	0	PUNCT
ijassa-294	225	1	f(x	f(x	PROPN
ijassa-294	225	2	,	,	PUNCT
ijassa-294	225	3	s	s	X
ijassa-294	225	4	)	)	PUNCT
ijassa-294	225	5	ds	ds	ADJ
ijassa-294	225	6	≤	≤	NOUN
ijassa-294	225	7	0	0	NUM
ijassa-294	225	8	for	for	ADP
ijassa-294	225	9	any	any	DET
ijassa-294	225	10	x	x	SYM
ijassa-294	225	11	∈	∈	PROPN
ijassa-294	225	12	ω	ω	PROPN
ijassa-294	225	13	.	.	PUNCT
ijassa-294	225	14	(	(	PUNCT
ijassa-294	225	15	15	15	NUM
ijassa-294	225	16	)	)	PUNCT
ijassa-294	225	17	in	in	ADP
ijassa-294	225	18	fact	fact	NOUN
ijassa-294	225	19	,	,	PUNCT
ijassa-294	225	20	as	as	SCONJ
ijassa-294	225	21	we	we	PRON
ijassa-294	225	22	will	will	AUX
ijassa-294	225	23	see	see	VERB
ijassa-294	225	24	in	in	ADP
ijassa-294	225	25	the	the	DET
ijassa-294	225	26	following	follow	VERB
ijassa-294	225	27	proposition	proposition	NOUN
ijassa-294	225	28	,	,	PUNCT
ijassa-294	225	29	the	the	DET
ijassa-294	225	30	condition	condition	NOUN
ijassa-294	225	31	(	(	PUNCT
ijassa-294	225	32	15	15	NUM
ijassa-294	225	33	)	)	PUNCT
ijassa-294	225	34	is	be	AUX
ijassa-294	225	35	more	more	ADV
ijassa-294	225	36	strong	strong	ADJ
ijassa-294	225	37	than∫	than∫	NOUN
ijassa-294	226	1	c	c	NOUN
ijassa-294	226	2	0	0	NUM
ijassa-294	226	3	f(s	f(	NOUN
ijassa-294	226	4	)	)	PUNCT
ijassa-294	226	5	ds	ds	ADJ
ijassa-294	226	6	≤	≤	NUM
ijassa-294	226	7	0	0	NUM
ijassa-294	226	8	.	.	PUNCT
ijassa-294	227	1	therefore	therefore	ADV
ijassa-294	227	2	,	,	PUNCT
ijassa-294	227	3	by	by	ADP
ijassa-294	227	4	theorem	theorem	NOUN
ijassa-294	227	5	2.2	2.2	NUM
ijassa-294	227	6	,	,	PUNCT
ijassa-294	227	7	the	the	DET
ijassa-294	227	8	conjecture	conjecture	NOUN
ijassa-294	227	9	is	be	AUX
ijassa-294	227	10	right	right	ADJ
ijassa-294	227	11	.	.	PUNCT
ijassa-294	228	1	proposition	proposition	NOUN
ijassa-294	228	2	4.1	4.1	NUM
ijassa-294	228	3	.	.	PUNCT
ijassa-294	229	1	if	if	SCONJ
ijassa-294	229	2	f(x	f(x	PROPN
ijassa-294	229	3	,	,	PUNCT
ijassa-294	229	4	u	u	NOUN
ijassa-294	229	5	)	)	PUNCT
ijassa-294	229	6	satisfies	satisfie	NOUN
ijassa-294	229	7	(	(	PUNCT
ijassa-294	229	8	f1)–(f3	f1)–(f3	NOUN
ijassa-294	229	9	)	)	PUNCT
ijassa-294	229	10	and	and	CCONJ
ijassa-294	229	11	∫	∫	PROPN
ijassa-294	229	12	c(x	c(x	NOUN
ijassa-294	229	13	)	)	PUNCT
ijassa-294	229	14	0	0	PUNCT
ijassa-294	230	1	f(x	f(x	PROPN
ijassa-294	230	2	,	,	PUNCT
ijassa-294	230	3	s	s	X
ijassa-294	230	4	)	)	PUNCT
ijassa-294	230	5	ds	ds	ADJ
ijassa-294	230	6	≤	≤	NOUN
ijassa-294	230	7	0	0	NUM
ijassa-294	230	8	for	for	ADP
ijassa-294	230	9	any	any	DET
ijassa-294	230	10	x	x	SYM
ijassa-294	230	11	∈	∈	PROPN
ijassa-294	230	12	ω	ω	NOUN
ijassa-294	230	13	,	,	PUNCT
ijassa-294	230	14	we	we	PRON
ijassa-294	230	15	have	have	VERB
ijassa-294	230	16	∫	∫	PROPN
ijassa-294	230	17	c	c	PROPN
ijassa-294	230	18	0	0	NUM
ijassa-294	230	19	f(s	f(	NOUN
ijassa-294	230	20	)	)	PUNCT
ijassa-294	231	1	ds	ds	ADJ
ijassa-294	231	2	≤	≤	NUM
ijassa-294	231	3	0	0	NUM
ijassa-294	231	4	.	.	PUNCT
ijassa-294	232	1	proof	proof	NOUN
ijassa-294	232	2	.	.	PUNCT
ijassa-294	233	1	from	from	ADP
ijassa-294	233	2	(	(	PUNCT
ijassa-294	233	3	f1)–(f3	f1)–(f3	NOUN
ijassa-294	233	4	)	)	PUNCT
ijassa-294	233	5	,	,	PUNCT
ijassa-294	233	6	we	we	PRON
ijassa-294	233	7	can	can	AUX
ijassa-294	233	8	easily	easily	ADV
ijassa-294	233	9	see	see	VERB
ijassa-294	233	10	that	that	SCONJ
ijassa-294	233	11	f(x	f(x	PROPN
ijassa-294	233	12	,	,	PUNCT
ijassa-294	233	13	s	s	NOUN
ijassa-294	233	14	)	)	PUNCT
ijassa-294	233	15	≤	≤	NOUN
ijassa-294	233	16	0	0	PUNCT
ijassa-294	233	17	when	when	SCONJ
ijassa-294	233	18	s	s	VERB
ijassa-294	233	19	∈	∈	PROPN
ijassa-294	233	20	[	[	X
ijassa-294	233	21	c(x	c(x	NOUN
ijassa-294	233	22	)	)	PUNCT
ijassa-294	233	23	,	,	PUNCT
ijassa-294	233	24	c	c	NOUN
ijassa-294	233	25	]	]	PUNCT
ijassa-294	233	26	.	.	PUNCT
ijassa-294	234	1	thus	thus	ADV
ijassa-294	234	2	,	,	PUNCT
ijassa-294	234	3	we	we	PRON
ijassa-294	234	4	have	have	VERB
ijassa-294	234	5	∫	∫	PROPN
ijassa-294	234	6	c	c	PROPN
ijassa-294	234	7	c(x	c(x	PROPN
ijassa-294	234	8	)	)	PUNCT
ijassa-294	234	9	f(x	f(x	PROPN
ijassa-294	234	10	,	,	PUNCT
ijassa-294	234	11	s	s	X
ijassa-294	234	12	)	)	PUNCT
ijassa-294	234	13	ds	ds	ADJ
ijassa-294	234	14	≤	≤	NOUN
ijassa-294	234	15	0	0	NUM
ijassa-294	234	16	.	.	PUNCT
ijassa-294	235	1	then	then	ADV
ijassa-294	235	2	,	,	PUNCT
ijassa-294	235	3	for	for	ADP
ijassa-294	235	4	any	any	DET
ijassa-294	235	5	x	x	SYM
ijassa-294	235	6	∈	∈	PROPN
ijassa-294	235	7	ω	ω	NOUN
ijassa-294	235	8	,	,	PUNCT
ijassa-294	235	9	we	we	PRON
ijassa-294	235	10	have	have	VERB
ijassa-294	235	11	0	0	NUM
ijassa-294	235	12	≥	≥	NUM
ijassa-294	235	13	∫	∫	PROPN
ijassa-294	235	14	c(x	c(x	NOUN
ijassa-294	235	15	)	)	PUNCT
ijassa-294	235	16	0	0	PUNCT
ijassa-294	236	1	f(x	f(x	PROPN
ijassa-294	236	2	,	,	PUNCT
ijassa-294	236	3	s	s	X
ijassa-294	236	4	)	)	PUNCT
ijassa-294	236	5	ds	ds	PROPN
ijassa-294	236	6	=	=	SYM
ijassa-294	236	7	∫	∫	PROPN
ijassa-294	236	8	c	c	NOUN
ijassa-294	236	9	0	0	PUNCT
ijassa-294	236	10	f(x	f(x	PROPN
ijassa-294	236	11	,	,	PUNCT
ijassa-294	236	12	s	s	AUX
ijassa-294	236	13	)	)	PUNCT
ijassa-294	236	14	ds−	ds−	PROPN
ijassa-294	236	15	∫	∫	PROPN
ijassa-294	236	16	c	c	PROPN
ijassa-294	236	17	c(x	c(x	PROPN
ijassa-294	236	18	)	)	PUNCT
ijassa-294	236	19	f(x	f(x	PROPN
ijassa-294	236	20	,	,	PUNCT
ijassa-294	236	21	s	s	X
ijassa-294	236	22	)	)	PUNCT
ijassa-294	236	23	ds	ds	ADJ
ijassa-294	236	24	≥	≥	NUM
ijassa-294	236	25	∫	∫	PROPN
ijassa-294	236	26	c	c	PROPN
ijassa-294	236	27	0	0	NUM
ijassa-294	237	1	f(x	f(x	PROPN
ijassa-294	237	2	,	,	PUNCT
ijassa-294	237	3	s	s	NOUN
ijassa-294	237	4	)	)	PUNCT
ijassa-294	237	5	ds	ds	NOUN
ijassa-294	237	6	.	.	PROPN
ijassa-294	238	1	in	in	ADP
ijassa-294	238	2	particular	particular	ADJ
ijassa-294	238	3	,	,	PUNCT
ijassa-294	238	4	∫	∫	PROPN
ijassa-294	238	5	c	c	PROPN
ijassa-294	238	6	0	0	NUM
ijassa-294	238	7	f(s	f(	NOUN
ijassa-294	238	8	)	)	PUNCT
ijassa-294	238	9	ds	ds	ADJ
ijassa-294	238	10	≤	≤	NOUN
ijassa-294	238	11	0	0	NUM
ijassa-294	238	12	.	.	PUNCT
ijassa-294	239	1	now	now	ADV
ijassa-294	239	2	,	,	PUNCT
ijassa-294	239	3	we	we	PRON
ijassa-294	239	4	give	give	VERB
ijassa-294	239	5	some	some	DET
ijassa-294	239	6	examples	example	NOUN
ijassa-294	239	7	which	which	PRON
ijassa-294	239	8	satisfy	satisfy	VERB
ijassa-294	239	9	our	our	PRON
ijassa-294	239	10	hypotheses	hypothesis	NOUN
ijassa-294	239	11	.	.	PUNCT
ijassa-294	240	1	example	example	NOUN
ijassa-294	240	2	4.1	4.1	NUM
ijassa-294	240	3	.	.	PUNCT
ijassa-294	241	1	let	let	VERB
ijassa-294	241	2	m(t	m(t	NOUN
ijassa-294	241	3	)	)	PUNCT
ijassa-294	241	4	=	=	PUNCT
ijassa-294	242	1	a	a	DET
ijassa-294	242	2	+	+	X
ijassa-294	242	3	bt	bt	NOUN
ijassa-294	242	4	with	with	ADP
ijassa-294	242	5	t	t	PROPN
ijassa-294	242	6	=	=	SYM
ijassa-294	242	7	∫	∫	PROPN
ijassa-294	242	8	ω	ω	NUM
ijassa-294	242	9	1	1	NUM
ijassa-294	242	10	2	2	NUM
ijassa-294	242	11	|∇u|	|∇u|	ADJ
ijassa-294	242	12	2	2	NUM
ijassa-294	242	13	dx	dx	NOUN
ijassa-294	242	14	,	,	PUNCT
ijassa-294	242	15	here	here	ADV
ijassa-294	242	16	a	a	PRON
ijassa-294	242	17	,	,	PUNCT
ijassa-294	242	18	b	b	NOUN
ijassa-294	242	19	are	be	AUX
ijassa-294	242	20	two	two	NUM
ijassa-294	242	21	positive	positive	ADJ
ijassa-294	242	22	constants	constant	NOUN
ijassa-294	242	23	and	and	CCONJ
ijassa-294	242	24	f(x	f(x	PROPN
ijassa-294	242	25	,	,	PUNCT
ijassa-294	242	26	u	u	NOUN
ijassa-294	242	27	)	)	PUNCT
ijassa-294	242	28	=	=	SYM
ijassa-294	242	29	u(u	u(u	ADP
ijassa-294	242	30	−	−	NOUN
ijassa-294	242	31	b(x))(c(x	b(x))(c(x	NOUN
ijassa-294	242	32	)	)	PUNCT
ijassa-294	242	33	−	−	PROPN
ijassa-294	242	34	u	u	NOUN
ijassa-294	242	35	)	)	PUNCT
ijassa-294	242	36	with	with	ADP
ijassa-294	242	37	b(x	b(x	NOUN
ijassa-294	242	38	)	)	PUNCT
ijassa-294	242	39	∈	∈	PROPN
ijassa-294	242	40	c(ω	c(ω	PROPN
ijassa-294	242	41	)	)	PUNCT
ijassa-294	242	42	,	,	PUNCT
ijassa-294	242	43	c(x	c(x	NOUN
ijassa-294	242	44	)	)	PUNCT
ijassa-294	242	45	∈	∈	PROPN
ijassa-294	242	46	c1(ω	c1(ω	NOUN
ijassa-294	242	47	)	)	PUNCT
ijassa-294	243	1	such	such	ADJ
ijassa-294	243	2	that	that	SCONJ
ijassa-294	243	3	0	0	NUM
ijassa-294	243	4	<	<	X
ijassa-294	243	5	b(x	b(x	NOUN
ijassa-294	243	6	)	)	PUNCT
ijassa-294	243	7	<	<	X
ijassa-294	243	8	c(x	c(x	NOUN
ijassa-294	243	9	)	)	PUNCT
ijassa-294	243	10	for	for	ADP
ijassa-294	243	11	any	any	DET
ijassa-294	243	12	x	x	SYM
ijassa-294	243	13	∈	∈	PROPN
ijassa-294	243	14	ω	ω	NOUN
ijassa-294	243	15	.	.	PUNCT
ijassa-294	244	1	it	it	PRON
ijassa-294	244	2	is	be	AUX
ijassa-294	244	3	clear	clear	ADJ
ijassa-294	244	4	that	that	SCONJ
ijassa-294	244	5	m(t	m(t	PROPN
ijassa-294	244	6	)	)	PUNCT
ijassa-294	244	7	and	and	CCONJ
ijassa-294	244	8	f(x	f(x	PROPN
ijassa-294	244	9	,	,	PUNCT
ijassa-294	244	10	u	u	NOUN
ijassa-294	244	11	)	)	PUNCT
ijassa-294	244	12	verify	verify	VERB
ijassa-294	244	13	our	our	PRON
ijassa-294	244	14	assumptions	assumption	NOUN
ijassa-294	244	15	(	(	PUNCT
ijassa-294	244	16	m	m	NOUN
ijassa-294	244	17	)	)	PUNCT
ijassa-294	244	18	and	and	CCONJ
ijassa-294	244	19	(	(	PUNCT
ijassa-294	244	20	f1)–(f3	f1)–(f3	NOUN
ijassa-294	244	21	)	)	PUNCT
ijassa-294	244	22	.	.	PUNCT
ijassa-294	245	1	example	example	NOUN
ijassa-294	246	1	4.2	4.2	NUM
ijassa-294	246	2	.	.	PUNCT
ijassa-294	247	1	we	we	PRON
ijassa-294	247	2	consider	consider	VERB
ijassa-294	247	3	a	a	DET
ijassa-294	247	4	special	special	ADJ
ijassa-294	247	5	case	case	NOUN
ijassa-294	247	6	of	of	ADP
ijassa-294	247	7	example	example	NOUN
ijassa-294	247	8	4.1	4.1	NUM
ijassa-294	247	9	:	:	PUNCT
ijassa-294	247	10	{	{	PUNCT
ijassa-294	247	11	∆u+	∆u+	NOUN
ijassa-294	247	12	λu(u−	λu(u−	PUNCT
ijassa-294	247	13	b(x))(c(x)−	b(x))(c(x)−	PROPN
ijassa-294	247	14	u	u	NOUN
ijassa-294	247	15	)	)	PUNCT
ijassa-294	247	16	=	=	SYM
ijassa-294	247	17	0	0	NUM
ijassa-294	247	18	in	in	ADP
ijassa-294	247	19	ω	ω	PROPN
ijassa-294	247	20	,	,	PUNCT
ijassa-294	247	21	u	u	NOUN
ijassa-294	247	22	=	=	NOUN
ijassa-294	247	23	0	0	NUM
ijassa-294	247	24	on	on	ADP
ijassa-294	247	25	∂ω	∂ω	PROPN
ijassa-294	247	26	,	,	PUNCT
ijassa-294	247	27	(	(	PUNCT
ijassa-294	247	28	16	16	NUM
ijassa-294	247	29	)	)	PUNCT
ijassa-294	247	30	90	90	NUM
ijassa-294	247	31	ma	ma	NOUN
ijassa-294	247	32	:	:	PUNCT
ijassa-294	247	33	existence	existence	NOUN
ijassa-294	247	34	and	and	CCONJ
ijassa-294	247	35	nonexistence	nonexistence	NOUN
ijassa-294	247	36	of	of	ADP
ijassa-294	247	37	positive	positive	ADJ
ijassa-294	247	38	solutions	solution	NOUN
ijassa-294	247	39	for	for	ADP
ijassa-294	247	40	a	a	DET
ijassa-294	247	41	kirchhoff	kirchhoff	NOUN
ijassa-294	247	42	-	-	PUNCT
ijassa-294	247	43	type	type	NOUN
ijassa-294	247	44	.	.	PUNCT
ijassa-294	247	45	.	.	PUNCT
ijassa-294	247	46	.	.	PUNCT
ijassa-294	247	47	.	.	PUNCT
ijassa-294	247	48	.	.	PUNCT
ijassa-294	247	49	.	.	PUNCT
ijassa-294	248	1	where	where	SCONJ
ijassa-294	248	2	b(x	b(x	NOUN
ijassa-294	248	3	)	)	PUNCT
ijassa-294	248	4	∈	∈	PROPN
ijassa-294	248	5	c(ω	c(ω	PROPN
ijassa-294	248	6	)	)	PUNCT
ijassa-294	248	7	,	,	PUNCT
ijassa-294	248	8	c(x	c(x	NOUN
ijassa-294	248	9	)	)	PUNCT
ijassa-294	248	10	∈	∈	PROPN
ijassa-294	248	11	c1(ω	c1(ω	NOUN
ijassa-294	248	12	)	)	PUNCT
ijassa-294	248	13	such	such	ADJ
ijassa-294	248	14	that	that	SCONJ
ijassa-294	248	15	0	0	NUM
ijassa-294	248	16	<	<	X
ijassa-294	248	17	b(x	b(x	NOUN
ijassa-294	248	18	)	)	PUNCT
ijassa-294	248	19	<	<	X
ijassa-294	248	20	c(x	c(x	NOUN
ijassa-294	248	21	)	)	PUNCT
ijassa-294	248	22	for	for	ADP
ijassa-294	248	23	any	any	DET
ijassa-294	248	24	x	x	SYM
ijassa-294	248	25	∈	∈	PROPN
ijassa-294	248	26	ω	ω	NOUN
ijassa-294	248	27	.	.	PUNCT
ijassa-294	249	1	we	we	PRON
ijassa-294	249	2	have	have	AUX
ijassa-294	249	3	known	know	VERB
ijassa-294	249	4	that	that	SCONJ
ijassa-294	249	5	f(x	f(x	PROPN
ijassa-294	249	6	,	,	PUNCT
ijassa-294	249	7	u	u	NOUN
ijassa-294	249	8	)	)	PUNCT
ijassa-294	249	9	satisfies	satisfie	NOUN
ijassa-294	249	10	(	(	PUNCT
ijassa-294	249	11	f1)–(f3	f1)–(f3	NOUN
ijassa-294	249	12	)	)	PUNCT
ijassa-294	249	13	from	from	ADP
ijassa-294	249	14	example	example	NOUN
ijassa-294	249	15	4.1	4.1	NUM
ijassa-294	249	16	.	.	PUNCT
ijassa-294	250	1	moreover	moreover	ADV
ijassa-294	250	2	,	,	PUNCT
ijassa-294	250	3	we	we	PRON
ijassa-294	250	4	have∫	have∫	VERB
ijassa-294	250	5	c(x	c(x	NOUN
ijassa-294	250	6	)	)	PUNCT
ijassa-294	250	7	0	0	PUNCT
ijassa-294	251	1	f(x	f(x	PROPN
ijassa-294	251	2	,	,	PUNCT
ijassa-294	251	3	s	s	X
ijassa-294	251	4	)	)	PUNCT
ijassa-294	251	5	ds	ds	ADJ
ijassa-294	251	6	=	=	PUNCT
ijassa-294	251	7	∫	∫	PROPN
ijassa-294	251	8	c(x	c(x	NOUN
ijassa-294	251	9	)	)	PUNCT
ijassa-294	251	10	0	0	PUNCT
ijassa-294	252	1	s(s−	s(s−	ADV
ijassa-294	252	2	b(x))(c(x)−	b(x))(c(x)−	PROPN
ijassa-294	252	3	s	s	X
ijassa-294	252	4	)	)	PUNCT
ijassa-294	252	5	ds	ds	NOUN
ijassa-294	252	6	=	=	SYM
ijassa-294	252	7	1	1	NUM
ijassa-294	252	8	12	12	NUM
ijassa-294	253	1	[	[	X
ijassa-294	253	2	c(x)]3(c(x)−	c(x)]3(c(x)−	PROPN
ijassa-294	253	3	2b(x	2b(x	NUM
ijassa-294	253	4	)	)	PUNCT
ijassa-294	253	5	)	)	PUNCT
ijassa-294	253	6	.	.	PUNCT
ijassa-294	254	1	then	then	ADV
ijassa-294	254	2	by	by	ADP
ijassa-294	254	3	theorem	theorem	NOUN
ijassa-294	254	4	2.1	2.1	NUM
ijassa-294	254	5	,	,	PUNCT
ijassa-294	254	6	if	if	SCONJ
ijassa-294	254	7	there	there	PRON
ijassa-294	254	8	exists	exist	VERB
ijassa-294	254	9	an	an	DET
ijassa-294	254	10	open	open	ADJ
ijassa-294	254	11	subset	subset	NOUN
ijassa-294	254	12	ω1	ω1	PROPN
ijassa-294	254	13	⊂	⊂	PROPN
ijassa-294	254	14	ω	ω	PROPN
ijassa-294	254	15	,	,	PUNCT
ijassa-294	254	16	such	such	ADJ
ijassa-294	254	17	that	that	DET
ijassa-294	254	18	c(x	c(x	NOUN
ijassa-294	254	19	)	)	PUNCT
ijassa-294	254	20	>	>	X
ijassa-294	254	21	2b(x	2b(x	NUM
ijassa-294	254	22	)	)	PUNCT
ijassa-294	254	23	in	in	ADP
ijassa-294	254	24	ω1	ω1	PROPN
ijassa-294	254	25	,	,	PUNCT
ijassa-294	254	26	then	then	ADV
ijassa-294	254	27	(	(	PUNCT
ijassa-294	254	28	16	16	NUM
ijassa-294	254	29	)	)	PUNCT
ijassa-294	254	30	has	have	VERB
ijassa-294	254	31	at	at	ADV
ijassa-294	254	32	least	least	ADV
ijassa-294	254	33	two	two	NUM
ijassa-294	254	34	positive	positive	ADJ
ijassa-294	254	35	solutions	solution	NOUN
ijassa-294	254	36	for	for	ADP
ijassa-294	254	37	large	large	ADJ
ijassa-294	254	38	λ	λ	NOUN
ijassa-294	254	39	.	.	PUNCT
ijassa-294	255	1	if	if	SCONJ
ijassa-294	255	2	c(x	c(x	NOUN
ijassa-294	255	3	)	)	PUNCT
ijassa-294	255	4	≡	≡	PROPN
ijassa-294	255	5	1	1	NUM
ijassa-294	255	6	for	for	ADP
ijassa-294	255	7	all	all	DET
ijassa-294	255	8	x	x	SYM
ijassa-294	255	9	∈	∈	PROPN
ijassa-294	255	10	ω	ω	NOUN
ijassa-294	255	11	,	,	PUNCT
ijassa-294	255	12	we	we	PRON
ijassa-294	255	13	obtain∫	obtain∫	VERB
ijassa-294	255	14	1	1	NUM
ijassa-294	255	15	0	0	NUM
ijassa-294	255	16	f(s	f(	NOUN
ijassa-294	255	17	)	)	PUNCT
ijassa-294	255	18	ds	ds	NOUN
ijassa-294	255	19	=	=	SYM
ijassa-294	255	20	∫	∫	PROPN
ijassa-294	255	21	1	1	NUM
ijassa-294	255	22	0	0	NUM
ijassa-294	255	23	max	max	PROPN
ijassa-294	255	24	x∈ω	x∈ω	NOUN
ijassa-294	255	25	s(s−	s(s−	PROPN
ijassa-294	255	26	b(x))(1−	b(x))(1−	PROPN
ijassa-294	255	27	s	s	PART
ijassa-294	255	28	)	)	PUNCT
ijassa-294	255	29	ds	ds	PROPN
ijassa-294	255	30	=	=	SYM
ijassa-294	255	31	∫	∫	PROPN
ijassa-294	255	32	1	1	NUM
ijassa-294	255	33	0	0	NUM
ijassa-294	255	34	max	max	PROPN
ijassa-294	255	35	x∈ω	x∈ω	NOUN
ijassa-294	256	1	[	[	X
ijassa-294	256	2	s2	s2	NOUN
ijassa-294	256	3	−	−	PROPN
ijassa-294	256	4	s3	s3	PROPN
ijassa-294	256	5	+	+	CCONJ
ijassa-294	256	6	b(x)(s2	b(x)(s2	NOUN
ijassa-294	256	7	−	−	PROPN
ijassa-294	256	8	s	s	PART
ijassa-294	256	9	)	)	PUNCT
ijassa-294	256	10	]	]	PUNCT
ijassa-294	256	11	ds	ds	PROPN
ijassa-294	256	12	=	=	SYM
ijassa-294	256	13	1	1	NUM
ijassa-294	256	14	12	12	NUM
ijassa-294	256	15	−	−	PROPN
ijassa-294	256	16	b	b	PROPN
ijassa-294	256	17	6	6	NUM
ijassa-294	256	18	,	,	PUNCT
ijassa-294	256	19	since	since	SCONJ
ijassa-294	256	20	s2	s2	PROPN
ijassa-294	256	21	−	−	PROPN
ijassa-294	256	22	s	s	PART
ijassa-294	256	23	≤	≤	NUM
ijassa-294	256	24	0	0	NUM
ijassa-294	256	25	for	for	ADP
ijassa-294	256	26	s	s	X
ijassa-294	256	27	∈	∈	PROPN
ijassa-294	257	1	[	[	X
ijassa-294	257	2	0	0	NUM
ijassa-294	257	3	,	,	PUNCT
ijassa-294	257	4	1	1	NUM
ijassa-294	257	5	]	]	PUNCT
ijassa-294	257	6	.	.	PUNCT
ijassa-294	258	1	then	then	ADV
ijassa-294	258	2	by	by	ADP
ijassa-294	258	3	theorem	theorem	NOUN
ijassa-294	258	4	2.2	2.2	NUM
ijassa-294	258	5	,	,	PUNCT
ijassa-294	258	6	if	if	SCONJ
ijassa-294	258	7	b	b	NOUN
ijassa-294	258	8	=	=	SYM
ijassa-294	258	9	minx∈ω	minx∈ω	NOUN
ijassa-294	258	10	b(x	b(x	NOUN
ijassa-294	258	11	)	)	PUNCT
ijassa-294	258	12	≥	≥	NOUN
ijassa-294	258	13	1	1	NUM
ijassa-294	258	14	2	2	NUM
ijassa-294	258	15	,	,	PUNCT
ijassa-294	258	16	then	then	ADV
ijassa-294	258	17	(	(	PUNCT
ijassa-294	258	18	16	16	NUM
ijassa-294	258	19	)	)	PUNCT
ijassa-294	258	20	has	have	VERB
ijassa-294	258	21	no	no	DET
ijassa-294	258	22	positive	positive	ADJ
ijassa-294	258	23	solution	solution	NOUN
ijassa-294	258	24	for	for	ADP
ijassa-294	258	25	any	any	DET
ijassa-294	258	26	λ	λ	PROPN
ijassa-294	258	27	>	>	X
ijassa-294	258	28	0	0	PROPN
ijassa-294	258	29	.	.	PUNCT
ijassa-294	258	30	example	example	NOUN
ijassa-294	259	1	4.3	4.3	NUM
ijassa-294	259	2	.	.	PUNCT
ijassa-294	260	1	let	let	VERB
ijassa-294	260	2	m(t	m(t	NOUN
ijassa-294	260	3	)	)	PUNCT
ijassa-294	260	4	≡	≡	PROPN
ijassa-294	260	5	1	1	NUM
ijassa-294	260	6	and	and	CCONJ
ijassa-294	260	7	f(x	f(x	PROPN
ijassa-294	260	8	,	,	PUNCT
ijassa-294	260	9	s	s	PART
ijassa-294	260	10	)	)	PUNCT
ijassa-294	260	11	=	=	SYM
ijassa-294	260	12	s(s	s(s	PROPN
ijassa-294	260	13	−	−	PROPN
ijassa-294	260	14	1)(c(x	1)(c(x	NUM
ijassa-294	260	15	)	)	PUNCT
ijassa-294	261	1	−	−	PROPN
ijassa-294	261	2	s	s	X
ijassa-294	261	3	)	)	PUNCT
ijassa-294	261	4	with	with	ADP
ijassa-294	261	5	3	3	NUM
ijassa-294	261	6	2	2	NUM
ijassa-294	261	7	≤	≤	NUM
ijassa-294	261	8	c(x	c(x	NOUN
ijassa-294	261	9	)	)	PUNCT
ijassa-294	261	10	for	for	ADP
ijassa-294	261	11	any	any	DET
ijassa-294	261	12	x	x	SYM
ijassa-294	261	13	∈	∈	PROPN
ijassa-294	261	14	ω	ω	NOUN
ijassa-294	261	15	.	.	PUNCT
ijassa-294	262	1	we	we	PRON
ijassa-294	262	2	can	can	AUX
ijassa-294	262	3	easily	easily	ADV
ijassa-294	262	4	obtain∫	obtain∫	VERB
ijassa-294	262	5	c	c	NOUN
ijassa-294	262	6	0	0	NUM
ijassa-294	262	7	f(s	f(	NOUN
ijassa-294	262	8	)	)	PUNCT
ijassa-294	263	1	ds	ds	ADJ
ijassa-294	263	2	=	=	SYM
ijassa-294	263	3	∫	∫	PROPN
ijassa-294	263	4	c	c	NOUN
ijassa-294	263	5	0	0	NUM
ijassa-294	263	6	max	max	PROPN
ijassa-294	263	7	x∈ω	x∈ω	NOUN
ijassa-294	263	8	s(s−	s(s−	PROPN
ijassa-294	263	9	1)(c(x)−	1)(c(x)−	PROPN
ijassa-294	263	10	s	s	NOUN
ijassa-294	263	11	)	)	PUNCT
ijassa-294	263	12	ds	ds	PROPN
ijassa-294	263	13	=	=	SYM
ijassa-294	263	14	∫	∫	PROPN
ijassa-294	263	15	c	c	NOUN
ijassa-294	263	16	0	0	PUNCT
ijassa-294	263	17	(	(	PUNCT
ijassa-294	263	18	c(x)s2	c(x)s2	VERB
ijassa-294	263	19	−	−	PROPN
ijassa-294	263	20	s3	s3	PROPN
ijassa-294	263	21	+	+	CCONJ
ijassa-294	263	22	s2	s2	PROPN
ijassa-294	263	23	−	−	PROPN
ijassa-294	263	24	c(x)s	c(x)s	PROPN
ijassa-294	263	25	)	)	PUNCT
ijassa-294	263	26	ds	ds	PROPN
ijassa-294	263	27	=	=	SYM
ijassa-294	263	28	c3	c3	PROPN
ijassa-294	263	29	3	3	NUM
ijassa-294	263	30	−	−	PROPN
ijassa-294	263	31	c4	c4	NOUN
ijassa-294	263	32	4	4	NUM
ijassa-294	263	33	+	+	NUM
ijassa-294	263	34	∫	∫	PROPN
ijassa-294	263	35	c	c	NOUN
ijassa-294	263	36	0	0	NUM
ijassa-294	263	37	max	max	PROPN
ijassa-294	263	38	x∈ω	x∈ω	PROPN
ijassa-294	263	39	c(x)(s2	c(x)(s2	VERB
ijassa-294	263	40	−	−	PROPN
ijassa-294	263	41	s	s	X
ijassa-294	263	42	)	)	PUNCT
ijassa-294	263	43	ds	ds	PROPN
ijassa-294	263	44	=	=	SYM
ijassa-294	263	45	c3	c3	PROPN
ijassa-294	263	46	3	3	NUM
ijassa-294	263	47	−	−	PROPN
ijassa-294	263	48	c4	c4	NOUN
ijassa-294	263	49	4	4	NUM
ijassa-294	263	50	+	+	CCONJ
ijassa-294	263	51	max	max	PROPN
ijassa-294	263	52	x∈ω	x∈ω	PROPN
ijassa-294	263	53	c(x	c(x	PROPN
ijassa-294	263	54	)	)	PUNCT
ijassa-294	263	55	(	(	PUNCT
ijassa-294	263	56	c3	c3	NOUN
ijassa-294	263	57	3	3	NUM
ijassa-294	263	58	−	−	PROPN
ijassa-294	263	59	c2	c2	PROPN
ijassa-294	263	60	2	2	NUM
ijassa-294	263	61	)	)	PUNCT
ijassa-294	263	62	ds	ds	PROPN
ijassa-294	263	63	=	=	SYM
ijassa-294	263	64	c3	c3	PROPN
ijassa-294	263	65	3	3	NUM
ijassa-294	263	66	−	−	PROPN
ijassa-294	263	67	c4	c4	NOUN
ijassa-294	263	68	4	4	NUM
ijassa-294	263	69	+	+	SYM
ijassa-294	263	70	c	c	PROPN
ijassa-294	263	71	(	(	PUNCT
ijassa-294	263	72	c3	c3	NOUN
ijassa-294	263	73	3	3	NUM
ijassa-294	263	74	−	−	PROPN
ijassa-294	263	75	c2	c2	PROPN
ijassa-294	263	76	2	2	NUM
ijassa-294	263	77	)	)	PUNCT
ijassa-294	263	78	ds	ds	PROPN
ijassa-294	263	79	=	=	SYM
ijassa-294	263	80	c3	c3	PROPN
ijassa-294	263	81	12	12	NUM
ijassa-294	264	1	[	[	X
ijassa-294	264	2	c−	c−	X
ijassa-294	264	3	2	2	NUM
ijassa-294	264	4	]	]	PUNCT
ijassa-294	264	5	.	.	PUNCT
ijassa-294	265	1	so	so	ADV
ijassa-294	265	2	∫	∫	PROPN
ijassa-294	265	3	c	c	NOUN
ijassa-294	265	4	0	0	NUM
ijassa-294	265	5	f(s	f(	NOUN
ijassa-294	265	6	)	)	PUNCT
ijassa-294	265	7	ds	ds	ADJ
ijassa-294	265	8	≤	≤	NOUN
ijassa-294	265	9	0	0	PUNCT
ijassa-294	266	1	if	if	SCONJ
ijassa-294	266	2	and	and	CCONJ
ijassa-294	266	3	only	only	ADV
ijassa-294	266	4	if	if	SCONJ
ijassa-294	266	5	c	c	PROPN
ijassa-294	266	6	≤	≤	ADV
ijassa-294	266	7	2	2	NUM
ijassa-294	266	8	.	.	PUNCT
ijassa-294	267	1	on	on	ADP
ijassa-294	267	2	the	the	DET
ijassa-294	267	3	other	other	ADJ
ijassa-294	267	4	hand,∫	hand,∫	PROPN
ijassa-294	267	5	c(x	c(x	PROPN
ijassa-294	267	6	)	)	PUNCT
ijassa-294	267	7	0	0	PUNCT
ijassa-294	268	1	f(x	f(x	PROPN
ijassa-294	268	2	,	,	PUNCT
ijassa-294	268	3	s	s	X
ijassa-294	268	4	)	)	PUNCT
ijassa-294	268	5	ds	ds	PROPN
ijassa-294	268	6	=	=	SYM
ijassa-294	268	7	∫	∫	PROPN
ijassa-294	268	8	c	c	NOUN
ijassa-294	268	9	0	0	PUNCT
ijassa-294	269	1	s(s−	s(s−	PROPN
ijassa-294	269	2	1)(c(x)−	1)(c(x)−	NUM
ijassa-294	269	3	s	s	NOUN
ijassa-294	269	4	)	)	PUNCT
ijassa-294	269	5	ds−	ds−	PROPN
ijassa-294	269	6	∫	∫	PROPN
ijassa-294	269	7	c	c	PROPN
ijassa-294	269	8	c(x	c(x	PROPN
ijassa-294	269	9	)	)	PUNCT
ijassa-294	270	1	s(s−	s(s−	PROPN
ijassa-294	270	2	1)(c(x)−	1)(c(x)−	NUM
ijassa-294	270	3	s	s	NOUN
ijassa-294	270	4	)	)	PUNCT
ijassa-294	270	5	ds	ds	ADJ
ijassa-294	270	6	≥	≥	NUM
ijassa-294	270	7	∫	∫	PROPN
ijassa-294	271	1	c	c	NOUN
ijassa-294	271	2	0	0	PUNCT
ijassa-294	272	1	s(s−	s(s−	PROPN
ijassa-294	272	2	1)(c(x)−	1)(c(x)−	NUM
ijassa-294	272	3	s	s	NOUN
ijassa-294	272	4	)	)	PUNCT
ijassa-294	272	5	ds	ds	NOUN
ijassa-294	272	6	=	=	NOUN
ijassa-294	272	7	−c	−c	NOUN
ijassa-294	272	8	4	4	NUM
ijassa-294	272	9	4	4	NUM
ijassa-294	272	10	+	+	SYM
ijassa-294	272	11	1	1	NUM
ijassa-294	272	12	+	+	CCONJ
ijassa-294	272	13	c(x	c(x	NOUN
ijassa-294	272	14	)	)	PUNCT
ijassa-294	272	15	3	3	NUM
ijassa-294	272	16	c3	c3	NOUN
ijassa-294	272	17	−	−	PROPN
ijassa-294	272	18	c(x	c(x	NOUN
ijassa-294	272	19	)	)	PUNCT
ijassa-294	272	20	2	2	NUM
ijassa-294	272	21	c2	c2	PROPN
ijassa-294	272	22	.	.	PUNCT
ijassa-294	273	1	advances	advance	NOUN
ijassa-294	273	2	in	in	ADP
ijassa-294	273	3	systems	system	NOUN
ijassa-294	273	4	science	science	NOUN
ijassa-294	273	5	and	and	CCONJ
ijassa-294	273	6	applications	application	NOUN
ijassa-294	273	7	(	(	PUNCT
ijassa-294	273	8	2011	2011	NUM
ijassa-294	273	9	)	)	PUNCT
ijassa-294	273	10	,	,	PUNCT
ijassa-294	273	11	vol	vol	NOUN
ijassa-294	273	12	.	.	PROPN
ijassa-294	274	1	11	11	NUM
ijassa-294	274	2	,	,	PUNCT
ijassa-294	274	3	no	no	INTJ
ijassa-294	274	4	.	.	NOUN
ijassa-294	274	5	1	1	NUM
ijassa-294	274	6	-	-	SYM
ijassa-294	274	7	2	2	NUM
ijassa-294	274	8	91	91	NUM
ijassa-294	274	9	if	if	SCONJ
ijassa-294	274	10	∫	∫	PROPN
ijassa-294	274	11	c(x	c(x	NOUN
ijassa-294	274	12	)	)	PUNCT
ijassa-294	274	13	0	0	PUNCT
ijassa-294	275	1	f(x	f(x	PROPN
ijassa-294	275	2	,	,	PUNCT
ijassa-294	275	3	s	s	X
ijassa-294	275	4	)	)	PUNCT
ijassa-294	275	5	ds	ds	ADJ
ijassa-294	275	6	≤	≤	NOUN
ijassa-294	275	7	0	0	NUM
ijassa-294	275	8	for	for	ADP
ijassa-294	275	9	any	any	DET
ijassa-294	275	10	x	x	SYM
ijassa-294	275	11	∈	∈	PROPN
ijassa-294	275	12	ω	ω	NOUN
ijassa-294	275	13	,	,	PUNCT
ijassa-294	275	14	we	we	PRON
ijassa-294	275	15	have	have	VERB
ijassa-294	275	16	0	0	NUM
ijassa-294	275	17	≥	≥	NOUN
ijassa-294	275	18	−c	−c	NOUN
ijassa-294	275	19	4	4	NUM
ijassa-294	275	20	4	4	NUM
ijassa-294	275	21	+	+	SYM
ijassa-294	275	22	1	1	NUM
ijassa-294	275	23	+	+	CCONJ
ijassa-294	275	24	c(x	c(x	NOUN
ijassa-294	275	25	)	)	PUNCT
ijassa-294	275	26	3	3	NUM
ijassa-294	275	27	c3	c3	NOUN
ijassa-294	275	28	−	−	PROPN
ijassa-294	275	29	c(x	c(x	NOUN
ijassa-294	275	30	)	)	PUNCT
ijassa-294	275	31	2	2	NUM
ijassa-294	275	32	c2	c2	PROPN
ijassa-294	275	33	⇒	⇒	VERB
ijassa-294	275	34	4(1	4(1	NUM
ijassa-294	275	35	+	+	CCONJ
ijassa-294	275	36	c(x))c−	c(x))c−	PROPN
ijassa-294	275	37	6c(x	6c(x	NOUN
ijassa-294	275	38	)	)	PUNCT
ijassa-294	275	39	≤	≤	NOUN
ijassa-294	275	40	3c2	3c2	NUM
ijassa-294	275	41	.	.	PUNCT
ijassa-294	276	1	in	in	ADP
ijassa-294	276	2	particular	particular	ADJ
ijassa-294	276	3	,	,	PUNCT
ijassa-294	276	4	we	we	PRON
ijassa-294	276	5	have	have	VERB
ijassa-294	276	6	4(1	4(1	NOUN
ijassa-294	276	7	+	+	CCONJ
ijassa-294	276	8	c)c−	c)c−	PROPN
ijassa-294	276	9	6c	6c	NOUN
ijassa-294	276	10	≤	≤	ADV
ijassa-294	276	11	3c2	3c2	NUM
ijassa-294	276	12	⇒	⇒	NOUN
ijassa-294	276	13	c	c	PROPN
ijassa-294	276	14	≤	≤	ADV
ijassa-294	276	15	2	2	NUM
ijassa-294	276	16	.	.	PUNCT
ijassa-294	277	1	however	however	ADV
ijassa-294	277	2	,	,	PUNCT
ijassa-294	277	3	it	it	PRON
ijassa-294	277	4	is	be	AUX
ijassa-294	277	5	clear	clear	ADJ
ijassa-294	277	6	that∫	that∫	NOUN
ijassa-294	277	7	c	c	NOUN
ijassa-294	277	8	0	0	NUM
ijassa-294	277	9	f(s	f(	NOUN
ijassa-294	277	10	)	)	PUNCT
ijassa-294	277	11	ds	ds	ADJ
ijassa-294	277	12	≤	≤	NOUN
ijassa-294	277	13	0	0	NUM
ijassa-294	277	14	;	;	PUNCT
ijassa-294	277	15	∫	∫	PROPN
ijassa-294	277	16	c(x	c(x	PROPN
ijassa-294	277	17	)	)	PUNCT
ijassa-294	277	18	0	0	PUNCT
ijassa-294	278	1	f(x	f(x	PROPN
ijassa-294	278	2	,	,	PUNCT
ijassa-294	278	3	s	s	X
ijassa-294	278	4	)	)	PUNCT
ijassa-294	278	5	ds	ds	ADJ
ijassa-294	278	6	≤	≤	NOUN
ijassa-294	278	7	0	0	NUM
ijassa-294	278	8	for	for	ADP
ijassa-294	278	9	any	any	DET
ijassa-294	278	10	x	x	SYM
ijassa-294	278	11	∈	∈	PROPN
ijassa-294	278	12	ω	ω	PROPN
ijassa-294	278	13	.	.	PUNCT
ijassa-294	279	1	therefore	therefore	ADV
ijassa-294	279	2	,	,	PUNCT
ijassa-294	279	3	the	the	DET
ijassa-294	279	4	condition	condition	NOUN
ijassa-294	279	5	“	"	PUNCT
ijassa-294	279	6	∫	∫	PROPN
ijassa-294	279	7	c(x	c(x	PROPN
ijassa-294	279	8	)	)	PUNCT
ijassa-294	279	9	0	0	PUNCT
ijassa-294	280	1	f(x	f(x	PROPN
ijassa-294	280	2	,	,	PUNCT
ijassa-294	280	3	s	s	X
ijassa-294	280	4	)	)	PUNCT
ijassa-294	280	5	ds	ds	ADJ
ijassa-294	280	6	≤	≤	NOUN
ijassa-294	280	7	0	0	NUM
ijassa-294	280	8	for	for	ADP
ijassa-294	280	9	any	any	DET
ijassa-294	280	10	x	x	SYM
ijassa-294	280	11	∈	∈	PROPN
ijassa-294	280	12	ω	ω	PROPN
ijassa-294	280	13	”	"	PUNCT
ijassa-294	280	14	is	be	AUX
ijassa-294	280	15	more	more	ADV
ijassa-294	280	16	strong	strong	ADJ
ijassa-294	280	17	than	than	ADP
ijassa-294	280	18	the	the	DET
ijassa-294	280	19	condition	condition	NOUN
ijassa-294	280	20	“	"	PUNCT
ijassa-294	280	21	∫	∫	PROPN
ijassa-294	280	22	c	c	PROPN
ijassa-294	280	23	0	0	NUM
ijassa-294	280	24	f(s	f(	NOUN
ijassa-294	280	25	)	)	PUNCT
ijassa-294	280	26	ds	ds	ADJ
ijassa-294	280	27	≤	≤	NOUN
ijassa-294	280	28	0	0	NUM
ijassa-294	280	29	”	"	PUNCT
ijassa-294	280	30	in	in	ADP
ijassa-294	280	31	this	this	DET
ijassa-294	280	32	example	example	NOUN
ijassa-294	280	33	,	,	PUNCT
ijassa-294	280	34	which	which	PRON
ijassa-294	280	35	verifies	verifie	NOUN
ijassa-294	280	36	proposition	proposition	VERB
ijassa-294	280	37	4.1	4.1	NUM
ijassa-294	280	38	by	by	ADP
ijassa-294	280	39	a	a	DET
ijassa-294	280	40	concrete	concrete	ADJ
ijassa-294	280	41	example	example	NOUN
ijassa-294	280	42	.	.	PUNCT
ijassa-294	281	1	remark	remark	VERB
ijassa-294	281	2	4.1	4.1	NUM
ijassa-294	281	3	.	.	PUNCT
ijassa-294	282	1	in	in	ADP
ijassa-294	282	2	[	[	X
ijassa-294	282	3	25	25	NUM
ijassa-294	282	4	]	]	PUNCT
ijassa-294	282	5	,	,	PUNCT
ijassa-294	282	6	dancer	dancer	NOUN
ijassa-294	282	7	and	and	CCONJ
ijassa-294	282	8	yan	yan	PROPN
ijassa-294	282	9	proved	prove	VERB
ijassa-294	282	10	when	when	SCONJ
ijassa-294	282	11	c(x	c(x	NOUN
ijassa-294	282	12	)	)	PUNCT
ijassa-294	282	13	≡	≡	PROPN
ijassa-294	282	14	1	1	NUM
ijassa-294	282	15	and	and	CCONJ
ijassa-294	282	16	{	{	PUNCT
ijassa-294	282	17	x	x	SYM
ijassa-294	282	18	∈	∈	PROPN
ijassa-294	282	19	ω	ω	NOUN
ijassa-294	282	20	:	:	PUNCT
ijassa-294	282	21	b(x	b(x	NOUN
ijassa-294	282	22	)	)	PUNCT
ijassa-294	282	23	<	<	X
ijassa-294	282	24	1/2	1/2	NUM
ijassa-294	282	25	}	}	PUNCT
ijassa-294	282	26	is	be	AUX
ijassa-294	282	27	of	of	ADP
ijassa-294	282	28	positive	positive	ADJ
ijassa-294	282	29	measure	measure	NOUN
ijassa-294	282	30	,	,	PUNCT
ijassa-294	282	31	then	then	ADV
ijassa-294	282	32	(	(	PUNCT
ijassa-294	282	33	16	16	NUM
ijassa-294	282	34	)	)	PUNCT
ijassa-294	282	35	may	may	AUX
ijassa-294	282	36	have	have	VERB
ijassa-294	282	37	many	many	ADJ
ijassa-294	282	38	positive	positive	ADJ
ijassa-294	282	39	solutions	solution	NOUN
ijassa-294	282	40	of	of	ADP
ijassa-294	282	41	local	local	ADJ
ijassa-294	282	42	minimum	minimum	ADJ
ijassa-294	282	43	type	type	NOUN
ijassa-294	282	44	.	.	PUNCT
ijassa-294	283	1	the	the	DET
ijassa-294	283	2	results	result	NOUN
ijassa-294	283	3	of	of	ADP
ijassa-294	283	4	example	example	NOUN
ijassa-294	283	5	4.2	4.2	NUM
ijassa-294	283	6	shows	show	VERB
ijassa-294	283	7	that	that	SCONJ
ijassa-294	283	8	the	the	DET
ijassa-294	283	9	condition	condition	NOUN
ijassa-294	283	10	∫	∫	PROPN
ijassa-294	283	11	1	1	NUM
ijassa-294	283	12	0	0	NUM
ijassa-294	283	13	f(s	f(	NOUN
ijassa-294	283	14	)	)	PUNCT
ijassa-294	283	15	ds	ds	ADJ
ijassa-294	283	16	≤	≤	NOUN
ijassa-294	283	17	0	0	NUM
ijassa-294	283	18	is	be	AUX
ijassa-294	283	19	optimal	optimal	ADJ
ijassa-294	283	20	for	for	ADP
ijassa-294	283	21	the	the	DET
ijassa-294	283	22	nonexistence	nonexistence	NOUN
ijassa-294	283	23	of	of	ADP
ijassa-294	283	24	positive	positive	ADJ
ijassa-294	283	25	solution	solution	NOUN
ijassa-294	283	26	of	of	ADP
ijassa-294	283	27	(	(	PUNCT
ijassa-294	283	28	16	16	NUM
ijassa-294	283	29	)	)	PUNCT
ijassa-294	283	30	.	.	PUNCT
ijassa-294	284	1	however	however	ADV
ijassa-294	284	2	,	,	PUNCT
ijassa-294	284	3	we	we	PRON
ijassa-294	284	4	do	do	AUX
ijassa-294	284	5	not	not	PART
ijassa-294	284	6	know	know	VERB
ijassa-294	284	7	whether	whether	SCONJ
ijassa-294	284	8	∫	∫	PROPN
ijassa-294	284	9	c	c	NOUN
ijassa-294	284	10	0	0	NUM
ijassa-294	284	11	f(s	f(	NOUN
ijassa-294	284	12	)	)	PUNCT
ijassa-294	284	13	ds	ds	ADJ
ijassa-294	284	14	≤	≤	NOUN
ijassa-294	284	15	0	0	NUM
ijassa-294	284	16	is	be	AUX
ijassa-294	284	17	optimal	optimal	ADJ
ijassa-294	284	18	for	for	ADP
ijassa-294	284	19	the	the	DET
ijassa-294	284	20	nonexistence	nonexistence	NOUN
ijassa-294	284	21	of	of	ADP
ijassa-294	284	22	positive	positive	ADJ
ijassa-294	284	23	solution	solution	NOUN
ijassa-294	284	24	of	of	ADP
ijassa-294	284	25	(	(	PUNCT
ijassa-294	284	26	1	1	NUM
ijassa-294	284	27	)	)	PUNCT
ijassa-294	284	28	.	.	PUNCT
ijassa-294	285	1	references	reference	NOUN
ijassa-294	285	2	[	[	X
ijassa-294	285	3	1	1	NUM
ijassa-294	285	4	]	]	X
ijassa-294	285	5	g.liu	g.liu	X
ijassa-294	285	6	,	,	PUNCT
ijassa-294	285	7	,	,	PUNCT
ijassa-294	285	8	y.	y.	PROPN
ijassa-294	285	9	wang	wang	PROPN
ijassa-294	285	10	,	,	PUNCT
ijassa-294	285	11	&	&	CCONJ
ijassa-294	285	12	j.	j.	PROPN
ijassa-294	285	13	shi	shi	PROPN
ijassa-294	285	14	,	,	PUNCT
ijassa-294	285	15	existence	existence	NOUN
ijassa-294	285	16	and	and	CCONJ
ijassa-294	285	17	nonexistence	nonexistence	NOUN
ijassa-294	285	18	of	of	ADP
ijassa-294	285	19	positive	positive	ADJ
ijassa-294	285	20	solutions	solution	NOUN
ijassa-294	285	21	of	of	ADP
ijassa-294	285	22	semilinear	semilinear	ADJ
ijassa-294	285	23	elliptic	elliptic	ADJ
ijassa-294	285	24	equation	equation	NOUN
ijassa-294	285	25	with	with	ADP
ijassa-294	285	26	inhomogeneous	inhomogeneous	ADJ
ijassa-294	285	27	strong	strong	ADJ
ijassa-294	285	28	allee	allee	NOUN
ijassa-294	285	29	effect	effect	NOUN
ijassa-294	285	30	,	,	PUNCT
ijassa-294	285	31	appl	appl	PROPN
ijassa-294	285	32	.	.	PROPN
ijassa-294	285	33	math	math	PROPN
ijassa-294	285	34	.	.	PUNCT
ijassa-294	286	1	mech	mech	PROPN
ijassa-294	286	2	.	.	PUNCT
ijassa-294	287	1	-engl	-engl	PROPN
ijassa-294	287	2	.	.	PUNCT
ijassa-294	288	1	ed	ed	NOUN
ijassa-294	288	2	.	.	PUNCT
ijassa-294	289	1	30(11	30(11	NUM
ijassa-294	289	2	)	)	PUNCT
ijassa-294	289	3	,	,	PUNCT
ijassa-294	289	4	1461	1461	NUM
ijassa-294	289	5	-	-	SYM
ijassa-294	289	6	1468	1468	NUM
ijassa-294	289	7	(	(	PUNCT
ijassa-294	289	8	2009	2009	NUM
ijassa-294	289	9	)	)	PUNCT
ijassa-294	290	1	[	[	X
ijassa-294	290	2	2	2	X
ijassa-294	290	3	]	]	PUNCT
ijassa-294	290	4	g.kirchhoff	g.kirchhoff	X
ijassa-294	290	5	,	,	PUNCT
ijassa-294	290	6	mechanik	mechanik	PROPN
ijassa-294	290	7	,	,	PUNCT
ijassa-294	290	8	teubner	teubner	NOUN
ijassa-294	290	9	,	,	PUNCT
ijassa-294	290	10	leipzig	leipzig	NOUN
ijassa-294	290	11	.	.	PUNCT
ijassa-294	291	1	(	(	PUNCT
ijassa-294	291	2	1883	1883	NUM
ijassa-294	291	3	)	)	PUNCT
ijassa-294	291	4	.	.	PUNCT
ijassa-294	292	1	[	[	X
ijassa-294	292	2	3	3	X
ijassa-294	292	3	]	]	X
ijassa-294	292	4	j.	j.	PROPN
ijassa-294	292	5	l.	l.	PROPN
ijassa-294	292	6	lions	lions	PROPN
ijassa-294	292	7	,	,	PUNCT
ijassa-294	292	8	on	on	ADP
ijassa-294	292	9	some	some	DET
ijassa-294	292	10	questions	question	NOUN
ijassa-294	292	11	in	in	ADP
ijassa-294	292	12	boundary	boundary	ADJ
ijassa-294	292	13	value	value	NOUN
ijassa-294	292	14	problems	problem	NOUN
ijassa-294	292	15	of	of	ADP
ijassa-294	292	16	mathematical	mathematical	ADJ
ijassa-294	292	17	physics	physics	NOUN
ijassa-294	292	18	,	,	PUNCT
ijassa-294	292	19	in	in	ADP
ijassa-294	292	20	:	:	PUNCT
ijassa-294	292	21	proceedings	proceeding	NOUN
ijassa-294	292	22	of	of	ADP
ijassa-294	292	23	international	international	ADJ
ijassa-294	292	24	symposium	symposium	NOUN
ijassa-294	292	25	on	on	ADP
ijassa-294	292	26	continuum	continuum	ADJ
ijassa-294	292	27	mechanics	mechanic	NOUN
ijassa-294	292	28	and	and	CCONJ
ijassa-294	292	29	partial	partial	ADJ
ijassa-294	292	30	differential	differential	NOUN
ijassa-294	292	31	equations	equation	NOUN
ijassa-294	292	32	.	.	PUNCT
ijassa-294	293	1	rio	rio	PROPN
ijassa-294	293	2	de	de	PROPN
ijassa-294	293	3	janeiro	janeiro	PROPN
ijassa-294	293	4	,	,	PUNCT
ijassa-294	293	5	1977	1977	NUM
ijassa-294	293	6	,	,	PUNCT
ijassa-294	293	7	in	in	ADP
ijassa-294	293	8	:	:	PUNCT
ijassa-294	293	9	de	de	X
ijassa-294	293	10	la	la	NOUN
ijassa-294	293	11	penha	penha	NOUN
ijassa-294	293	12	,	,	PUNCT
ijassa-294	293	13	medeiros	medeiros	PROPN
ijassa-294	293	14	(	(	PUNCT
ijassa-294	293	15	eds	eds	PROPN
ijassa-294	293	16	.	.	PUNCT
ijassa-294	293	17	)	)	PUNCT
ijassa-294	293	18	,	,	PUNCT
ijassa-294	293	19	math	math	NOUN
ijassa-294	293	20	.	.	PUNCT
ijassa-294	294	1	stud	stud	PROPN
ijassa-294	294	2	.	.	PUNCT
ijassa-294	295	1	,	,	PUNCT
ijassa-294	295	2	vol	vol	NOUN
ijassa-294	295	3	.	.	PROPN
ijassa-294	295	4	30	30	NUM
ijassa-294	295	5	,	,	PUNCT
ijassa-294	295	6	north	north	NOUN
ijassa-294	295	7	-	-	PUNCT
ijassa-294	295	8	holland	holland	NOUN
ijassa-294	295	9	,	,	PUNCT
ijassa-294	295	10	1978	1978	NUM
ijassa-294	295	11	,	,	PUNCT
ijassa-294	295	12	pp	pp	ADJ
ijassa-294	295	13	.	.	PUNCT
ijassa-294	296	1	284	284	NUM
ijassa-294	296	2	-	-	SYM
ijassa-294	296	3	346	346	NUM
ijassa-294	296	4	.	.	PUNCT
ijassa-294	297	1	[	[	X
ijassa-294	297	2	4	4	NUM
ijassa-294	297	3	]	]	PUNCT
ijassa-294	297	4	a.	a.	NOUN
ijassa-294	297	5	arosio	arosio	PROPN
ijassa-294	297	6	,	,	PUNCT
ijassa-294	297	7	&	&	CCONJ
ijassa-294	297	8	s.pannizi	s.pannizi	PROPN
ijassa-294	297	9	,	,	PUNCT
ijassa-294	297	10	on	on	ADP
ijassa-294	297	11	the	the	DET
ijassa-294	297	12	well	well	NOUN
ijassa-294	297	13	-	-	PUNCT
ijassa-294	297	14	posedness	posedness	NOUN
ijassa-294	297	15	of	of	ADP
ijassa-294	297	16	the	the	DET
ijassa-294	297	17	kirchhoff	kirchhoff	PROPN
ijassa-294	297	18	string	string	PROPN
ijassa-294	297	19	.	.	PUNCT
ijassa-294	298	1	trans	trans	PROPN
ijassa-294	298	2	.	.	PUNCT
ijassa-294	299	1	amer	amer	PROPN
ijassa-294	299	2	.	.	PUNCT
ijassa-294	299	3	math	math	PROPN
ijassa-294	299	4	.	.	PUNCT
ijassa-294	300	1	soc	soc	PROPN
ijassa-294	300	2	.	.	PUNCT
ijassa-294	301	1	348	348	NUM
ijassa-294	301	2	(	(	PUNCT
ijassa-294	301	3	1996	1996	NUM
ijassa-294	301	4	)	)	PUNCT
ijassa-294	301	5	305	305	NUM
ijassa-294	301	6	-	-	SYM
ijassa-294	301	7	330	330	NUM
ijassa-294	301	8	.	.	PUNCT
ijassa-294	302	1	[	[	X
ijassa-294	302	2	5	5	NUM
ijassa-294	302	3	]	]	PUNCT
ijassa-294	302	4	cavalcante	cavalcante	NOUN
ijassa-294	302	5	,	,	PUNCT
ijassa-294	302	6	cavalcante	cavalcante	ADJ
ijassa-294	302	7	m.	m.	NOUN
ijassa-294	302	8	m.	m.	NOUN
ijassa-294	302	9	,	,	PUNCT
ijassa-294	302	10	,	,	PUNCT
ijassa-294	302	11	v.n	v.n	PROPN
ijassa-294	302	12	.	.	PROPN
ijassa-294	302	13	,	,	PUNCT
ijassa-294	302	14	&	&	CCONJ
ijassa-294	302	15	j.a	j.a	PROPN
ijassa-294	302	16	.	.	PROPN
ijassa-294	302	17	soriano	soriano	PROPN
ijassa-294	302	18	,	,	PUNCT
ijassa-294	302	19	global	global	ADJ
ijassa-294	302	20	existence	existence	NOUN
ijassa-294	302	21	and	and	CCONJ
ijassa-294	302	22	uniform	uniform	ADJ
ijassa-294	302	23	decay	decay	NOUN
ijassa-294	302	24	rates	rate	NOUN
ijassa-294	302	25	for	for	ADP
ijassa-294	302	26	the	the	DET
ijassa-294	302	27	kirchhoff	kirchhoff	NOUN
ijassa-294	302	28	-	-	PUNCT
ijassa-294	302	29	carrier	carrier	NOUN
ijassa-294	302	30	equation	equation	NOUN
ijassa-294	302	31	with	with	ADP
ijassa-294	302	32	nonlinear	nonlinear	ADJ
ijassa-294	302	33	dissipation	dissipation	NOUN
ijassa-294	302	34	.	.	PUNCT
ijassa-294	303	1	adv	adv	PROPN
ijassa-294	303	2	.	.	PUNCT
ijassa-294	303	3	differential	differential	PROPN
ijassa-294	303	4	equations	equation	NOUN
ijassa-294	303	5	6	6	NUM
ijassa-294	303	6	(	(	PUNCT
ijassa-294	303	7	2001	2001	NUM
ijassa-294	303	8	)	)	PUNCT
ijassa-294	303	9	701	701	NUM
ijassa-294	303	10	-	-	SYM
ijassa-294	303	11	730	730	NUM
ijassa-294	303	12	.	.	PUNCT
ijassa-294	304	1	[	[	X
ijassa-294	304	2	6	6	NUM
ijassa-294	304	3	]	]	PUNCT
ijassa-294	304	4	f.	f.	PROPN
ijassa-294	304	5	j.	j.	PROPN
ijassa-294	304	6	s.	s.	PROPN
ijassa-294	304	7	a.	a.	PROPN
ijassa-294	304	8	a	a	DET
ijassa-294	304	9	corrê	corrê	NOUN
ijassa-294	304	10	,	,	PUNCT
ijassa-294	304	11	s.d.b.menezes	s.d.b.menezes	PROPN
ijassa-294	304	12	,	,	PUNCT
ijassa-294	304	13	&	&	CCONJ
ijassa-294	304	14	j.	j.	PROPN
ijassa-294	304	15	ferreira	ferreira	PROPN
ijassa-294	304	16	,	,	PUNCT
ijassa-294	304	17	on	on	ADP
ijassa-294	304	18	a	a	DET
ijassa-294	304	19	class	class	NOUN
ijassa-294	304	20	of	of	ADP
ijassa-294	304	21	problems	problem	NOUN
ijassa-294	304	22	involving	involve	VERB
ijassa-294	304	23	a	a	DET
ijassa-294	304	24	nonlocal	nonlocal	ADJ
ijassa-294	304	25	operator	operator	NOUN
ijassa-294	304	26	.	.	PUNCT
ijassa-294	305	1	appl	appl	PROPN
ijassa-294	305	2	.	.	PROPN
ijassa-294	305	3	math	math	PROPN
ijassa-294	305	4	.	.	PUNCT
ijassa-294	306	1	comput	comput	NOUN
ijassa-294	306	2	.	.	PUNCT
ijassa-294	307	1	147	147	NUM
ijassa-294	307	2	(	(	PUNCT
ijassa-294	307	3	2004	2004	NUM
ijassa-294	307	4	)	)	PUNCT
ijassa-294	307	5	475	475	NUM
ijassa-294	307	6	-	-	SYM
ijassa-294	307	7	489	489	NUM
ijassa-294	307	8	.	.	PUNCT
ijassa-294	308	1	[	[	X
ijassa-294	308	2	7	7	X
ijassa-294	308	3	]	]	X
ijassa-294	308	4	f.	f.	PROPN
ijassa-294	308	5	j.	j.	PROPN
ijassa-294	308	6	s.	s.	PROPN
ijassa-294	308	7	a.	a.	PROPN
ijassa-294	308	8	corrêa	corrêa	PROPN
ijassa-294	308	9	,	,	PUNCT
ijassa-294	308	10	&	&	CCONJ
ijassa-294	308	11	g.m	g.m	PROPN
ijassa-294	308	12	.	.	PROPN
ijassa-294	308	13	figueiredo	figueiredo	PROPN
ijassa-294	308	14	,	,	PUNCT
ijassa-294	308	15	on	on	ADP
ijassa-294	308	16	a	a	DET
ijassa-294	308	17	elliptic	elliptic	ADJ
ijassa-294	308	18	equation	equation	NOUN
ijassa-294	308	19	of	of	ADP
ijassa-294	308	20	p	p	PROPN
ijassa-294	308	21	-	-	PUNCT
ijassa-294	308	22	kirchhoff	kirchhoff	NOUN
ijassa-294	308	23	type	type	NOUN
ijassa-294	308	24	via	via	ADP
ijassa-294	308	25	variational	variational	ADJ
ijassa-294	308	26	methods	method	NOUN
ijassa-294	308	27	.	.	PUNCT
ijassa-294	309	1	bull	bull	NOUN
ijassa-294	309	2	.	.	PUNCT
ijassa-294	310	1	austral	austral	PROPN
ijassa-294	310	2	.	.	PUNCT
ijassa-294	310	3	math	math	NOUN
ijassa-294	310	4	.	.	PUNCT
ijassa-294	311	1	soc	soc	PROPN
ijassa-294	311	2	.	.	PUNCT
ijassa-294	312	1	vol	vol	NOUN
ijassa-294	312	2	.	.	PROPN
ijassa-294	313	1	74	74	NUM
ijassa-294	313	2	(	(	PUNCT
ijassa-294	313	3	2006	2006	NUM
ijassa-294	313	4	)	)	PUNCT
ijassa-294	313	5	263	263	NUM
ijassa-294	313	6	-	-	SYM
ijassa-294	313	7	277	277	NUM
ijassa-294	313	8	.	.	PUNCT
ijassa-294	314	1	92	92	NUM
ijassa-294	314	2	ma	ma	NOUN
ijassa-294	314	3	:	:	PUNCT
ijassa-294	314	4	existence	existence	NOUN
ijassa-294	314	5	and	and	CCONJ
ijassa-294	314	6	nonexistence	nonexistence	NOUN
ijassa-294	314	7	of	of	ADP
ijassa-294	314	8	positive	positive	ADJ
ijassa-294	314	9	solutions	solution	NOUN
ijassa-294	314	10	for	for	ADP
ijassa-294	314	11	a	a	DET
ijassa-294	314	12	kirchhoff	kirchhoff	NOUN
ijassa-294	314	13	-	-	PUNCT
ijassa-294	314	14	type	type	NOUN
ijassa-294	314	15	.	.	PUNCT
ijassa-294	314	16	.	.	PUNCT
ijassa-294	314	17	.	.	PUNCT
ijassa-294	314	18	.	.	PUNCT
ijassa-294	314	19	.	.	PUNCT
ijassa-294	314	20	.	.	PUNCT
ijassa-294	315	1	[	[	X
ijassa-294	315	2	8	8	NUM
ijassa-294	315	3	]	]	PUNCT
ijassa-294	315	4	p.d’ancona	p.d’ancona	NOUN
ijassa-294	315	5	,	,	PUNCT
ijassa-294	315	6	,	,	PUNCT
ijassa-294	315	7	&	&	CCONJ
ijassa-294	315	8	s.	s.	PROPN
ijassa-294	315	9	spagnolo	spagnolo	PROPN
ijassa-294	315	10	,	,	PUNCT
ijassa-294	315	11	global	global	ADJ
ijassa-294	315	12	solvability	solvability	NOUN
ijassa-294	315	13	for	for	ADP
ijassa-294	315	14	the	the	DET
ijassa-294	315	15	degenerate	degenerate	ADJ
ijassa-294	315	16	kirchhoff	kirchhoff	NOUN
ijassa-294	315	17	equation	equation	NOUN
ijassa-294	315	18	with	with	ADP
ijassa-294	315	19	real	real	ADJ
ijassa-294	315	20	analytic	analytic	ADJ
ijassa-294	315	21	data	datum	NOUN
ijassa-294	315	22	.	.	PUNCT
ijassa-294	316	1	invent	invent	NOUN
ijassa-294	316	2	.	.	PUNCT
ijassa-294	317	1	math	math	NOUN
ijassa-294	317	2	.	.	PUNCT
ijassa-294	318	1	108	108	NUM
ijassa-294	318	2	(	(	PUNCT
ijassa-294	318	3	1992	1992	NUM
ijassa-294	318	4	)	)	PUNCT
ijassa-294	318	5	247	247	NUM
ijassa-294	318	6	-	-	SYM
ijassa-294	318	7	262	262	NUM
ijassa-294	318	8	.	.	PUNCT
ijassa-294	319	1	[	[	X
ijassa-294	319	2	9	9	NUM
ijassa-294	319	3	]	]	PUNCT
ijassa-294	319	4	m.chipot	m.chipot	NOUN
ijassa-294	319	5	,	,	PUNCT
ijassa-294	319	6	,	,	PUNCT
ijassa-294	319	7	&	&	CCONJ
ijassa-294	319	8	b.	b.	PROPN
ijassa-294	319	9	lovat	lovat	PROPN
ijassa-294	319	10	,	,	PUNCT
ijassa-294	319	11	some	some	DET
ijassa-294	319	12	remarks	remark	NOUN
ijassa-294	319	13	on	on	ADP
ijassa-294	319	14	nonlocal	nonlocal	ADJ
ijassa-294	319	15	elliptic	elliptic	ADJ
ijassa-294	319	16	and	and	CCONJ
ijassa-294	319	17	parabolic	parabolic	ADJ
ijassa-294	319	18	problems	problem	NOUN
ijassa-294	319	19	.	.	PUNCT
ijassa-294	320	1	nonlinear	nonlinear	ADJ
ijassa-294	320	2	anal	anal	NOUN
ijassa-294	320	3	.	.	PUNCT
ijassa-294	321	1	30	30	NUM
ijassa-294	321	2	(	(	PUNCT
ijassa-294	321	3	1997	1997	NUM
ijassa-294	321	4	)	)	PUNCT
ijassa-294	321	5	4619	4619	NUM
ijassa-294	321	6	-	-	SYM
ijassa-294	321	7	4627	4627	NUM
ijassa-294	321	8	.	.	PUNCT
ijassa-294	322	1	[	[	X
ijassa-294	322	2	10	10	NUM
ijassa-294	322	3	]	]	PUNCT
ijassa-294	322	4	m.dreher	m.dreher	NOUN
ijassa-294	322	5	,	,	PUNCT
ijassa-294	322	6	the	the	DET
ijassa-294	322	7	kirchhoff	kirchhoff	NOUN
ijassa-294	322	8	equation	equation	NOUN
ijassa-294	322	9	for	for	ADP
ijassa-294	322	10	the	the	DET
ijassa-294	322	11	p	p	NOUN
ijassa-294	322	12	-	-	PUNCT
ijassa-294	322	13	laplacian	laplacian	NOUN
ijassa-294	323	1	.	.	PUNCT
ijassa-294	323	2	rend	rend	PROPN
ijassa-294	323	3	.	.	PUNCT
ijassa-294	324	1	semin	semin	PROPN
ijassa-294	324	2	.	.	PUNCT
ijassa-294	325	1	mat	mat	PROPN
ijassa-294	325	2	.	.	PROPN
ijassa-294	325	3	univ	univ	PROPN
ijassa-294	325	4	.	.	PUNCT
ijassa-294	325	5	politec	politec	NOUN
ijassa-294	325	6	.	.	PUNCT
ijassa-294	326	1	torino	torino	PROPN
ijassa-294	326	2	64	64	NUM
ijassa-294	326	3	(	(	PUNCT
ijassa-294	326	4	2006	2006	NUM
ijassa-294	326	5	)	)	PUNCT
ijassa-294	326	6	217	217	NUM
ijassa-294	326	7	-	-	SYM
ijassa-294	326	8	238	238	NUM
ijassa-294	326	9	.	.	PUNCT
ijassa-294	327	1	[	[	X
ijassa-294	327	2	11	11	NUM
ijassa-294	327	3	]	]	PUNCT
ijassa-294	327	4	m.dreher	m.dreher	NOUN
ijassa-294	327	5	,	,	PUNCT
ijassa-294	327	6	the	the	DET
ijassa-294	327	7	ware	ware	NOUN
ijassa-294	327	8	equation	equation	NOUN
ijassa-294	327	9	for	for	ADP
ijassa-294	327	10	the	the	DET
ijassa-294	327	11	p	p	NOUN
ijassa-294	327	12	-	-	PUNCT
ijassa-294	327	13	laplacian	laplacian	NOUN
ijassa-294	327	14	.	.	PUNCT
ijassa-294	328	1	hokkaido	hokkaido	PROPN
ijassa-294	328	2	math	math	PROPN
ijassa-294	328	3	.	.	PUNCT
ijassa-294	329	1	j.	j.	PROPN
ijassa-294	329	2	36	36	NUM
ijassa-294	329	3	(	(	PUNCT
ijassa-294	329	4	2007	2007	NUM
ijassa-294	329	5	)	)	PUNCT
ijassa-294	329	6	21	21	NUM
ijassa-294	329	7	-	-	SYM
ijassa-294	329	8	52	52	NUM
ijassa-294	329	9	.	.	PUNCT
ijassa-294	330	1	[	[	X
ijassa-294	330	2	12	12	NUM
ijassa-294	330	3	]	]	X
ijassa-294	330	4	g.ai	g.ai	PROPN
ijassa-294	330	5	,	,	PUNCT
ijassa-294	330	6	&	&	CCONJ
ijassa-294	330	7	r.	r.	PROPN
ijassa-294	330	8	hao	hao	PROPN
ijassa-294	330	9	,	,	PUNCT
ijassa-294	330	10	existence	existence	NOUN
ijassa-294	330	11	of	of	ADP
ijassa-294	330	12	solutions	solution	NOUN
ijassa-294	330	13	for	for	ADP
ijassa-294	330	14	a	a	DET
ijassa-294	330	15	p(x)-kirchhoff	p(x)-kirchhoff	NOUN
ijassa-294	330	16	-	-	PUNCT
ijassa-294	330	17	type	type	NOUN
ijassa-294	330	18	equation	equation	NOUN
ijassa-294	330	19	.	.	PUNCT
ijassa-294	331	1	j.	j.	PROPN
ijassa-294	331	2	math	math	PROPN
ijassa-294	331	3	.	.	PUNCT
ijassa-294	332	1	anal	anal	PROPN
ijassa-294	332	2	.	.	PUNCT
ijassa-294	332	3	appl	appl	PROPN
ijassa-294	332	4	.	.	PUNCT
ijassa-294	333	1	359	359	NUM
ijassa-294	333	2	(	(	PUNCT
ijassa-294	333	3	2009	2009	NUM
ijassa-294	333	4	)	)	PUNCT
ijassa-294	333	5	275	275	NUM
ijassa-294	333	6	-	-	SYM
ijassa-294	333	7	284	284	NUM
ijassa-294	333	8	.	.	PUNCT
ijassa-294	334	1	[	[	X
ijassa-294	334	2	13	13	NUM
ijassa-294	334	3	]	]	X
ijassa-294	334	4	dai	dai	PROPN
ijassa-294	334	5	,	,	PUNCT
ijassa-294	334	6	g.	g.	PROPN
ijassa-294	334	7	,	,	PUNCT
ijassa-294	334	8	&	&	CCONJ
ijassa-294	334	9	liu	liu	PROPN
ijassa-294	334	10	,	,	PUNCT
ijassa-294	334	11	d.	d.	PROPN
ijassa-294	334	12	infinitely	infinitely	ADV
ijassa-294	334	13	many	many	ADJ
ijassa-294	334	14	positive	positive	ADJ
ijassa-294	334	15	solutions	solution	NOUN
ijassa-294	334	16	for	for	ADP
ijassa-294	334	17	a	a	DET
ijassa-294	334	18	p(x)-kirchhoff	p(x)-kirchhoff	NOUN
ijassa-294	334	19	-	-	PUNCT
ijassa-294	334	20	type	type	NOUN
ijassa-294	334	21	equation	equation	NOUN
ijassa-294	334	22	.	.	PUNCT
ijassa-294	335	1	j.	j.	PROPN
ijassa-294	335	2	math	math	PROPN
ijassa-294	335	3	.	.	PUNCT
ijassa-294	336	1	anal	anal	PROPN
ijassa-294	336	2	.	.	PUNCT
ijassa-294	336	3	appl	appl	PROPN
ijassa-294	336	4	.	.	PUNCT
ijassa-294	337	1	359	359	NUM
ijassa-294	337	2	(	(	PUNCT
ijassa-294	337	3	2009	2009	NUM
ijassa-294	337	4	)	)	PUNCT
ijassa-294	337	5	704	704	NUM
ijassa-294	337	6	-	-	SYM
ijassa-294	337	7	710	710	NUM
ijassa-294	337	8	.	.	PUNCT
ijassa-294	338	1	[	[	X
ijassa-294	338	2	14	14	NUM
ijassa-294	338	3	]	]	X
ijassa-294	338	4	fan	fan	NOUN
ijassa-294	338	5	,	,	PUNCT
ijassa-294	338	6	x.	x.	PROPN
ijassa-294	338	7	l.	l.	PROPN
ijassa-294	338	8	on	on	ADP
ijassa-294	338	9	nonlocal	nonlocal	ADJ
ijassa-294	338	10	p(x)-laplacian	p(x)-laplacian	ADJ
ijassa-294	338	11	dirichlet	dirichlet	NOUN
ijassa-294	338	12	problems	problem	NOUN
ijassa-294	338	13	.	.	PUNCT
ijassa-294	339	1	nonlinear	nonlinear	ADJ
ijassa-294	339	2	anal	anal	NOUN
ijassa-294	339	3	.	.	PUNCT
ijassa-294	340	1	72	72	NUM
ijassa-294	340	2	(	(	PUNCT
ijassa-294	340	3	2010	2010	NUM
ijassa-294	340	4	)	)	PUNCT
ijassa-294	340	5	3314	3314	NUM
ijassa-294	340	6	-	-	SYM
ijassa-294	340	7	3323	3323	NUM
ijassa-294	340	8	.	.	PUNCT
ijassa-294	341	1	[	[	X
ijassa-294	341	2	15	15	NUM
ijassa-294	341	3	]	]	X
ijassa-294	341	4	he	he	PRON
ijassa-294	341	5	,	,	PUNCT
ijassa-294	341	6	x.	x.	PROPN
ijassa-294	341	7	,	,	PUNCT
ijassa-294	341	8	&	&	CCONJ
ijassa-294	341	9	zou	zou	PROPN
ijassa-294	341	10	,	,	PUNCT
ijassa-294	341	11	w.	w.	PROPN
ijassa-294	341	12	infinitely	infinitely	ADV
ijassa-294	341	13	many	many	ADJ
ijassa-294	341	14	positive	positive	ADJ
ijassa-294	341	15	solutions	solution	NOUN
ijassa-294	341	16	for	for	ADP
ijassa-294	341	17	kirchhoff	kirchhoff	NOUN
ijassa-294	341	18	-	-	PUNCT
ijassa-294	341	19	type	type	NOUN
ijassa-294	341	20	problems	problem	NOUN
ijassa-294	341	21	.	.	PUNCT
ijassa-294	342	1	nonlinear	nonlinear	ADJ
ijassa-294	342	2	anal	anal	NOUN
ijassa-294	342	3	.	.	PUNCT
ijassa-294	343	1	70	70	NUM
ijassa-294	343	2	(	(	PUNCT
ijassa-294	343	3	2009	2009	NUM
ijassa-294	343	4	)	)	PUNCT
ijassa-294	343	5	1407	1407	NUM
ijassa-294	343	6	-	-	SYM
ijassa-294	343	7	1414	1414	NUM
ijassa-294	343	8	.	.	PUNCT
ijassa-294	344	1	[	[	X
ijassa-294	344	2	16	16	NUM
ijassa-294	344	3	]	]	PUNCT
ijassa-294	344	4	allee	allee	PROPN
ijassa-294	344	5	,	,	PUNCT
ijassa-294	344	6	w.	w.	PROPN
ijassa-294	344	7	c.	c.	PROPN
ijassa-294	344	8	the	the	DET
ijassa-294	344	9	social	social	ADJ
ijassa-294	344	10	life	life	NOUN
ijassa-294	344	11	of	of	ADP
ijassa-294	344	12	animals	animal	NOUN
ijassa-294	344	13	.	.	PUNCT
ijassa-294	345	1	w.w	w.w	PROPN
ijassa-294	345	2	norton	norton	PROPN
ijassa-294	345	3	,	,	PUNCT
ijassa-294	345	4	new	new	ADJ
ijassa-294	345	5	york(1938	york(1938	NOUN
ijassa-294	345	6	)	)	PUNCT
ijassa-294	345	7	.	.	PUNCT
ijassa-294	346	1	[	[	X
ijassa-294	346	2	17	17	NUM
ijassa-294	346	3	]	]	X
ijassa-294	346	4	cantrell	cantrell	PROPN
ijassa-294	346	5	,	,	PUNCT
ijassa-294	346	6	r.	r.	PROPN
ijassa-294	346	7	s.	s.	PROPN
ijassa-294	346	8	,	,	PUNCT
ijassa-294	346	9	&	&	CCONJ
ijassa-294	346	10	cosner	cosner	PROPN
ijassa-294	346	11	,	,	PUNCT
ijassa-294	346	12	c.	c.	PROPN
ijassa-294	346	13	spatial	spatial	ADJ
ijassa-294	346	14	ecology	ecology	NOUN
ijassa-294	346	15	via	via	ADP
ijassa-294	346	16	reaction	reaction	NOUN
ijassa-294	346	17	-	-	PUNCT
ijassa-294	346	18	diffusion	diffusion	NOUN
ijassa-294	346	19	equation	equation	NOUN
ijassa-294	346	20	.	.	PUNCT
ijassa-294	347	1	wiley	wiley	PROPN
ijassa-294	347	2	series	series	PROPN
ijassa-294	347	3	in	in	ADP
ijassa-294	347	4	mathematical	mathematical	ADJ
ijassa-294	347	5	and	and	CCONJ
ijassa-294	347	6	computational	computational	ADJ
ijassa-294	347	7	biology	biology	NOUN
ijassa-294	347	8	,	,	PUNCT
ijassa-294	347	9	john	john	PROPN
ijassa-294	347	10	wiley	wiley	PROPN
ijassa-294	347	11	sonsltd	sonsltd	PROPN
ijassa-294	347	12	.	.	PUNCT
ijassa-294	348	1	[	[	X
ijassa-294	348	2	18	18	NUM
ijassa-294	348	3	]	]	PUNCT
ijassa-294	348	4	gilbarg	gilbarg	NOUN
ijassa-294	348	5	,	,	PUNCT
ijassa-294	348	6	d.	d.	PROPN
ijassa-294	348	7	,	,	PUNCT
ijassa-294	348	8	&	&	CCONJ
ijassa-294	348	9	trudinger	trudinger	PROPN
ijassa-294	348	10	,	,	PUNCT
ijassa-294	348	11	s.	s.	PROPN
ijassa-294	348	12	elliptic	elliptic	ADJ
ijassa-294	348	13	partial	partial	ADJ
ijassa-294	348	14	differential	differential	ADJ
ijassa-294	348	15	equations	equation	NOUN
ijassa-294	348	16	of	of	ADP
ijassa-294	348	17	second	second	ADJ
ijassa-294	348	18	order	order	NOUN
ijassa-294	348	19	.	.	PUNCT
ijassa-294	348	20	springer	springer	NOUN
ijassa-294	348	21	-	-	PUNCT
ijassa-294	348	22	verlag	verlag	PROPN
ijassa-294	348	23	,	,	PUNCT
ijassa-294	348	24	berlin	berlin	PROPN
ijassa-294	348	25	.	.	PUNCT
ijassa-294	349	1	[	[	X
ijassa-294	349	2	19	19	NUM
ijassa-294	349	3	]	]	X
ijassa-294	349	4	lieberman	lieberman	PROPN
ijassa-294	349	5	,	,	PUNCT
ijassa-294	349	6	g.	g.	PROPN
ijassa-294	349	7	m.	m.	PROPN
ijassa-294	349	8	boundary	boundary	ADJ
ijassa-294	349	9	regularity	regularity	NOUN
ijassa-294	349	10	for	for	ADP
ijassa-294	349	11	solutions	solution	NOUN
ijassa-294	349	12	of	of	ADP
ijassa-294	349	13	degenerate	degenerate	ADJ
ijassa-294	349	14	elliptic	elliptic	ADJ
ijassa-294	349	15	equations	equation	NOUN
ijassa-294	349	16	.	.	PUNCT
ijassa-294	350	1	nonlinear	nonlinear	ADJ
ijassa-294	350	2	anal	anal	PROPN
ijassa-294	350	3	.	.	PUNCT
ijassa-294	351	1	tma	tma	PROPN
ijassa-294	351	2	12	12	NUM
ijassa-294	351	3	(	(	PUNCT
ijassa-294	351	4	1988	1988	NUM
ijassa-294	351	5	)	)	PUNCT
ijassa-294	351	6	1203	1203	NUM
ijassa-294	351	7	-	-	SYM
ijassa-294	351	8	1219	1219	NUM
ijassa-294	351	9	.	.	PUNCT
ijassa-294	352	1	[	[	X
ijassa-294	352	2	20	20	NUM
ijassa-294	352	3	]	]	SYM
ijassa-294	352	4	lieberman	lieberman	PROPN
ijassa-294	352	5	,	,	PUNCT
ijassa-294	352	6	g.	g.	PROPN
ijassa-294	352	7	m.	m.	PROPN
ijassa-294	352	8	the	the	DET
ijassa-294	352	9	natural	natural	ADJ
ijassa-294	352	10	generalization	generalization	NOUN
ijassa-294	352	11	of	of	ADP
ijassa-294	352	12	the	the	DET
ijassa-294	352	13	natural	natural	ADJ
ijassa-294	352	14	conditions	condition	NOUN
ijassa-294	352	15	of	of	ADP
ijassa-294	352	16	ladyzenskaja	ladyzenskaja	NOUN
ijassa-294	352	17	and	and	CCONJ
ijassa-294	352	18	ural’tzeva	ural’tzeva	PROPN
ijassa-294	352	19	for	for	ADP
ijassa-294	352	20	elliptic	elliptic	ADJ
ijassa-294	352	21	equations	equation	NOUN
ijassa-294	352	22	.	.	PUNCT
ijassa-294	353	1	comm	comm	NOUN
ijassa-294	353	2	.	.	PUNCT
ijassa-294	354	1	partial	partial	ADJ
ijassa-294	354	2	differential	differential	ADJ
ijassa-294	354	3	equations	equation	NOUN
ijassa-294	354	4	16	16	NUM
ijassa-294	354	5	(	(	PUNCT
ijassa-294	354	6	1991	1991	NUM
ijassa-294	354	7	)	)	PUNCT
ijassa-294	354	8	311361	311361	NUM
ijassa-294	354	9	.	.	PUNCT
ijassa-294	355	1	[	[	X
ijassa-294	355	2	21	21	NUM
ijassa-294	355	3	]	]	SYM
ijassa-294	355	4	g.dai	g.dai	PROPN
ijassa-294	355	5	,	,	PUNCT
ijassa-294	355	6	nonsmooth	nonsmooth	ADJ
ijassa-294	355	7	version	version	NOUN
ijassa-294	355	8	of	of	ADP
ijassa-294	355	9	fountain	fountain	NOUN
ijassa-294	355	10	theorem	theorem	NOUN
ijassa-294	355	11	and	and	CCONJ
ijassa-294	355	12	its	its	PRON
ijassa-294	355	13	application	application	NOUN
ijassa-294	355	14	to	to	ADP
ijassa-294	355	15	a	a	DET
ijassa-294	355	16	dirichlet	dirichlet	ADJ
ijassa-294	355	17	-	-	PUNCT
ijassa-294	355	18	type	type	NOUN
ijassa-294	355	19	differential	differential	ADJ
ijassa-294	355	20	inclusion	inclusion	NOUN
ijassa-294	355	21	problem	problem	NOUN
ijassa-294	355	22	.	.	PUNCT
ijassa-294	356	1	nonlinear	nonlinear	ADJ
ijassa-294	356	2	analysis	analysis	NOUN
ijassa-294	356	3	72	72	NUM
ijassa-294	356	4	(	(	PUNCT
ijassa-294	356	5	2010	2010	NUM
ijassa-294	356	6	)	)	PUNCT
ijassa-294	356	7	1454	1454	NUM
ijassa-294	356	8	-	-	SYM
ijassa-294	356	9	1461	1461	NUM
ijassa-294	356	10	[	[	X
ijassa-294	356	11	22	22	NUM
ijassa-294	356	12	]	]	X
ijassa-294	356	13	e.	e.	PROPN
ijassa-294	356	14	n.dancer	n.dancer	PROPN
ijassa-294	356	15	,	,	PUNCT
ijassa-294	356	16	&	&	CCONJ
ijassa-294	356	17	k.	k.	PROPN
ijassa-294	356	18	schmitt	schmitt	PROPN
ijassa-294	356	19	,	,	PUNCT
ijassa-294	356	20	on	on	ADP
ijassa-294	356	21	positive	positive	ADJ
ijassa-294	356	22	solution	solution	NOUN
ijassa-294	356	23	of	of	ADP
ijassa-294	356	24	semilinear	semilinear	ADJ
ijassa-294	356	25	elliptic	elliptic	ADJ
ijassa-294	356	26	equations	equation	NOUN
ijassa-294	356	27	.	.	PUNCT
ijassa-294	357	1	proc	proc	PROPN
ijassa-294	357	2	.	.	PUNCT
ijassa-294	358	1	amer	amer	PROPN
ijassa-294	358	2	.	.	PUNCT
ijassa-294	359	1	math.soc	math.soc	X
ijassa-294	359	2	.	.	PROPN
ijassa-294	360	1	101	101	NUM
ijassa-294	360	2	(	(	PUNCT
ijassa-294	360	3	1987	1987	NUM
ijassa-294	360	4	)	)	PUNCT
ijassa-294	360	5	,	,	PUNCT
ijassa-294	360	6	no.3	no.3	VERB
ijassa-294	360	7	,	,	PUNCT
ijassa-294	360	8	445	445	NUM
ijassa-294	360	9	-	-	SYM
ijassa-294	360	10	452	452	NUM
ijassa-294	360	11	.	.	PUNCT
ijassa-294	361	1	[	[	X
ijassa-294	361	2	23	23	NUM
ijassa-294	361	3	]	]	PUNCT
ijassa-294	361	4	b.	b.	PROPN
ijassa-294	361	5	gidas	gidas	PROPN
ijassa-294	361	6	,	,	PUNCT
ijassa-294	361	7	,	,	PUNCT
ijassa-294	361	8	w.	w.	PROPN
ijassa-294	361	9	ni	ni	PROPN
ijassa-294	361	10	,	,	PUNCT
ijassa-294	361	11	w.	w.	PROPN
ijassa-294	361	12	&	&	CCONJ
ijassa-294	361	13	nirenberg	nirenberg	PROPN
ijassa-294	361	14	,	,	PUNCT
ijassa-294	361	15	l.	l.	PROPN
ijassa-294	361	16	symmetry	symmetry	PROPN
ijassa-294	361	17	and	and	CCONJ
ijassa-294	361	18	related	related	ADJ
ijassa-294	361	19	properties	property	NOUN
ijassa-294	361	20	via	via	ADP
ijassa-294	361	21	the	the	DET
ijassa-294	361	22	maximum	maximum	ADJ
ijassa-294	361	23	principle	principle	NOUN
ijassa-294	361	24	.	.	PUNCT
ijassa-294	362	1	comm	comm	NOUN
ijassa-294	362	2	.	.	PUNCT
ijassa-294	363	1	math	math	NOUN
ijassa-294	363	2	.	.	PUNCT
ijassa-294	364	1	phys	phy	NOUN
ijassa-294	364	2	.	.	PUNCT
ijassa-294	365	1	68	68	NUM
ijassa-294	365	2	(	(	PUNCT
ijassa-294	365	3	1979	1979	NUM
ijassa-294	365	4	)	)	PUNCT
ijassa-294	365	5	,	,	PUNCT
ijassa-294	365	6	209	209	NUM
ijassa-294	365	7	-	-	SYM
ijassa-294	365	8	243	243	NUM
ijassa-294	365	9	.	.	PUNCT
ijassa-294	366	1	[	[	X
ijassa-294	366	2	24	24	NUM
ijassa-294	366	3	]	]	PUNCT
ijassa-294	366	4	m.	m.	NOUN
ijassa-294	366	5	willem	willem	PROPN
ijassa-294	366	6	,	,	PUNCT
ijassa-294	366	7	minimax	minimax	NOUN
ijassa-294	366	8	theorems	theorem	NOUN
ijassa-294	366	9	.	.	PUNCT
ijassa-294	366	10	birkhäuser	birkhäuser	NOUN
ijassa-294	366	11	,	,	PUNCT
ijassa-294	366	12	boston	boston	PROPN
ijassa-294	366	13	.	.	PUNCT
ijassa-294	367	1	[	[	X
ijassa-294	367	2	25	25	NUM
ijassa-294	367	3	]	]	X
ijassa-294	367	4	e.	e.	PROPN
ijassa-294	367	5	n.dancer	n.dancer	PROPN
ijassa-294	367	6	,	,	PUNCT
ijassa-294	367	7	,	,	PUNCT
ijassa-294	367	8	&	&	CCONJ
ijassa-294	367	9	s.	s.	PROPN
ijassa-294	367	10	yan	yan	PROPN
ijassa-294	367	11	,	,	PUNCT
ijassa-294	367	12	construction	construction	NOUN
ijassa-294	367	13	of	of	ADP
ijassa-294	367	14	various	various	ADJ
ijassa-294	367	15	types	type	NOUN
ijassa-294	367	16	of	of	ADP
ijassa-294	367	17	solutions	solution	NOUN
ijassa-294	367	18	for	for	ADP
ijassa-294	367	19	an	an	DET
ijassa-294	367	20	elliptic	elliptic	ADJ
ijassa-294	367	21	problem	problem	NOUN
ijassa-294	367	22	.	.	PUNCT
ijassa-294	368	1	calculus	calculus	NOUN
ijassa-294	368	2	variations	variation	NOUN
ijassa-294	368	3	and	and	CCONJ
ijassa-294	368	4	partial	partial	ADJ
ijassa-294	368	5	differential	differential	ADJ
ijassa-294	368	6	equations	equation	NOUN
ijassa-294	368	7	20(1)(2004	20(1)(2004	NUM
ijassa-294	368	8	)	)	PUNCT
ijassa-294	368	9	,	,	PUNCT
ijassa-294	368	10	93	93	NUM
ijassa-294	368	11	-	-	SYM
ijassa-294	368	12	118	118	NUM
ijassa-294	368	13	.	.	PUNCT