id	sid	tid	token	lemma	pos
ejde-350	1	1	electronic	electronic	ADJ
ejde-350	1	2	journal	journal	NOUN
ejde-350	1	3	of	of	ADP
ejde-350	1	4	differential	differential	ADJ
ejde-350	1	5	equations	equation	NOUN
ejde-350	1	6	,	,	PUNCT
ejde-350	1	7	vol	vol	NOUN
ejde-350	1	8	.	.	PUNCT
ejde-350	1	9	2020	2020	NUM
ejde-350	1	10	(	(	PUNCT
ejde-350	1	11	2020	2020	NUM
ejde-350	1	12	)	)	PUNCT
ejde-350	1	13	,	,	PUNCT
ejde-350	1	14	no	no	INTJ
ejde-350	1	15	.	.	NOUN
ejde-350	1	16	01	01	NUM
ejde-350	1	17	,	,	PUNCT
ejde-350	1	18	pp	pp	ADJ
ejde-350	1	19	.	.	PUNCT
ejde-350	2	1	1–17	1–17	NOUN
ejde-350	2	2	.	.	PUNCT
ejde-350	3	1	issn	issn	PROPN
ejde-350	3	2	:	:	PUNCT
ejde-350	3	3	1072	1072	NUM
ejde-350	3	4	-	-	SYM
ejde-350	3	5	6691	6691	NUM
ejde-350	3	6	.	.	PUNCT
ejde-350	4	1	url	url	PROPN
ejde-350	4	2	:	:	PUNCT
ejde-350	4	3	http://ejde.math.txstate.edu	http://ejde.math.txstate.edu	PROPN
ejde-350	4	4	or	or	CCONJ
ejde-350	4	5	http://ejde.math.unt.edu	http://ejde.math.unt.edu	VERB
ejde-350	4	6	fractional	fractional	ADJ
ejde-350	4	7	schrödinger	schrödinger	NOUN
ejde-350	4	8	-	-	PUNCT
ejde-350	4	9	poisson	poisson	NOUN
ejde-350	4	10	systems	system	NOUN
ejde-350	4	11	with	with	ADP
ejde-350	4	12	weighted	weight	VERB
ejde-350	4	13	hardy	hardy	ADJ
ejde-350	4	14	potential	potential	ADJ
ejde-350	4	15	and	and	CCONJ
ejde-350	4	16	critical	critical	ADJ
ejde-350	4	17	exponent	exponent	PROPN
ejde-350	4	18	yu	yu	PROPN
ejde-350	4	19	su	su	PROPN
ejde-350	4	20	,	,	PUNCT
ejde-350	4	21	haibo	haibo	PROPN
ejde-350	4	22	chen	chen	PROPN
ejde-350	4	23	,	,	PUNCT
ejde-350	4	24	senli	senli	PROPN
ejde-350	4	25	liu	liu	PROPN
ejde-350	4	26	,	,	PUNCT
ejde-350	4	27	xianwen	xianwen	PROPN
ejde-350	4	28	fang	fang	PROPN
ejde-350	4	29	communicated	communicate	VERB
ejde-350	4	30	by	by	ADP
ejde-350	4	31	claudianor	claudianor	PROPN
ejde-350	4	32	o.	o.	PROPN
ejde-350	4	33	alves	alves	PROPN
ejde-350	4	34	abstract	abstract	PROPN
ejde-350	4	35	.	.	PUNCT
ejde-350	5	1	in	in	ADP
ejde-350	5	2	this	this	DET
ejde-350	5	3	article	article	NOUN
ejde-350	5	4	we	we	PRON
ejde-350	5	5	consider	consider	VERB
ejde-350	5	6	the	the	DET
ejde-350	5	7	fractional	fractional	ADJ
ejde-350	5	8	schrödinger	schrödinger	NOUN
ejde-350	5	9	-	-	PUNCT
ejde-350	5	10	poisson	poisson	NOUN
ejde-350	5	11	system	system	NOUN
ejde-350	5	12	(	(	PUNCT
ejde-350	5	13	−∆)su−	−∆)su−	PROPN
ejde-350	5	14	µ	µ	PRON
ejde-350	5	15	φ(x/|x|	φ(x/|x|	NOUN
ejde-350	5	16	)	)	PUNCT
ejde-350	5	17	|x|2s	|x|2s	ADJ
ejde-350	5	18	u+	u+	NUM
ejde-350	5	19	λφu	λφu	NOUN
ejde-350	5	20	=	=	SYM
ejde-350	5	21	|u|2	|u|2	PROPN
ejde-350	5	22	∗	∗	PROPN
ejde-350	5	23	s−2u	s−2u	PROPN
ejde-350	5	24	,	,	PUNCT
ejde-350	5	25	in	in	ADP
ejde-350	5	26	r3	r3	PROPN
ejde-350	5	27	,	,	PUNCT
ejde-350	5	28	(	(	PUNCT
ejde-350	5	29	−∆)tφ	−∆)tφ	NOUN
ejde-350	5	30	=	=	SYM
ejde-350	5	31	u2	u2	PROPN
ejde-350	5	32	,	,	PUNCT
ejde-350	5	33	in	in	ADP
ejde-350	5	34	r3	r3	PROPN
ejde-350	5	35	,	,	PUNCT
ejde-350	6	1	where	where	SCONJ
ejde-350	6	2	s	s	VERB
ejde-350	6	3	∈	∈	PROPN
ejde-350	6	4	(	(	PUNCT
ejde-350	6	5	0	0	NUM
ejde-350	6	6	,	,	PUNCT
ejde-350	6	7	3/4	3/4	NUM
ejde-350	6	8	)	)	PUNCT
ejde-350	6	9	,	,	PUNCT
ejde-350	6	10	t	t	PROPN
ejde-350	6	11	∈	∈	PROPN
ejde-350	6	12	(	(	PUNCT
ejde-350	6	13	0	0	NUM
ejde-350	6	14	,	,	PUNCT
ejde-350	6	15	1	1	NUM
ejde-350	6	16	)	)	PUNCT
ejde-350	6	17	,	,	PUNCT
ejde-350	6	18	2	2	NUM
ejde-350	6	19	t	t	NOUN
ejde-350	6	20	+	+	CCONJ
ejde-350	6	21	4s	4s	NUM
ejde-350	6	22	=	=	SYM
ejde-350	6	23	3	3	NUM
ejde-350	6	24	,	,	PUNCT
ejde-350	6	25	λ	λ	X
ejde-350	6	26	>	>	X
ejde-350	6	27	0	0	NUM
ejde-350	6	28	and	and	CCONJ
ejde-350	6	29	2∗s	2∗s	NUM
ejde-350	6	30	=	=	SYM
ejde-350	6	31	6/(3	6/(3	NUM
ejde-350	6	32	−	−	NOUN
ejde-350	6	33	2s	2s	NUM
ejde-350	6	34	)	)	PUNCT
ejde-350	6	35	is	be	AUX
ejde-350	6	36	the	the	DET
ejde-350	6	37	sobolev	sobolev	ADJ
ejde-350	6	38	critical	critical	ADJ
ejde-350	6	39	exponent	exponent	NOUN
ejde-350	6	40	.	.	PUNCT
ejde-350	7	1	by	by	ADP
ejde-350	7	2	using	use	VERB
ejde-350	7	3	perturbation	perturbation	NOUN
ejde-350	7	4	method	method	NOUN
ejde-350	7	5	,	,	PUNCT
ejde-350	7	6	we	we	PRON
ejde-350	7	7	establish	establish	VERB
ejde-350	7	8	the	the	DET
ejde-350	7	9	existence	existence	NOUN
ejde-350	7	10	of	of	ADP
ejde-350	7	11	a	a	DET
ejde-350	7	12	solution	solution	NOUN
ejde-350	7	13	for	for	ADP
ejde-350	7	14	λ	λ	NOUN
ejde-350	7	15	small	small	ADJ
ejde-350	7	16	enough	enough	ADV
ejde-350	7	17	.	.	PUNCT
ejde-350	8	1	1	1	X
ejde-350	8	2	.	.	X
ejde-350	8	3	introduction	introduction	NOUN
ejde-350	8	4	in	in	ADP
ejde-350	8	5	this	this	DET
ejde-350	8	6	article	article	NOUN
ejde-350	8	7	we	we	PRON
ejde-350	8	8	consider	consider	VERB
ejde-350	8	9	the	the	DET
ejde-350	8	10	fractional	fractional	ADJ
ejde-350	8	11	schrödinger	schrödinger	NOUN
ejde-350	8	12	-	-	PUNCT
ejde-350	8	13	poisson	poisson	NOUN
ejde-350	8	14	system	system	NOUN
ejde-350	8	15	(	(	PUNCT
ejde-350	8	16	−∆)su−	−∆)su−	PROPN
ejde-350	8	17	µφ(x/|x|	µφ(x/|x|	NOUN
ejde-350	8	18	)	)	PUNCT
ejde-350	8	19	|x|2s	|x|2s	ADJ
ejde-350	8	20	u+	u+	NUM
ejde-350	8	21	λφu	λφu	NOUN
ejde-350	8	22	=	=	SYM
ejde-350	8	23	|u|2	|u|2	PROPN
ejde-350	8	24	∗	∗	PROPN
ejde-350	8	25	s−2u	s−2u	PROPN
ejde-350	8	26	,	,	PUNCT
ejde-350	8	27	in	in	ADP
ejde-350	8	28	r3	r3	PROPN
ejde-350	8	29	,	,	PUNCT
ejde-350	8	30	(	(	PUNCT
ejde-350	8	31	−∆)tφ	−∆)tφ	NOUN
ejde-350	8	32	=	=	SYM
ejde-350	8	33	u2	u2	PROPN
ejde-350	8	34	,	,	PUNCT
ejde-350	8	35	in	in	ADP
ejde-350	8	36	r3	r3	PROPN
ejde-350	8	37	,	,	PUNCT
ejde-350	8	38	(	(	PUNCT
ejde-350	8	39	1.1	1.1	NUM
ejde-350	8	40	)	)	PUNCT
ejde-350	8	41	where	where	SCONJ
ejde-350	8	42	s	s	VERB
ejde-350	8	43	∈	∈	PROPN
ejde-350	8	44	(	(	PUNCT
ejde-350	8	45	0	0	NUM
ejde-350	8	46	,	,	PUNCT
ejde-350	8	47	3/4	3/4	NUM
ejde-350	8	48	)	)	PUNCT
ejde-350	8	49	,	,	PUNCT
ejde-350	8	50	t	t	PROPN
ejde-350	8	51	∈	∈	PROPN
ejde-350	8	52	(	(	PUNCT
ejde-350	8	53	0	0	NUM
ejde-350	8	54	,	,	PUNCT
ejde-350	8	55	1	1	NUM
ejde-350	8	56	)	)	PUNCT
ejde-350	8	57	,	,	PUNCT
ejde-350	8	58	2t+	2t+	NUM
ejde-350	8	59	4s	4s	NUM
ejde-350	8	60	=	=	SYM
ejde-350	8	61	3	3	NUM
ejde-350	8	62	,	,	PUNCT
ejde-350	8	63	λ	λ	X
ejde-350	8	64	>	>	X
ejde-350	8	65	0	0	NUM
ejde-350	8	66	and	and	CCONJ
ejde-350	8	67	2∗s	2∗s	NUM
ejde-350	8	68	=	=	SYM
ejde-350	8	69	6/(3−	6/(3−	NUM
ejde-350	8	70	2s	2s	NUM
ejde-350	8	71	)	)	PUNCT
ejde-350	8	72	is	be	AUX
ejde-350	8	73	the	the	DET
ejde-350	8	74	sobolev	sobolev	ADJ
ejde-350	8	75	critical	critical	ADJ
ejde-350	8	76	exponent	exponent	NOUN
ejde-350	8	77	.	.	PUNCT
ejde-350	9	1	the	the	DET
ejde-350	9	2	function	function	NOUN
ejde-350	9	3	φ	φ	PROPN
ejde-350	9	4	and	and	CCONJ
ejde-350	9	5	the	the	DET
ejde-350	9	6	parameter	parameter	NOUN
ejde-350	9	7	µ	µ	X
ejde-350	9	8	satisfy	satisfy	VERB
ejde-350	9	9	the	the	DET
ejde-350	9	10	condition	condition	NOUN
ejde-350	9	11	(	(	PUNCT
ejde-350	9	12	a1	a1	NOUN
ejde-350	9	13	)	)	PUNCT
ejde-350	9	14	if	if	SCONJ
ejde-350	9	15	0	0	NUM
ejde-350	9	16	6	6	NUM
ejde-350	9	17	φ	φ	NUM
ejde-350	9	18	∈	∈	PROPN
ejde-350	9	19	l	l	NOUN
ejde-350	9	20	3	3	NUM
ejde-350	9	21	2s	2s	PROPN
ejde-350	9	22	(	(	PUNCT
ejde-350	9	23	s2	s2	PROPN
ejde-350	9	24	)	)	PUNCT
ejde-350	9	25	then	then	ADV
ejde-350	9	26	µ	µ	PROPN
ejde-350	9	27	∈	∈	PROPN
ejde-350	9	28	(	(	PUNCT
ejde-350	9	29	0,λ(φ	0,λ(φ	NUM
ejde-350	9	30	)	)	PUNCT
ejde-350	9	31	)	)	PUNCT
ejde-350	9	32	,	,	PUNCT
ejde-350	9	33	where	where	SCONJ
ejde-350	9	34	λ(φ	λ(φ	NOUN
ejde-350	9	35	)	)	PUNCT
ejde-350	9	36	is	be	AUX
ejde-350	9	37	defined	define	VERB
ejde-350	9	38	in	in	ADP
ejde-350	9	39	lemma	lemma	PROPN
ejde-350	9	40	2.1	2.1	NUM
ejde-350	9	41	below	below	ADV
ejde-350	9	42	.	.	PUNCT
ejde-350	10	1	in	in	ADP
ejde-350	10	2	quantum	quantum	ADJ
ejde-350	10	3	mechanics	mechanic	NOUN
ejde-350	10	4	a	a	DET
ejde-350	10	5	zero	zero	NUM
ejde-350	10	6	spin	spin	NOUN
ejde-350	10	7	relativistic	relativistic	ADJ
ejde-350	10	8	particle	particle	NOUN
ejde-350	10	9	of	of	ADP
ejde-350	10	10	charge	charge	NOUN
ejde-350	10	11	e	e	NOUN
ejde-350	10	12	and	and	CCONJ
ejde-350	10	13	mass	mass	PROPN
ejde-350	10	14	m	m	PROPN
ejde-350	10	15	in	in	ADP
ejde-350	10	16	the	the	DET
ejde-350	10	17	coulomb	coulomb	NOUN
ejde-350	10	18	field	field	NOUN
ejde-350	10	19	of	of	ADP
ejde-350	10	20	an	an	DET
ejde-350	10	21	infinitely	infinitely	ADV
ejde-350	10	22	heavy	heavy	ADJ
ejde-350	10	23	nucleus	nucleus	NOUN
ejde-350	10	24	of	of	ADP
ejde-350	10	25	charge	charge	NOUN
ejde-350	10	26	z	z	PROPN
ejde-350	10	27	is	be	AUX
ejde-350	10	28	described	describe	VERB
ejde-350	10	29	by	by	ADP
ejde-350	10	30	the	the	DET
ejde-350	10	31	hamiltonian	hamiltonian	NOUN
ejde-350	10	32	(	(	PUNCT
ejde-350	10	33	see	see	VERB
ejde-350	10	34	e.g.	e.g.	ADV
ejde-350	10	35	[	[	X
ejde-350	10	36	23	23	NUM
ejde-350	10	37	,	,	PUNCT
ejde-350	10	38	28	28	NUM
ejde-350	10	39	]	]	PUNCT
ejde-350	10	40	)	)	PUNCT
ejde-350	10	41	h(p	h(p	NOUN
ejde-350	10	42	,	,	PUNCT
ejde-350	10	43	x	x	X
ejde-350	10	44	)	)	PUNCT
ejde-350	10	45	=	=	SYM
ejde-350	10	46	(	(	PUNCT
ejde-350	10	47	p2	p2	PROPN
ejde-350	10	48	+	+	SYM
ejde-350	10	49	m2)1/2	m2)1/2	PROPN
ejde-350	11	1	−	−	PROPN
ejde-350	12	1	ze2	ze2	NOUN
ejde-350	13	1	|x|	|x|	PROPN
ejde-350	13	2	.	.	PUNCT
ejde-350	14	1	fall	fall	VERB
ejde-350	14	2	and	and	CCONJ
ejde-350	14	3	felli	felli	VERB
ejde-350	15	1	[	[	X
ejde-350	15	2	16	16	NUM
ejde-350	15	3	]	]	PUNCT
ejde-350	15	4	,	,	PUNCT
ejde-350	15	5	extended	extend	VERB
ejde-350	15	6	the	the	DET
ejde-350	15	7	study	study	NOUN
ejde-350	15	8	of	of	ADP
ejde-350	15	9	h(p	h(p	PROPN
ejde-350	15	10	,	,	PUNCT
ejde-350	15	11	x	x	NOUN
ejde-350	15	12	)	)	PUNCT
ejde-350	15	13	to	to	ADP
ejde-350	15	14	h̃(p	h̃(p	NOUN
ejde-350	15	15	,	,	PUNCT
ejde-350	15	16	x	x	NOUN
ejde-350	15	17	)	)	PUNCT
ejde-350	15	18	=	=	SYM
ejde-350	15	19	(	(	PUNCT
ejde-350	15	20	p2	p2	X
ejde-350	15	21	+	+	PROPN
ejde-350	15	22	m2)s	m2)s	NOUN
ejde-350	15	23	−	−	PROPN
ejde-350	15	24	φ	φ	PROPN
ejde-350	15	25	(	(	PUNCT
ejde-350	15	26	x	x	SYM
ejde-350	15	27	|x|	|x|	PROPN
ejde-350	15	28	)	)	PUNCT
ejde-350	15	29	|x|2s	|x|2s	NOUN
ejde-350	15	30	.	.	PUNCT
ejde-350	16	1	2010	2010	NUM
ejde-350	16	2	mathematics	mathematic	NOUN
ejde-350	16	3	subject	subject	NOUN
ejde-350	16	4	classification	classification	NOUN
ejde-350	16	5	.	.	PUNCT
ejde-350	17	1	35b38	35b38	NUM
ejde-350	17	2	,	,	PUNCT
ejde-350	17	3	35j47	35j47	NUM
ejde-350	17	4	.	.	PUNCT
ejde-350	18	1	key	key	ADJ
ejde-350	18	2	words	word	NOUN
ejde-350	18	3	and	and	CCONJ
ejde-350	18	4	phrases	phrase	NOUN
ejde-350	18	5	.	.	PUNCT
ejde-350	19	1	fractional	fractional	ADJ
ejde-350	19	2	schrödinger	schrödinger	NOUN
ejde-350	19	3	-	-	PUNCT
ejde-350	19	4	poisson	poisson	NOUN
ejde-350	19	5	system	system	NOUN
ejde-350	19	6	;	;	PUNCT
ejde-350	19	7	weighted	weight	VERB
ejde-350	19	8	hardy	hardy	ADJ
ejde-350	19	9	potential	potential	NOUN
ejde-350	19	10	;	;	PUNCT
ejde-350	19	11	critical	critical	ADJ
ejde-350	19	12	exponent	exponent	NOUN
ejde-350	19	13	.	.	PUNCT
ejde-350	20	1	c	c	X
ejde-350	20	2	©	©	PROPN
ejde-350	20	3	2020	2020	NUM
ejde-350	20	4	texas	texas	PROPN
ejde-350	20	5	state	state	PROPN
ejde-350	20	6	university	university	PROPN
ejde-350	20	7	.	.	PUNCT
ejde-350	21	1	submitted	submit	VERB
ejde-350	21	2	october	october	PROPN
ejde-350	21	3	24	24	NUM
ejde-350	21	4	,	,	PUNCT
ejde-350	21	5	2019	2019	NUM
ejde-350	21	6	.	.	PUNCT
ejde-350	22	1	published	publish	VERB
ejde-350	22	2	january	january	PROPN
ejde-350	22	3	6	6	NUM
ejde-350	22	4	,	,	PUNCT
ejde-350	22	5	2020	2020	NUM
ejde-350	22	6	.	.	PUNCT
ejde-350	23	1	1	1	NUM
ejde-350	23	2	2	2	NUM
ejde-350	23	3	y.	y.	PROPN
ejde-350	23	4	su	su	PROPN
ejde-350	23	5	,	,	PUNCT
ejde-350	23	6	h.	h.	PROPN
ejde-350	23	7	chen	chen	PROPN
ejde-350	23	8	,	,	PUNCT
ejde-350	23	9	s.	s.	PROPN
ejde-350	23	10	liu	liu	PROPN
ejde-350	23	11	,	,	PUNCT
ejde-350	23	12	x.	x.	PROPN
ejde-350	23	13	fang	fang	PROPN
ejde-350	23	14	ejde-2020/01	ejde-2020/01	NOUN
ejde-350	23	15	they	they	PRON
ejde-350	23	16	considered	consider	VERB
ejde-350	23	17	the	the	DET
ejde-350	23	18	operator	operator	NOUN
ejde-350	23	19	h̃(i∇	h̃(i∇	NOUN
ejde-350	23	20	,	,	PUNCT
ejde-350	23	21	x	x	NOUN
ejde-350	23	22	)	)	PUNCT
ejde-350	23	23	=	=	SYM
ejde-350	23	24	(	(	PUNCT
ejde-350	24	1	−∆	−∆	X
ejde-350	24	2	+	+	NOUN
ejde-350	24	3	m2)s	m2)s	NOUN
ejde-350	24	4	−	−	PROPN
ejde-350	24	5	φ	φ	PROPN
ejde-350	24	6	(	(	PUNCT
ejde-350	24	7	x	x	SYM
ejde-350	24	8	|x|	|x|	PROPN
ejde-350	24	9	)	)	PUNCT
ejde-350	24	10	|x|2s	|x|2s	NOUN
ejde-350	24	11	.	.	PUNCT
ejde-350	25	1	for	for	ADP
ejde-350	25	2	φ	φ	PROPN
ejde-350	25	3	≡	≡	PROPN
ejde-350	25	4	0	0	PROPN
ejde-350	25	5	,	,	PUNCT
ejde-350	25	6	the	the	DET
ejde-350	25	7	operator	operator	NOUN
ejde-350	25	8	h̃(i∇	h̃(i∇	NOUN
ejde-350	25	9	,	,	PUNCT
ejde-350	25	10	x	x	NOUN
ejde-350	25	11	)	)	PUNCT
ejde-350	25	12	becomes	become	VERB
ejde-350	25	13	(	(	PUNCT
ejde-350	25	14	−∆	−∆	X
ejde-350	25	15	+	+	NUM
ejde-350	25	16	m2)s	m2)s	NOUN
ejde-350	25	17	,	,	PUNCT
ejde-350	25	18	for	for	ADP
ejde-350	25	19	more	more	ADJ
ejde-350	25	20	details	detail	NOUN
ejde-350	25	21	,	,	PUNCT
ejde-350	25	22	we	we	PRON
ejde-350	25	23	refer	refer	VERB
ejde-350	25	24	to	to	ADP
ejde-350	25	25	[	[	X
ejde-350	25	26	2	2	NUM
ejde-350	25	27	,	,	PUNCT
ejde-350	25	28	3	3	NUM
ejde-350	25	29	]	]	PUNCT
ejde-350	25	30	.	.	PUNCT
ejde-350	26	1	in	in	ADP
ejde-350	26	2	this	this	DET
ejde-350	26	3	article	article	NOUN
ejde-350	26	4	,	,	PUNCT
ejde-350	26	5	we	we	PRON
ejde-350	26	6	study	study	VERB
ejde-350	26	7	h̃(i∇	h̃(i∇	ADJ
ejde-350	26	8	,	,	PUNCT
ejde-350	26	9	x	x	NOUN
ejde-350	26	10	)	)	PUNCT
ejde-350	26	11	,	,	PUNCT
ejde-350	26	12	i.	i.	PROPN
ejde-350	26	13	e.	e.	PROPN
ejde-350	26	14	when	when	SCONJ
ejde-350	26	15	m	m	VERB
ejde-350	26	16	=	=	NOUN
ejde-350	26	17	0	0	NUM
ejde-350	26	18	.	.	PUNCT
ejde-350	27	1	in	in	ADP
ejde-350	27	2	nonrelativistic	nonrelativistic	ADJ
ejde-350	27	3	molecular	molecular	ADJ
ejde-350	27	4	physics	physics	NOUN
ejde-350	27	5	,	,	PUNCT
ejde-350	27	6	the	the	DET
ejde-350	27	7	interaction	interaction	NOUN
ejde-350	27	8	between	between	ADP
ejde-350	27	9	an	an	DET
ejde-350	27	10	electric	electric	ADJ
ejde-350	27	11	charge	charge	NOUN
ejde-350	27	12	and	and	CCONJ
ejde-350	27	13	the	the	DET
ejde-350	27	14	dipole	dipole	NOUN
ejde-350	27	15	moment	moment	NOUN
ejde-350	27	16	d	d	X
ejde-350	27	17	∈	∈	PROPN
ejde-350	27	18	rn	rn	PROPN
ejde-350	27	19	of	of	ADP
ejde-350	27	20	a	a	DET
ejde-350	27	21	molecule	molecule	NOUN
ejde-350	27	22	is	be	AUX
ejde-350	27	23	described	describe	VERB
ejde-350	27	24	by	by	ADP
ejde-350	27	25	an	an	DET
ejde-350	27	26	inverse	inverse	ADJ
ejde-350	27	27	square	square	NOUN
ejde-350	27	28	potential	potential	NOUN
ejde-350	27	29	with	with	ADP
ejde-350	27	30	an	an	DET
ejde-350	27	31	anisotropic	anisotropic	NOUN
ejde-350	27	32	coupling	coupling	NOUN
ejde-350	27	33	strength	strength	NOUN
ejde-350	27	34	.	.	PUNCT
ejde-350	28	1	in	in	ADP
ejde-350	28	2	particular	particular	ADJ
ejde-350	28	3	the	the	DET
ejde-350	28	4	schrödinger	schrödinger	NOUN
ejde-350	28	5	equation	equation	NOUN
ejde-350	28	6	for	for	ADP
ejde-350	28	7	the	the	DET
ejde-350	28	8	wave	wave	NOUN
ejde-350	28	9	function	function	NOUN
ejde-350	28	10	of	of	ADP
ejde-350	28	11	an	an	DET
ejde-350	28	12	electron	electron	NOUN
ejde-350	28	13	interacting	interact	VERB
ejde-350	28	14	with	with	ADP
ejde-350	28	15	a	a	DET
ejde-350	28	16	polar	polar	ADJ
ejde-350	28	17	molecule	molecule	NOUN
ejde-350	28	18	(	(	PUNCT
ejde-350	28	19	supposed	suppose	VERB
ejde-350	28	20	to	to	PART
ejde-350	28	21	be	be	AUX
ejde-350	28	22	point	point	NOUN
ejde-350	28	23	-	-	PUNCT
ejde-350	28	24	like	like	ADJ
ejde-350	28	25	)	)	PUNCT
ejde-350	28	26	can	can	AUX
ejde-350	28	27	be	be	AUX
ejde-350	28	28	written	write	VERB
ejde-350	28	29	as	as	ADP
ejde-350	28	30	h	h	NOUN
ejde-350	28	31	=	=	PUNCT
ejde-350	29	1	−	−	PROPN
ejde-350	29	2	~	~	PUNCT
ejde-350	29	3	2	2	NUM
ejde-350	29	4	m	m	NOUN
ejde-350	29	5	∆	∆	NOUN
ejde-350	30	1	+	+	CCONJ
ejde-350	30	2	e	e	X
ejde-350	30	3	x	x	PUNCT
ejde-350	30	4	·	·	PUNCT
ejde-350	30	5	d	d	X
ejde-350	30	6	|x|3	|x|3	PROPN
ejde-350	30	7	−	−	PROPN
ejde-350	30	8	e	e	NOUN
ejde-350	30	9	,	,	PUNCT
ejde-350	30	10	where	where	SCONJ
ejde-350	30	11	d	d	NOUN
ejde-350	30	12	is	be	AUX
ejde-350	30	13	the	the	DET
ejde-350	30	14	dipole	dipole	ADJ
ejde-350	30	15	moment	moment	NOUN
ejde-350	30	16	of	of	ADP
ejde-350	30	17	the	the	DET
ejde-350	30	18	molecule	molecule	NOUN
ejde-350	30	19	,	,	PUNCT
ejde-350	30	20	e	e	NOUN
ejde-350	30	21	and	and	CCONJ
ejde-350	30	22	m	m	PROPN
ejde-350	30	23	denote	denote	VERB
ejde-350	30	24	the	the	DET
ejde-350	30	25	charge	charge	NOUN
ejde-350	30	26	and	and	CCONJ
ejde-350	30	27	the	the	DET
ejde-350	30	28	mass	mass	NOUN
ejde-350	30	29	of	of	ADP
ejde-350	30	30	the	the	DET
ejde-350	30	31	electron	electron	NOUN
ejde-350	30	32	(	(	PUNCT
ejde-350	30	33	see	see	VERB
ejde-350	30	34	[	[	X
ejde-350	30	35	26	26	NUM
ejde-350	30	36	]	]	NUM
ejde-350	30	37	)	)	PUNCT
ejde-350	30	38	.	.	PUNCT
ejde-350	31	1	we	we	PRON
ejde-350	31	2	consider	consider	VERB
ejde-350	31	3	the	the	DET
ejde-350	31	4	operator	operator	NOUN
ejde-350	31	5	ld	ld	NOUN
ejde-350	31	6	:	:	PUNCT
ejde-350	31	7	=	=	SYM
ejde-350	31	8	−∆−	−∆−	PROPN
ejde-350	31	9	2me|d|	2me|d|	NUM
ejde-350	31	10	~	~	PUNCT
ejde-350	31	11	x	x	SYM
ejde-350	31	12	·	·	PUNCT
ejde-350	31	13	d	d	X
ejde-350	31	14	|x|3	|x|3	PROPN
ejde-350	31	15	,	,	PUNCT
ejde-350	31	16	in	in	ADP
ejde-350	31	17	rn	rn	PROPN
ejde-350	31	18	,	,	PUNCT
ejde-350	31	19	where	where	SCONJ
ejde-350	31	20	n	n	X
ejde-350	31	21	>	>	X
ejde-350	31	22	3	3	NUM
ejde-350	31	23	,	,	PUNCT
ejde-350	31	24	being	be	AUX
ejde-350	31	25	|d|	|d|	PROPN
ejde-350	31	26	the	the	DET
ejde-350	31	27	magnitude	magnitude	NOUN
ejde-350	31	28	of	of	ADP
ejde-350	31	29	the	the	DET
ejde-350	31	30	dipole	dipole	NOUN
ejde-350	31	31	moment	moment	NOUN
ejde-350	31	32	d	d	NOUN
ejde-350	31	33	,	,	PUNCT
ejde-350	31	34	and	and	CCONJ
ejde-350	31	35	d	d	X
ejde-350	31	36	=	=	SYM
ejde-350	31	37	d	d	PROPN
ejde-350	31	38	|d|	|d|	PROPN
ejde-350	31	39	denotes	denote	VERB
ejde-350	31	40	the	the	DET
ejde-350	31	41	orientation	orientation	NOUN
ejde-350	31	42	of	of	ADP
ejde-350	31	43	d.	d.	PROPN
ejde-350	31	44	the	the	DET
ejde-350	31	45	laplace	laplace	NOUN
ejde-350	31	46	operator	operator	NOUN
ejde-350	31	47	with	with	ADP
ejde-350	31	48	dipole	dipole	NOUN
ejde-350	31	49	-	-	PUNCT
ejde-350	31	50	type	type	NOUN
ejde-350	31	51	potential	potential	NOUN
ejde-350	31	52	(	(	PUNCT
ejde-350	31	53	purely	purely	ADV
ejde-350	31	54	angular	angular	ADJ
ejde-350	31	55	multiples	multiple	NOUN
ejde-350	31	56	of	of	ADP
ejde-350	31	57	radial	radial	ADJ
ejde-350	31	58	inverse	inverse	NOUN
ejde-350	31	59	square	square	ADJ
ejde-350	31	60	potentials	potential	NOUN
ejde-350	31	61	):	):	PUNCT
ejde-350	31	62	lφ	lφ	X
ejde-350	31	63	:	:	PUNCT
ejde-350	31	64	=	=	SYM
ejde-350	31	65	−∆−	−∆−	NUM
ejde-350	31	66	µφ(x/|x|	µφ(x/|x|	NOUN
ejde-350	31	67	)	)	PUNCT
ejde-350	31	68	|x|2	|x|2	NOUN
ejde-350	31	69	,	,	PUNCT
ejde-350	31	70	in	in	ADP
ejde-350	31	71	rn	rn	PROPN
ejde-350	31	72	,	,	PUNCT
ejde-350	31	73	where	where	SCONJ
ejde-350	31	74	n	n	X
ejde-350	31	75	>	>	X
ejde-350	31	76	3	3	X
ejde-350	31	77	.	.	X
ejde-350	32	1	we	we	PRON
ejde-350	32	2	consider	consider	VERB
ejde-350	32	3	the	the	DET
ejde-350	32	4	more	more	ADV
ejde-350	32	5	general	general	ADJ
ejde-350	32	6	class	class	NOUN
ejde-350	32	7	of	of	ADP
ejde-350	32	8	operator	operator	NOUN
ejde-350	32	9	h̃(i∇	h̃(i∇	NOUN
ejde-350	32	10	,	,	PUNCT
ejde-350	32	11	x	x	NOUN
ejde-350	32	12	)	)	PUNCT
ejde-350	32	13	with	with	ADP
ejde-350	32	14	zero	zero	NUM
ejde-350	32	15	mass	mass	PROPN
ejde-350	32	16	,	,	PUNCT
ejde-350	32	17	ls	ls	PROPN
ejde-350	32	18	,	,	PUNCT
ejde-350	32	19	φ	φ	NOUN
ejde-350	32	20	:	:	PUNCT
ejde-350	32	21	=	=	SYM
ejde-350	32	22	(	(	PUNCT
ejde-350	32	23	−∆)s	−∆)s	NOUN
ejde-350	32	24	−	−	PROPN
ejde-350	32	25	µφ(x/|x|	µφ(x/|x|	SYM
ejde-350	32	26	)	)	PUNCT
ejde-350	32	27	|x|2s	|x|2s	NOUN
ejde-350	32	28	.	.	PUNCT
ejde-350	33	1	if	if	SCONJ
ejde-350	33	2	φ	φ	PROPN
ejde-350	33	3	≡	≡	PROPN
ejde-350	33	4	0	0	NUM
ejde-350	33	5	,	,	PUNCT
ejde-350	33	6	then	then	ADV
ejde-350	33	7	ls	ls	PROPN
ejde-350	33	8	,	,	PUNCT
ejde-350	33	9	φ	φ	PROPN
ejde-350	33	10	becomes	become	VERB
ejde-350	33	11	the	the	DET
ejde-350	33	12	fractional	fractional	ADJ
ejde-350	33	13	laplacian	laplacian	ADJ
ejde-350	33	14	operator	operator	NOUN
ejde-350	33	15	(	(	PUNCT
ejde-350	33	16	−∆)s	−∆)s	NOUN
ejde-350	33	17	.	.	PUNCT
ejde-350	34	1	if	if	SCONJ
ejde-350	34	2	φ	φ	PROPN
ejde-350	34	3	≡	≡	PROPN
ejde-350	34	4	1	1	NUM
ejde-350	34	5	,	,	PUNCT
ejde-350	34	6	then	then	ADV
ejde-350	34	7	ls	ls	PROPN
ejde-350	34	8	,	,	PUNCT
ejde-350	34	9	φ	φ	PROPN
ejde-350	34	10	is	be	AUX
ejde-350	34	11	the	the	DET
ejde-350	34	12	fractional	fractional	ADJ
ejde-350	34	13	laplacian	laplacian	ADJ
ejde-350	34	14	operator	operator	NOUN
ejde-350	34	15	with	with	ADP
ejde-350	34	16	hardy	hardy	ADJ
ejde-350	34	17	potential	potential	NOUN
ejde-350	34	18	(	(	PUNCT
ejde-350	34	19	−∆)s	−∆)s	PROPN
ejde-350	34	20	−	−	PROPN
ejde-350	34	21	µ	µ	PRON
ejde-350	34	22	|x|2s	|x|2s	NOUN
ejde-350	34	23	.	.	PUNCT
ejde-350	35	1	if	if	SCONJ
ejde-350	35	2	s	s	NOUN
ejde-350	35	3	=	=	SYM
ejde-350	35	4	1	1	NUM
ejde-350	35	5	,	,	PUNCT
ejde-350	35	6	then	then	ADV
ejde-350	35	7	ls	ls	PROPN
ejde-350	35	8	,	,	PUNCT
ejde-350	35	9	φ	φ	PROPN
ejde-350	35	10	becomes	become	VERB
ejde-350	35	11	lφ	lφ	ADP
ejde-350	35	12	.	.	PUNCT
ejde-350	36	1	from	from	ADP
ejde-350	36	2	the	the	DET
ejde-350	36	3	mathematical	mathematical	ADJ
ejde-350	36	4	point	point	NOUN
ejde-350	36	5	of	of	ADP
ejde-350	36	6	view	view	NOUN
ejde-350	36	7	,	,	PUNCT
ejde-350	36	8	a	a	DET
ejde-350	36	9	reason	reason	NOUN
ejde-350	36	10	of	of	ADP
ejde-350	36	11	interest	interest	NOUN
ejde-350	36	12	in	in	ADP
ejde-350	36	13	potentials	potential	NOUN
ejde-350	36	14	of	of	ADP
ejde-350	36	15	the	the	DET
ejde-350	36	16	type	type	NOUN
ejde-350	36	17	φ	φ	NOUN
ejde-350	36	18	(	(	PUNCT
ejde-350	36	19	x	x	PROPN
ejde-350	36	20	|x|	|x|	PROPN
ejde-350	36	21	)	)	PUNCT
ejde-350	36	22	/|x|	/|x|	PUNCT
ejde-350	37	1	2s	2s	NUM
ejde-350	37	2	relies	rely	VERB
ejde-350	37	3	in	in	ADP
ejde-350	37	4	their	their	PRON
ejde-350	37	5	criticality	criticality	NOUN
ejde-350	37	6	with	with	ADP
ejde-350	37	7	respect	respect	NOUN
ejde-350	37	8	to	to	ADP
ejde-350	37	9	the	the	DET
ejde-350	37	10	differential	differential	ADJ
ejde-350	37	11	operator	operator	NOUN
ejde-350	37	12	(	(	PUNCT
ejde-350	37	13	−∆)s	−∆)s	NOUN
ejde-350	37	14	;	;	PUNCT
ejde-350	37	15	indeed	indeed	ADV
ejde-350	37	16	,	,	PUNCT
ejde-350	37	17	they	they	PRON
ejde-350	37	18	have	have	VERB
ejde-350	37	19	the	the	DET
ejde-350	37	20	same	same	ADJ
ejde-350	37	21	homogeneity	homogeneity	NOUN
ejde-350	37	22	as	as	ADP
ejde-350	37	23	the	the	DET
ejde-350	37	24	fractional	fractional	ADJ
ejde-350	37	25	laplacian	laplacian	NOUN
ejde-350	37	26	(	(	PUNCT
ejde-350	37	27	−∆)s	−∆)s	NOUN
ejde-350	37	28	,	,	PUNCT
ejde-350	37	29	hence	hence	ADV
ejde-350	37	30	they	they	PRON
ejde-350	37	31	can	can	AUX
ejde-350	37	32	not	not	PART
ejde-350	37	33	be	be	AUX
ejde-350	37	34	regarded	regard	VERB
ejde-350	37	35	as	as	ADP
ejde-350	37	36	a	a	DET
ejde-350	37	37	lower	low	ADJ
ejde-350	37	38	order	order	NOUN
ejde-350	37	39	perturbation	perturbation	NOUN
ejde-350	37	40	term	term	NOUN
ejde-350	37	41	.	.	PUNCT
ejde-350	38	1	we	we	PRON
ejde-350	38	2	mention	mention	VERB
ejde-350	38	3	that	that	SCONJ
ejde-350	38	4	the	the	DET
ejde-350	38	5	operator	operator	NOUN
ejde-350	38	6	with	with	ADP
ejde-350	38	7	singular	singular	ADJ
ejde-350	38	8	potentials	potential	NOUN
ejde-350	38	9	have	have	AUX
ejde-350	38	10	been	be	AUX
ejde-350	38	11	widely	widely	ADV
ejde-350	38	12	studied	study	VERB
ejde-350	38	13	,	,	PUNCT
ejde-350	38	14	see	see	VERB
ejde-350	38	15	for	for	ADP
ejde-350	38	16	example	example	NOUN
ejde-350	38	17	[	[	X
ejde-350	38	18	1	1	NUM
ejde-350	38	19	,	,	PUNCT
ejde-350	38	20	13	13	NUM
ejde-350	38	21	,	,	PUNCT
ejde-350	38	22	14	14	NUM
ejde-350	38	23	,	,	PUNCT
ejde-350	38	24	15	15	NUM
ejde-350	38	25	,	,	PUNCT
ejde-350	38	26	17	17	NUM
ejde-350	38	27	,	,	PUNCT
ejde-350	38	28	18	18	NUM
ejde-350	38	29	,	,	PUNCT
ejde-350	38	30	19	19	NUM
ejde-350	38	31	,	,	PUNCT
ejde-350	38	32	20	20	NUM
ejde-350	38	33	,	,	PUNCT
ejde-350	38	34	21	21	NUM
ejde-350	38	35	,	,	PUNCT
ejde-350	38	36	34	34	NUM
ejde-350	38	37	,	,	PUNCT
ejde-350	38	38	36	36	NUM
ejde-350	38	39	,	,	PUNCT
ejde-350	38	40	38	38	NUM
ejde-350	38	41	,	,	PUNCT
ejde-350	38	42	39	39	NUM
ejde-350	38	43	]	]	PUNCT
ejde-350	38	44	and	and	CCONJ
ejde-350	38	45	references	reference	NOUN
ejde-350	38	46	therein	therein	ADV
ejde-350	38	47	.	.	PUNCT
ejde-350	39	1	on	on	ADP
ejde-350	39	2	the	the	DET
ejde-350	39	3	other	other	ADJ
ejde-350	39	4	hand	hand	NOUN
ejde-350	39	5	,	,	PUNCT
ejde-350	39	6	if	if	SCONJ
ejde-350	39	7	µ	µ	X
ejde-350	39	8	=	=	SYM
ejde-350	39	9	0	0	NUM
ejde-350	39	10	and	and	CCONJ
ejde-350	39	11	λ	λ	X
ejde-350	39	12	=	=	NOUN
ejde-350	39	13	1	1	NUM
ejde-350	39	14	,	,	PUNCT
ejde-350	39	15	then	then	ADV
ejde-350	39	16	system	system	NOUN
ejde-350	39	17	(	(	PUNCT
ejde-350	39	18	1.1	1.1	NUM
ejde-350	39	19	)	)	PUNCT
ejde-350	39	20	becomes	become	VERB
ejde-350	39	21	the	the	DET
ejde-350	39	22	system	system	NOUN
ejde-350	39	23	:	:	PUNCT
ejde-350	39	24	(	(	PUNCT
ejde-350	39	25	−∆)su+	−∆)su+	NOUN
ejde-350	39	26	φu	φu	NOUN
ejde-350	39	27	=	=	PUNCT
ejde-350	39	28	|u|2	|u|2	PROPN
ejde-350	39	29	∗	∗	PROPN
ejde-350	39	30	s−2u	s−2u	PROPN
ejde-350	39	31	,	,	PUNCT
ejde-350	39	32	in	in	ADP
ejde-350	39	33	r3	r3	PROPN
ejde-350	39	34	,	,	PUNCT
ejde-350	39	35	(	(	PUNCT
ejde-350	39	36	−∆)tφ	−∆)tφ	NOUN
ejde-350	39	37	=	=	SYM
ejde-350	39	38	u2	u2	PROPN
ejde-350	39	39	,	,	PUNCT
ejde-350	39	40	in	in	ADP
ejde-350	39	41	r3	r3	PROPN
ejde-350	39	42	.	.	PUNCT
ejde-350	40	1	(	(	PUNCT
ejde-350	40	2	1.2	1.2	NUM
ejde-350	40	3	)	)	PUNCT
ejde-350	40	4	for	for	ADP
ejde-350	40	5	this	this	DET
ejde-350	40	6	system	system	NOUN
ejde-350	40	7	there	there	PRON
ejde-350	40	8	are	be	VERB
ejde-350	40	9	four	four	NUM
ejde-350	40	10	cases	case	NOUN
ejde-350	40	11	:	:	PUNCT
ejde-350	40	12	(	(	PUNCT
ejde-350	40	13	i	i	NOUN
ejde-350	40	14	)	)	PUNCT
ejde-350	40	15	s	s	PART
ejde-350	40	16	=	=	X
ejde-350	40	17	t	t	X
ejde-350	40	18	=	=	SYM
ejde-350	40	19	1	1	NUM
ejde-350	40	20	;	;	PUNCT
ejde-350	40	21	(	(	PUNCT
ejde-350	40	22	ii	ii	NOUN
ejde-350	40	23	)	)	PUNCT
ejde-350	40	24	s	s	PART
ejde-350	40	25	=	=	SYM
ejde-350	40	26	1	1	NUM
ejde-350	40	27	and	and	CCONJ
ejde-350	40	28	t	t	PROPN
ejde-350	40	29	6=	6=	PROPN
ejde-350	40	30	1	1	NUM
ejde-350	40	31	;	;	PUNCT
ejde-350	40	32	(	(	PUNCT
ejde-350	40	33	iii	iii	X
ejde-350	40	34	)	)	PUNCT
ejde-350	40	35	s	s	PART
ejde-350	40	36	=	=	X
ejde-350	40	37	t	t	PROPN
ejde-350	40	38	6=	6=	PROPN
ejde-350	40	39	1	1	NUM
ejde-350	40	40	;	;	PUNCT
ejde-350	40	41	(	(	PUNCT
ejde-350	40	42	iv	iv	X
ejde-350	40	43	)	)	PUNCT
ejde-350	40	44	s	s	PART
ejde-350	40	45	6=	6=	NUM
ejde-350	40	46	1	1	NUM
ejde-350	40	47	,	,	PUNCT
ejde-350	40	48	t	t	PROPN
ejde-350	40	49	6=	6=	PROPN
ejde-350	40	50	1	1	NUM
ejde-350	40	51	,	,	PUNCT
ejde-350	40	52	and	and	CCONJ
ejde-350	40	53	2t+	2t+	NUM
ejde-350	40	54	4s	4s	NUM
ejde-350	40	55	>	>	X
ejde-350	40	56	3	3	X
ejde-350	40	57	.	.	PUNCT
ejde-350	41	1	(	(	PUNCT
ejde-350	41	2	i	i	NOUN
ejde-350	41	3	)	)	PUNCT
ejde-350	41	4	for	for	ADP
ejde-350	41	5	s	s	NOUN
ejde-350	41	6	=	=	X
ejde-350	41	7	t	t	X
ejde-350	41	8	=	=	SYM
ejde-350	41	9	1	1	NUM
ejde-350	41	10	,	,	PUNCT
ejde-350	41	11	system	system	NOUN
ejde-350	41	12	(	(	PUNCT
ejde-350	41	13	1.2	1.2	NUM
ejde-350	41	14	)	)	PUNCT
ejde-350	41	15	reduces	reduce	VERB
ejde-350	41	16	to	to	ADP
ejde-350	41	17	the	the	DET
ejde-350	41	18	schrödinger	schrödinger	NOUN
ejde-350	41	19	–	–	PUNCT
ejde-350	41	20	poisson	poisson	NOUN
ejde-350	41	21	system	system	NOUN
ejde-350	41	22	−∆u+	−∆u+	NOUN
ejde-350	41	23	φu	φu	NOUN
ejde-350	41	24	=	=	PROPN
ejde-350	41	25	|u|p−2u	|u|p−2u	PROPN
ejde-350	41	26	,	,	PUNCT
ejde-350	41	27	in	in	ADP
ejde-350	41	28	r3	r3	PROPN
ejde-350	41	29	,	,	PUNCT
ejde-350	41	30	−∆φ	−∆φ	X
ejde-350	41	31	=	=	PROPN
ejde-350	41	32	u2	u2	PROPN
ejde-350	41	33	,	,	PUNCT
ejde-350	41	34	in	in	ADP
ejde-350	41	35	r3	r3	PROPN
ejde-350	41	36	.	.	PUNCT
ejde-350	42	1	(	(	PUNCT
ejde-350	42	2	1.3	1.3	NUM
ejde-350	42	3	)	)	PUNCT
ejde-350	42	4	ejde-2020/01	ejde-2020/01	NOUN
ejde-350	42	5	fractional	fractional	ADJ
ejde-350	42	6	schrödinger	schrödinger	NOUN
ejde-350	42	7	-	-	PUNCT
ejde-350	42	8	poisson	poisson	NOUN
ejde-350	42	9	system	system	NOUN
ejde-350	42	10	3	3	NUM
ejde-350	42	11	the	the	DET
ejde-350	42	12	schrödinger	schrödinger	NOUN
ejde-350	42	13	-	-	PUNCT
ejde-350	42	14	poisson	poisson	NOUN
ejde-350	42	15	system	system	NOUN
ejde-350	42	16	arises	arise	VERB
ejde-350	42	17	in	in	ADP
ejde-350	42	18	many	many	ADJ
ejde-350	42	19	mathematical	mathematical	ADJ
ejde-350	42	20	physical	physical	ADJ
ejde-350	42	21	context	context	NOUN
ejde-350	42	22	,	,	PUNCT
ejde-350	42	23	such	such	ADJ
ejde-350	42	24	as	as	ADP
ejde-350	42	25	in	in	ADP
ejde-350	42	26	quantum	quantum	ADJ
ejde-350	42	27	electrodynamics	electrodynamic	NOUN
ejde-350	42	28	,	,	PUNCT
ejde-350	42	29	to	to	PART
ejde-350	42	30	describe	describe	VERB
ejde-350	42	31	the	the	DET
ejde-350	42	32	interaction	interaction	NOUN
ejde-350	42	33	between	between	ADP
ejde-350	42	34	a	a	DET
ejde-350	42	35	charge	charge	NOUN
ejde-350	42	36	particle	particle	NOUN
ejde-350	42	37	interacting	interact	VERB
ejde-350	42	38	with	with	ADP
ejde-350	42	39	the	the	DET
ejde-350	42	40	electromagnetic	electromagnetic	ADJ
ejde-350	42	41	field	field	NOUN
ejde-350	42	42	,	,	PUNCT
ejde-350	42	43	and	and	CCONJ
ejde-350	42	44	in	in	ADP
ejde-350	42	45	semiconductor	semiconductor	NOUN
ejde-350	42	46	theory	theory	NOUN
ejde-350	42	47	,	,	PUNCT
ejde-350	42	48	in	in	ADP
ejde-350	42	49	nonlinear	nonlinear	ADJ
ejde-350	42	50	optics	optic	NOUN
ejde-350	42	51	and	and	CCONJ
ejde-350	42	52	in	in	ADP
ejde-350	42	53	plasma	plasma	NOUN
ejde-350	42	54	physics	physics	NOUN
ejde-350	42	55	(	(	PUNCT
ejde-350	42	56	see	see	VERB
ejde-350	42	57	[	[	X
ejde-350	42	58	8	8	NUM
ejde-350	42	59	]	]	PUNCT
ejde-350	42	60	for	for	ADP
ejde-350	42	61	more	more	ADJ
ejde-350	42	62	details	detail	NOUN
ejde-350	42	63	in	in	ADP
ejde-350	42	64	the	the	DET
ejde-350	42	65	physics	physics	NOUN
ejde-350	42	66	aspects	aspect	NOUN
ejde-350	42	67	)	)	PUNCT
ejde-350	42	68	.	.	PUNCT
ejde-350	43	1	system	system	NOUN
ejde-350	43	2	(	(	PUNCT
ejde-350	43	3	1.3	1.3	NUM
ejde-350	43	4	)	)	PUNCT
ejde-350	43	5	has	have	AUX
ejde-350	43	6	been	be	AUX
ejde-350	43	7	investigated	investigate	VERB
ejde-350	43	8	by	by	ADP
ejde-350	43	9	many	many	ADJ
ejde-350	43	10	researchers	researcher	NOUN
ejde-350	43	11	,	,	PUNCT
ejde-350	43	12	see	see	VERB
ejde-350	43	13	for	for	ADP
ejde-350	43	14	example	example	NOUN
ejde-350	43	15	:	:	PUNCT
ejde-350	44	1	[	[	X
ejde-350	44	2	6	6	NUM
ejde-350	44	3	,	,	PUNCT
ejde-350	44	4	11	11	NUM
ejde-350	44	5	]	]	PUNCT
ejde-350	44	6	for	for	ADP
ejde-350	44	7	|u|p−2u	|u|p−2u	PROPN
ejde-350	44	8	(	(	PUNCT
ejde-350	44	9	4	4	NUM
ejde-350	44	10	<	<	X
ejde-350	44	11	p	p	X
ejde-350	44	12	<	<	X
ejde-350	44	13	6	6	NUM
ejde-350	44	14	)	)	PUNCT
ejde-350	44	15	,	,	PUNCT
ejde-350	44	16	[	[	X
ejde-350	44	17	47	47	NUM
ejde-350	44	18	]	]	PUNCT
ejde-350	44	19	for	for	ADP
ejde-350	44	20	|u|p−2u	|u|p−2u	PROPN
ejde-350	44	21	(	(	PUNCT
ejde-350	44	22	3	3	NUM
ejde-350	44	23	<	<	X
ejde-350	44	24	p	p	X
ejde-350	44	25	<	<	X
ejde-350	44	26	4	4	NUM
ejde-350	44	27	)	)	PUNCT
ejde-350	44	28	,	,	PUNCT
ejde-350	45	1	[	[	X
ejde-350	45	2	40	40	NUM
ejde-350	45	3	]	]	PUNCT
ejde-350	45	4	for	for	ADP
ejde-350	45	5	|u|p−2u	|u|p−2u	PROPN
ejde-350	45	6	(	(	PUNCT
ejde-350	45	7	1	1	NUM
ejde-350	45	8	<	<	X
ejde-350	45	9	p	p	X
ejde-350	45	10	<	<	X
ejde-350	45	11	2	2	NUM
ejde-350	45	12	)	)	PUNCT
ejde-350	45	13	.	.	PUNCT
ejde-350	46	1	(	(	PUNCT
ejde-350	46	2	ii	ii	NOUN
ejde-350	46	3	)	)	PUNCT
ejde-350	46	4	for	for	ADP
ejde-350	46	5	s	s	NOUN
ejde-350	46	6	=	=	SYM
ejde-350	46	7	1	1	NUM
ejde-350	46	8	and	and	CCONJ
ejde-350	46	9	t	t	PROPN
ejde-350	46	10	6=	6=	NUM
ejde-350	46	11	1	1	NUM
ejde-350	46	12	,	,	PUNCT
ejde-350	46	13	mercuri	mercuri	ADJ
ejde-350	46	14	,	,	PUNCT
ejde-350	46	15	moroz	moroz	ADJ
ejde-350	46	16	and	and	CCONJ
ejde-350	46	17	van	van	PROPN
ejde-350	46	18	schaftingen	schaftingen	NOUN
ejde-350	47	1	[	[	X
ejde-350	47	2	32	32	NUM
ejde-350	47	3	]	]	PUNCT
ejde-350	47	4	studied	study	VERB
ejde-350	47	5	the	the	DET
ejde-350	47	6	schrödinger	schrödinger	NOUN
ejde-350	47	7	–	–	PUNCT
ejde-350	47	8	poisson	poisson	NOUN
ejde-350	47	9	–	–	PUNCT
ejde-350	47	10	slater	slater	NOUN
ejde-350	47	11	equation	equation	NOUN
ejde-350	47	12	−∆u+	−∆u+	NOUN
ejde-350	47	13	(	(	PUNCT
ejde-350	47	14	iα	iα	INTJ
ejde-350	47	15	∗	∗	NOUN
ejde-350	47	16	|u|q	|u|q	PROPN
ejde-350	47	17	)	)	PUNCT
ejde-350	48	1	|u|q−2u	|u|q−2u	NOUN
ejde-350	48	2	=	=	SYM
ejde-350	48	3	|u|p−2u	|u|p−2u	PROPN
ejde-350	48	4	,	,	PUNCT
ejde-350	48	5	in	in	ADP
ejde-350	48	6	r3	r3	PROPN
ejde-350	48	7	,	,	PUNCT
ejde-350	48	8	(	(	PUNCT
ejde-350	48	9	1.4	1.4	NUM
ejde-350	48	10	)	)	PUNCT
ejde-350	48	11	where	where	SCONJ
ejde-350	48	12	p	p	X
ejde-350	48	13	>	>	X
ejde-350	48	14	1	1	NUM
ejde-350	48	15	,	,	PUNCT
ejde-350	48	16	q	q	ADJ
ejde-350	48	17	>	>	X
ejde-350	48	18	1	1	NUM
ejde-350	48	19	,	,	PUNCT
ejde-350	48	20	α	α	PROPN
ejde-350	48	21	∈	∈	PROPN
ejde-350	48	22	(	(	PUNCT
ejde-350	48	23	0	0	NUM
ejde-350	48	24	,	,	PUNCT
ejde-350	48	25	n	n	CCONJ
ejde-350	48	26	)	)	PUNCT
ejde-350	48	27	,	,	PUNCT
ejde-350	48	28	and	and	CCONJ
ejde-350	48	29	iα	iα	VERB
ejde-350	48	30	=	=	SYM
ejde-350	48	31	γ	γ	X
ejde-350	48	32	(	(	PUNCT
ejde-350	48	33	3−α	3−α	NUM
ejde-350	48	34	2	2	NUM
ejde-350	48	35	)	)	PUNCT
ejde-350	48	36	2απ	2απ	NOUN
ejde-350	48	37	3	3	NUM
ejde-350	48	38	2	2	NUM
ejde-350	48	39	γ(α2	γ(α2	NOUN
ejde-350	48	40	)	)	PUNCT
ejde-350	48	41	·	·	PUNCT
ejde-350	49	1	1	1	NUM
ejde-350	49	2	|x|3−α	|x|3−α	X
ejde-350	49	3	is	be	AUX
ejde-350	49	4	the	the	DET
ejde-350	49	5	riesz	riesz	NOUN
ejde-350	49	6	potential	potential	NOUN
ejde-350	49	7	.	.	PUNCT
ejde-350	50	1	equation	equation	NOUN
ejde-350	50	2	(	(	PUNCT
ejde-350	50	3	1.4	1.4	NUM
ejde-350	50	4	)	)	PUNCT
ejde-350	50	5	is	be	AUX
ejde-350	50	6	formally	formally	ADV
ejde-350	50	7	equivalent	equivalent	ADJ
ejde-350	50	8	to	to	ADP
ejde-350	50	9	the	the	DET
ejde-350	50	10	following	follow	VERB
ejde-350	50	11	system	system	NOUN
ejde-350	50	12	(	(	PUNCT
ejde-350	50	13	see	see	VERB
ejde-350	50	14	[	[	X
ejde-350	50	15	32	32	NUM
ejde-350	50	16	,	,	PUNCT
ejde-350	50	17	page	page	NOUN
ejde-350	50	18	146	146	NUM
ejde-350	50	19	,	,	PUNCT
ejde-350	50	20	line	line	NOUN
ejde-350	50	21	10	10	NUM
ejde-350	50	22	]	]	PUNCT
ejde-350	50	23	):	):	PUNCT
ejde-350	51	1	−∆u+	−∆u+	NOUN
ejde-350	51	2	φ|u|q−2u	φ|u|q−2u	PROPN
ejde-350	51	3	=	=	SYM
ejde-350	51	4	|u|p−2u	|u|p−2u	PROPN
ejde-350	51	5	,	,	PUNCT
ejde-350	51	6	in	in	ADP
ejde-350	51	7	r3	r3	PROPN
ejde-350	51	8	,	,	PUNCT
ejde-350	51	9	(	(	PUNCT
ejde-350	51	10	−∆)α/2φ	−∆)α/2φ	NOUN
ejde-350	51	11	=	=	SYM
ejde-350	52	1	|u|q	|u|q	PROPN
ejde-350	52	2	,	,	PUNCT
ejde-350	52	3	in	in	ADP
ejde-350	52	4	r3	r3	PROPN
ejde-350	52	5	.	.	PUNCT
ejde-350	53	1	(	(	PUNCT
ejde-350	53	2	1.5	1.5	NUM
ejde-350	53	3	)	)	PUNCT
ejde-350	53	4	the	the	DET
ejde-350	53	5	existence	existence	NOUN
ejde-350	53	6	of	of	ADP
ejde-350	53	7	nonnegative	nonnegative	ADJ
ejde-350	53	8	ground	ground	NOUN
ejde-350	53	9	state	state	NOUN
ejde-350	53	10	solution	solution	NOUN
ejde-350	53	11	of	of	ADP
ejde-350	53	12	(	(	PUNCT
ejde-350	53	13	1.4	1.4	NUM
ejde-350	53	14	)	)	PUNCT
ejde-350	53	15	was	be	AUX
ejde-350	53	16	established	establish	VERB
ejde-350	53	17	when	when	SCONJ
ejde-350	53	18	the	the	DET
ejde-350	53	19	parameters	parameter	NOUN
ejde-350	53	20	satisfy	satisfy	VERB
ejde-350	53	21	:	:	PUNCT
ejde-350	53	22	either	either	CCONJ
ejde-350	53	23	q	q	X
ejde-350	53	24	>	>	X
ejde-350	53	25	3	3	NUM
ejde-350	53	26	+	+	CCONJ
ejde-350	53	27	α	α	NOUN
ejde-350	53	28	and	and	CCONJ
ejde-350	53	29	2(α+	2(α+	NUM
ejde-350	53	30	2q	2q	NOUN
ejde-350	53	31	)	)	PUNCT
ejde-350	53	32	α+	α+	X
ejde-350	53	33	2	2	NUM
ejde-350	53	34	<	<	X
ejde-350	53	35	p	p	X
ejde-350	53	36	<	<	X
ejde-350	53	37	6	6	NUM
ejde-350	53	38	,	,	PUNCT
ejde-350	53	39	or	or	CCONJ
ejde-350	53	40	q	q	ADJ
ejde-350	53	41	<	<	X
ejde-350	53	42	3	3	NUM
ejde-350	53	43	+	+	SYM
ejde-350	53	44	α	α	NOUN
ejde-350	53	45	and	and	CCONJ
ejde-350	53	46	6	6	NUM
ejde-350	53	47	<	<	X
ejde-350	53	48	p	p	X
ejde-350	53	49	<	<	X
ejde-350	53	50	2(α+	2(α+	NUM
ejde-350	53	51	2q	2q	NOUN
ejde-350	53	52	)	)	PUNCT
ejde-350	53	53	α+	α+	DET
ejde-350	53	54	2	2	NUM
ejde-350	53	55	.	.	PUNCT
ejde-350	54	1	see	see	VERB
ejde-350	54	2	[	[	X
ejde-350	54	3	32	32	NUM
ejde-350	54	4	,	,	PUNCT
ejde-350	54	5	theorem	theorem	VERB
ejde-350	54	6	3	3	NUM
ejde-350	54	7	]	]	PUNCT
ejde-350	54	8	.	.	PUNCT
ejde-350	55	1	moreover	moreover	ADV
ejde-350	55	2	,	,	PUNCT
ejde-350	55	3	some	some	DET
ejde-350	55	4	qualitative	qualitative	ADJ
ejde-350	55	5	properties	property	NOUN
ejde-350	55	6	of	of	ADP
ejde-350	55	7	the	the	DET
ejde-350	55	8	solutions	solution	NOUN
ejde-350	55	9	were	be	AUX
ejde-350	55	10	estudied	estudie	VERB
ejde-350	55	11	.	.	PUNCT
ejde-350	56	1	li	li	PROPN
ejde-350	56	2	,	,	PUNCT
ejde-350	56	3	gao	gao	PROPN
ejde-350	56	4	and	and	CCONJ
ejde-350	56	5	zhu	zhu	PROPN
ejde-350	57	1	[	[	X
ejde-350	57	2	27	27	NUM
ejde-350	57	3	]	]	PUNCT
ejde-350	57	4	proved	prove	VERB
ejde-350	57	5	the	the	DET
ejde-350	57	6	existence	existence	NOUN
ejde-350	57	7	of	of	ADP
ejde-350	57	8	sign	sign	NOUN
ejde-350	57	9	-	-	PUNCT
ejde-350	57	10	changing	change	VERB
ejde-350	57	11	solution	solution	NOUN
ejde-350	57	12	of	of	ADP
ejde-350	57	13	kirchhoff	kirchhoff	NOUN
ejde-350	57	14	type	type	NOUN
ejde-350	57	15	system	system	NOUN
ejde-350	57	16	with	with	ADP
ejde-350	57	17	hartree	hartree	ADJ
ejde-350	57	18	-	-	PUNCT
ejde-350	57	19	type	type	NOUN
ejde-350	57	20	nonlinearity	nonlinearity	NOUN
ejde-350	57	21	−(a+	−(a+	NOUN
ejde-350	57	22	b	b	NOUN
ejde-350	57	23	∫	∫	PROPN
ejde-350	57	24	r3	r3	PROPN
ejde-350	57	25	|∇u|2dx)∆u+	|∇u|2dx)∆u+	VERB
ejde-350	57	26	λv	λv	X
ejde-350	57	27	(	(	PUNCT
ejde-350	57	28	x)u+	x)u+	PROPN
ejde-350	57	29	φ|u|q−2u	φ|u|q−2u	PROPN
ejde-350	57	30	=	=	SYM
ejde-350	57	31	f(u	f(u	PROPN
ejde-350	57	32	)	)	PUNCT
ejde-350	57	33	,	,	PUNCT
ejde-350	57	34	in	in	ADP
ejde-350	57	35	r3	r3	PROPN
ejde-350	57	36	,	,	PUNCT
ejde-350	57	37	(	(	PUNCT
ejde-350	57	38	−∆)α/2φ	−∆)α/2φ	NOUN
ejde-350	57	39	=	=	SYM
ejde-350	57	40	l|u|q	l|u|q	PROPN
ejde-350	57	41	,	,	PUNCT
ejde-350	57	42	in	in	ADP
ejde-350	57	43	r3	r3	PROPN
ejde-350	57	44	,	,	PUNCT
ejde-350	57	45	(	(	PUNCT
ejde-350	57	46	1.6	1.6	NUM
ejde-350	57	47	)	)	PUNCT
ejde-350	57	48	where	where	SCONJ
ejde-350	57	49	a	a	DET
ejde-350	57	50	>	>	X
ejde-350	57	51	0	0	NUM
ejde-350	57	52	,	,	PUNCT
ejde-350	57	53	b	b	NOUN
ejde-350	57	54	,	,	PUNCT
ejde-350	57	55	l	l	NOUN
ejde-350	57	56	>	>	X
ejde-350	57	57	0	0	PROPN
ejde-350	57	58	,	,	PUNCT
ejde-350	57	59	α	α	PROPN
ejde-350	57	60	∈	∈	PROPN
ejde-350	57	61	(	(	PUNCT
ejde-350	57	62	0	0	NUM
ejde-350	57	63	,	,	PUNCT
ejde-350	57	64	3	3	NUM
ejde-350	57	65	)	)	PUNCT
ejde-350	57	66	,	,	PUNCT
ejde-350	58	1	q	q	PROPN
ejde-350	58	2	∈	∈	PROPN
ejde-350	59	1	[	[	X
ejde-350	59	2	2	2	NUM
ejde-350	59	3	,	,	PUNCT
ejde-350	59	4	3	3	NUM
ejde-350	59	5	+	+	SYM
ejde-350	59	6	α	α	NOUN
ejde-350	59	7	)	)	PUNCT
ejde-350	59	8	,	,	PUNCT
ejde-350	59	9	λ	λ	X
ejde-350	59	10	>	>	X
ejde-350	59	11	0	0	PUNCT
ejde-350	59	12	is	be	AUX
ejde-350	59	13	a	a	DET
ejde-350	59	14	parameter	parameter	NOUN
ejde-350	59	15	,	,	PUNCT
ejde-350	59	16	and	and	CCONJ
ejde-350	59	17	the	the	DET
ejde-350	59	18	functions	function	NOUN
ejde-350	59	19	v	v	VERB
ejde-350	59	20	and	and	CCONJ
ejde-350	59	21	f	f	PROPN
ejde-350	59	22	satisfy	satisfy	VERB
ejde-350	59	23	suitable	suitable	ADJ
ejde-350	59	24	assumptions	assumption	NOUN
ejde-350	59	25	.	.	PUNCT
ejde-350	60	1	for	for	ADP
ejde-350	60	2	recent	recent	ADJ
ejde-350	60	3	works	work	NOUN
ejde-350	60	4	,	,	PUNCT
ejde-350	60	5	we	we	PRON
ejde-350	60	6	refer	refer	VERB
ejde-350	60	7	to	to	ADP
ejde-350	60	8	[	[	X
ejde-350	60	9	4	4	NUM
ejde-350	60	10	]	]	PUNCT
ejde-350	60	11	and	and	CCONJ
ejde-350	60	12	the	the	DET
ejde-350	60	13	references	reference	NOUN
ejde-350	60	14	therein	therein	ADV
ejde-350	60	15	.	.	PUNCT
ejde-350	61	1	(	(	PUNCT
ejde-350	61	2	iii	iii	X
ejde-350	61	3	)	)	PUNCT
ejde-350	61	4	for	for	ADP
ejde-350	61	5	s	s	NOUN
ejde-350	61	6	=	=	X
ejde-350	61	7	t	t	PROPN
ejde-350	61	8	6=	6=	NUM
ejde-350	61	9	1	1	NUM
ejde-350	61	10	,	,	PUNCT
ejde-350	61	11	the	the	DET
ejde-350	61	12	author	author	NOUN
ejde-350	61	13	in	in	ADP
ejde-350	61	14	[	[	X
ejde-350	61	15	43	43	NUM
ejde-350	61	16	]	]	PUNCT
ejde-350	61	17	applied	apply	VERB
ejde-350	61	18	the	the	DET
ejde-350	61	19	fountain	fountain	NOUN
ejde-350	61	20	theorem	theorem	ADJ
ejde-350	61	21	to	to	PART
ejde-350	61	22	prove	prove	VERB
ejde-350	61	23	the	the	DET
ejde-350	61	24	existence	existence	NOUN
ejde-350	61	25	of	of	ADP
ejde-350	61	26	infinitely	infinitely	ADV
ejde-350	61	27	many	many	ADJ
ejde-350	61	28	solutions	solution	NOUN
ejde-350	61	29	to	to	ADP
ejde-350	61	30	the	the	DET
ejde-350	61	31	system	system	NOUN
ejde-350	61	32	(	(	PUNCT
ejde-350	61	33	−∆)su+	−∆)su+	NOUN
ejde-350	61	34	v	v	X
ejde-350	61	35	(	(	PUNCT
ejde-350	61	36	x)u+	x)u+	NOUN
ejde-350	61	37	φu	φu	NOUN
ejde-350	61	38	=	=	SYM
ejde-350	61	39	f(x	f(x	PROPN
ejde-350	61	40	,	,	PUNCT
ejde-350	61	41	u	u	NOUN
ejde-350	61	42	)	)	PUNCT
ejde-350	61	43	,	,	PUNCT
ejde-350	61	44	in	in	ADP
ejde-350	61	45	r3	r3	PROPN
ejde-350	61	46	,	,	PUNCT
ejde-350	61	47	(	(	PUNCT
ejde-350	61	48	−∆)sφ	−∆)sφ	NOUN
ejde-350	61	49	=	=	SYM
ejde-350	61	50	γsu	γsu	PROPN
ejde-350	61	51	2	2	NUM
ejde-350	61	52	,	,	PUNCT
ejde-350	61	53	in	in	ADP
ejde-350	61	54	r3	r3	PROPN
ejde-350	61	55	.	.	PUNCT
ejde-350	62	1	(	(	PUNCT
ejde-350	62	2	iv	iv	X
ejde-350	62	3	)	)	PUNCT
ejde-350	62	4	for	for	ADP
ejde-350	62	5	s	s	PROPN
ejde-350	62	6	6=	6=	PROPN
ejde-350	62	7	1	1	NUM
ejde-350	62	8	,	,	PUNCT
ejde-350	62	9	t	t	PROPN
ejde-350	62	10	6=	6=	NUM
ejde-350	62	11	1	1	NUM
ejde-350	62	12	and	and	CCONJ
ejde-350	62	13	2t+	2t+	NUM
ejde-350	62	14	4s	4s	NUM
ejde-350	62	15	>	>	SYM
ejde-350	62	16	3	3	NUM
ejde-350	62	17	,	,	PUNCT
ejde-350	62	18	zhang	zhang	PROPN
ejde-350	62	19	,	,	PUNCT
ejde-350	62	20	do	do	VERB
ejde-350	62	21	ó	ó	NOUN
ejde-350	62	22	and	and	CCONJ
ejde-350	62	23	squassina	squassina	ADJ
ejde-350	63	1	[	[	X
ejde-350	63	2	46	46	NUM
ejde-350	63	3	]	]	PUNCT
ejde-350	63	4	investigated	investigate	VERB
ejde-350	63	5	the	the	DET
ejde-350	63	6	system	system	NOUN
ejde-350	63	7	(	(	PUNCT
ejde-350	63	8	−∆)su+	−∆)su+	NOUN
ejde-350	63	9	λφu	λφu	NOUN
ejde-350	63	10	=	=	SYM
ejde-350	63	11	f(u	f(u	PROPN
ejde-350	63	12	)	)	PUNCT
ejde-350	63	13	,	,	PUNCT
ejde-350	63	14	in	in	ADP
ejde-350	63	15	r3	r3	PROPN
ejde-350	63	16	,	,	PUNCT
ejde-350	63	17	(	(	PUNCT
ejde-350	63	18	−∆)tφ	−∆)tφ	NOUN
ejde-350	63	19	=	=	SYM
ejde-350	63	20	λu2	λu2	NOUN
ejde-350	63	21	,	,	PUNCT
ejde-350	63	22	in	in	ADP
ejde-350	63	23	r3	r3	PROPN
ejde-350	63	24	,	,	PUNCT
ejde-350	63	25	(	(	PUNCT
ejde-350	63	26	1.7	1.7	NUM
ejde-350	63	27	)	)	PUNCT
ejde-350	63	28	where	where	SCONJ
ejde-350	63	29	f	f	PROPN
ejde-350	63	30	is	be	AUX
ejde-350	63	31	a	a	DET
ejde-350	63	32	nonlinearity	nonlinearity	NOUN
ejde-350	63	33	of	of	ADP
ejde-350	63	34	berestycki	berestycki	ADJ
ejde-350	63	35	-	-	PUNCT
ejde-350	63	36	lions	lion	NOUN
ejde-350	63	37	type	type	NOUN
ejde-350	63	38	.	.	PUNCT
ejde-350	64	1	the	the	DET
ejde-350	64	2	authors	author	NOUN
ejde-350	64	3	proved	prove	VERB
ejde-350	64	4	that	that	DET
ejde-350	64	5	system	system	NOUN
ejde-350	64	6	(	(	PUNCT
ejde-350	64	7	1.7	1.7	NUM
ejde-350	64	8	)	)	PUNCT
ejde-350	64	9	admits	admit	VERB
ejde-350	64	10	a	a	DET
ejde-350	64	11	positive	positive	ADJ
ejde-350	64	12	radial	radial	ADJ
ejde-350	64	13	solution	solution	NOUN
ejde-350	64	14	if	if	SCONJ
ejde-350	64	15	λ	λ	PROPN
ejde-350	64	16	>	>	X
ejde-350	64	17	0	0	PUNCT
ejde-350	64	18	small	small	ADJ
ejde-350	64	19	enough	enough	ADV
ejde-350	64	20	.	.	PUNCT
ejde-350	65	1	liu	liu	PROPN
ejde-350	65	2	and	and	CCONJ
ejde-350	65	3	zhang	zhang	PROPN
ejde-350	66	1	[	[	X
ejde-350	66	2	30	30	NUM
ejde-350	66	3	]	]	SYM
ejde-350	66	4	4	4	NUM
ejde-350	66	5	y.	y.	PROPN
ejde-350	66	6	su	su	PROPN
ejde-350	66	7	,	,	PUNCT
ejde-350	66	8	h.	h.	PROPN
ejde-350	66	9	chen	chen	PROPN
ejde-350	66	10	,	,	PUNCT
ejde-350	66	11	s.	s.	PROPN
ejde-350	66	12	liu	liu	PROPN
ejde-350	66	13	,	,	PUNCT
ejde-350	66	14	x.	x.	PROPN
ejde-350	66	15	fang	fang	PROPN
ejde-350	66	16	ejde-2020/01	ejde-2020/01	PROPN
ejde-350	66	17	proved	prove	VERB
ejde-350	66	18	the	the	DET
ejde-350	66	19	existence	existence	NOUN
ejde-350	66	20	of	of	ADP
ejde-350	66	21	positive	positive	ADJ
ejde-350	66	22	ground	ground	NOUN
ejde-350	66	23	state	state	NOUN
ejde-350	66	24	solution	solution	NOUN
ejde-350	66	25	for	for	ADP
ejde-350	66	26	ε	ε	PROPN
ejde-350	66	27	>	>	X
ejde-350	66	28	0	0	PUNCT
ejde-350	66	29	sufficiently	sufficiently	ADV
ejde-350	66	30	small	small	ADJ
ejde-350	66	31	to	to	ADP
ejde-350	66	32	the	the	DET
ejde-350	66	33	system	system	NOUN
ejde-350	66	34	ε2s(−∆)su+	ε2s(−∆)su+	PROPN
ejde-350	66	35	v	v	NOUN
ejde-350	66	36	(	(	PUNCT
ejde-350	66	37	x)u+	x)u+	PROPN
ejde-350	66	38	φu	φu	NOUN
ejde-350	66	39	=	=	SYM
ejde-350	66	40	f(u	f(u	PROPN
ejde-350	66	41	)	)	PUNCT
ejde-350	67	1	+	+	CCONJ
ejde-350	67	2	|u|2	|u|2	PROPN
ejde-350	67	3	∗	∗	PROPN
ejde-350	67	4	s−2u	s−2u	PROPN
ejde-350	67	5	,	,	PUNCT
ejde-350	67	6	in	in	ADP
ejde-350	67	7	r3	r3	PROPN
ejde-350	67	8	,	,	PUNCT
ejde-350	67	9	ε2t(−∆)tφ	ε2t(−∆)tφ	X
ejde-350	68	1	=	=	SYM
ejde-350	68	2	u2	u2	PROPN
ejde-350	68	3	,	,	PUNCT
ejde-350	68	4	in	in	ADP
ejde-350	68	5	r3	r3	PROPN
ejde-350	68	6	,	,	PUNCT
ejde-350	68	7	where	where	SCONJ
ejde-350	68	8	v	v	X
ejde-350	68	9	∈	∈	PROPN
ejde-350	68	10	c1(r3,r+	c1(r3,r+	NOUN
ejde-350	68	11	)	)	PUNCT
ejde-350	68	12	and	and	CCONJ
ejde-350	68	13	f	f	PROPN
ejde-350	68	14	is	be	AUX
ejde-350	68	15	subcritical	subcritical	ADJ
ejde-350	68	16	.	.	PUNCT
ejde-350	69	1	for	for	ADP
ejde-350	69	2	more	more	ADJ
ejde-350	69	3	details	detail	NOUN
ejde-350	69	4	and	and	CCONJ
ejde-350	69	5	recent	recent	ADJ
ejde-350	69	6	works	work	NOUN
ejde-350	69	7	,	,	PUNCT
ejde-350	69	8	we	we	PRON
ejde-350	69	9	refer	refer	VERB
ejde-350	69	10	to	to	ADP
ejde-350	69	11	[	[	X
ejde-350	69	12	5	5	NUM
ejde-350	69	13	,	,	PUNCT
ejde-350	69	14	31	31	NUM
ejde-350	69	15	,	,	PUNCT
ejde-350	69	16	37	37	NUM
ejde-350	69	17	,	,	PUNCT
ejde-350	69	18	41	41	NUM
ejde-350	69	19	,	,	PUNCT
ejde-350	69	20	42	42	NUM
ejde-350	69	21	]	]	PUNCT
ejde-350	69	22	and	and	CCONJ
ejde-350	69	23	the	the	DET
ejde-350	69	24	references	reference	NOUN
ejde-350	69	25	therein	therein	ADV
ejde-350	69	26	.	.	PUNCT
ejde-350	70	1	in	in	ADP
ejde-350	70	2	[	[	X
ejde-350	70	3	30	30	NUM
ejde-350	70	4	,	,	PUNCT
ejde-350	70	5	41	41	NUM
ejde-350	70	6	,	,	PUNCT
ejde-350	70	7	42	42	NUM
ejde-350	70	8	,	,	PUNCT
ejde-350	70	9	46	46	NUM
ejde-350	70	10	]	]	PUNCT
ejde-350	70	11	the	the	DET
ejde-350	70	12	authors	author	NOUN
ejde-350	70	13	considered	consider	VERB
ejde-350	70	14	the	the	DET
ejde-350	70	15	existence	existence	NOUN
ejde-350	70	16	of	of	ADP
ejde-350	70	17	solution	solution	NOUN
ejde-350	70	18	for	for	ADP
ejde-350	70	19	system	system	NOUN
ejde-350	70	20	(	(	PUNCT
ejde-350	70	21	1.7	1.7	NUM
ejde-350	70	22	)	)	PUNCT
ejde-350	70	23	in	in	ADP
ejde-350	70	24	which	which	PRON
ejde-350	70	25	2	2	NUM
ejde-350	70	26	t	t	NOUN
ejde-350	70	27	+	+	CCONJ
ejde-350	70	28	4s	4s	NUM
ejde-350	70	29	>	>	SYM
ejde-350	70	30	3	3	X
ejde-350	70	31	.	.	PUNCT
ejde-350	71	1	therefore	therefore	ADV
ejde-350	71	2	,	,	PUNCT
ejde-350	71	3	it	it	PRON
ejde-350	71	4	is	be	AUX
ejde-350	71	5	natural	natural	ADJ
ejde-350	71	6	to	to	PART
ejde-350	71	7	ask	ask	VERB
ejde-350	71	8	whether	whether	SCONJ
ejde-350	71	9	system	system	NOUN
ejde-350	71	10	(	(	PUNCT
ejde-350	71	11	1.7	1.7	NUM
ejde-350	71	12	)	)	PUNCT
ejde-350	71	13	admits	admit	VERB
ejde-350	71	14	a	a	DET
ejde-350	71	15	solution	solution	NOUN
ejde-350	71	16	for	for	ADP
ejde-350	71	17	2t+	2t+	NUM
ejde-350	71	18	4s	4s	NUM
ejde-350	71	19	=	=	SYM
ejde-350	71	20	3	3	X
ejde-350	71	21	.	.	NOUN
ejde-350	71	22	to	to	ADP
ejde-350	71	23	the	the	DET
ejde-350	71	24	best	good	ADJ
ejde-350	71	25	of	of	ADP
ejde-350	71	26	our	our	PRON
ejde-350	71	27	knowledge	knowledge	NOUN
ejde-350	71	28	,	,	PUNCT
ejde-350	71	29	there	there	PRON
ejde-350	71	30	is	be	VERB
ejde-350	71	31	no	no	DET
ejde-350	71	32	result	result	NOUN
ejde-350	71	33	on	on	ADP
ejde-350	71	34	such	such	ADJ
ejde-350	71	35	question	question	NOUN
ejde-350	71	36	in	in	ADP
ejde-350	71	37	the	the	DET
ejde-350	71	38	current	current	ADJ
ejde-350	71	39	literature	literature	NOUN
ejde-350	71	40	.	.	PUNCT
ejde-350	72	1	motivated	motivate	VERB
ejde-350	72	2	by	by	ADP
ejde-350	72	3	the	the	DET
ejde-350	72	4	above	above	ADJ
ejde-350	72	5	facts	fact	NOUN
ejde-350	72	6	,	,	PUNCT
ejde-350	72	7	we	we	PRON
ejde-350	72	8	study	study	VERB
ejde-350	72	9	the	the	DET
ejde-350	72	10	existence	existence	NOUN
ejde-350	72	11	of	of	ADP
ejde-350	72	12	solution	solution	NOUN
ejde-350	72	13	for	for	ADP
ejde-350	72	14	system	system	NOUN
ejde-350	72	15	(	(	PUNCT
ejde-350	72	16	1.1	1.1	NUM
ejde-350	72	17	)	)	PUNCT
ejde-350	72	18	.	.	PUNCT
ejde-350	73	1	1.1	1.1	NUM
ejde-350	73	2	.	.	PUNCT
ejde-350	73	3	statement	statement	NOUN
ejde-350	73	4	of	of	ADP
ejde-350	73	5	results	result	NOUN
ejde-350	73	6	.	.	PUNCT
ejde-350	74	1	we	we	PRON
ejde-350	74	2	introduce	introduce	VERB
ejde-350	74	3	the	the	DET
ejde-350	74	4	energy	energy	NOUN
ejde-350	74	5	functional	functional	NOUN
ejde-350	74	6	associated	associate	VERB
ejde-350	74	7	with	with	ADP
ejde-350	74	8	system	system	NOUN
ejde-350	74	9	(	(	PUNCT
ejde-350	74	10	1.1	1.1	NUM
ejde-350	74	11	)	)	PUNCT
ejde-350	74	12	by	by	ADP
ejde-350	74	13	iλ(u	iλ(u	NOUN
ejde-350	74	14	)	)	PUNCT
ejde-350	74	15	=	=	SYM
ejde-350	74	16	1	1	NUM
ejde-350	74	17	2	2	X
ejde-350	74	18	‖u‖2φ	‖u‖2φ	NOUN
ejde-350	74	19	+	+	CCONJ
ejde-350	74	20	λ	λ	PROPN
ejde-350	74	21	4	4	NUM
ejde-350	74	22	∫	∫	NOUN
ejde-350	74	23	r3	r3	PROPN
ejde-350	74	24	∫	∫	PROPN
ejde-350	74	25	r3	r3	PROPN
ejde-350	74	26	|u(x)|2|u(y)|2	|u(x)|2|u(y)|2	PROPN
ejde-350	74	27	|x−	|x−	PROPN
ejde-350	74	28	y|3−2	y|3−2	PROPN
ejde-350	74	29	t	t	PROPN
ejde-350	74	30	dxdy	dxdy	PROPN
ejde-350	74	31	−	−	PROPN
ejde-350	74	32	1	1	NUM
ejde-350	74	33	2∗s	2∗s	NUM
ejde-350	74	34	∫	∫	NOUN
ejde-350	74	35	r3	r3	PROPN
ejde-350	74	36	|u|2	|u|2	PROPN
ejde-350	74	37	∗	∗	PROPN
ejde-350	74	38	sdx	sdx	PROPN
ejde-350	74	39	.	.	PUNCT
ejde-350	75	1	where	where	SCONJ
ejde-350	75	2	the	the	DET
ejde-350	75	3	norm	norm	NOUN
ejde-350	75	4	‖	‖	PROPN
ejde-350	75	5	·	·	PUNCT
ejde-350	75	6	‖φ	‖φ	PROPN
ejde-350	75	7	is	be	AUX
ejde-350	75	8	defined	define	VERB
ejde-350	75	9	in	in	ADP
ejde-350	75	10	section	section	NOUN
ejde-350	75	11	2	2	NUM
ejde-350	75	12	.	.	PUNCT
ejde-350	76	1	there	there	PRON
ejde-350	76	2	is	be	VERB
ejde-350	76	3	a	a	DET
ejde-350	76	4	difficulty	difficulty	NOUN
ejde-350	76	5	in	in	ADP
ejde-350	76	6	applying	apply	VERB
ejde-350	76	7	variational	variational	ADJ
ejde-350	76	8	methods	method	NOUN
ejde-350	76	9	to	to	ADP
ejde-350	76	10	the	the	DET
ejde-350	76	11	functional	functional	ADJ
ejde-350	76	12	iλ	iλ	NOUN
ejde-350	76	13	.	.	PUNCT
ejde-350	77	1	(	(	PUNCT
ejde-350	77	2	difficulty	difficulty	NOUN
ejde-350	77	3	)	)	PUNCT
ejde-350	77	4	since	since	SCONJ
ejde-350	77	5	2∗s	2∗s	NUM
ejde-350	77	6	<	<	SYM
ejde-350	77	7	4	4	NUM
ejde-350	77	8	,	,	PUNCT
ejde-350	77	9	we	we	PRON
ejde-350	77	10	know	know	VERB
ejde-350	77	11	that	that	SCONJ
ejde-350	77	12	the	the	DET
ejde-350	77	13	functional	functional	ADJ
ejde-350	77	14	iλ	iλ	NOUN
ejde-350	77	15	does	do	AUX
ejde-350	77	16	not	not	PART
ejde-350	77	17	satisfy	satisfy	VERB
ejde-350	77	18	mountain	mountain	NOUN
ejde-350	77	19	pass	pass	NOUN
ejde-350	77	20	theorem	theorem	PROPN
ejde-350	77	21	,	,	PUNCT
ejde-350	77	22	the	the	DET
ejde-350	77	23	boundedness	boundedness	NOUN
ejde-350	77	24	of	of	ADP
ejde-350	77	25	the	the	DET
ejde-350	77	26	palais	palais	PROPN
ejde-350	77	27	-	-	PUNCT
ejde-350	77	28	smale	smale	ADJ
ejde-350	77	29	sequence	sequence	NOUN
ejde-350	77	30	for	for	ADP
ejde-350	77	31	iλ	iλ	NOUN
ejde-350	77	32	is	be	AUX
ejde-350	77	33	hard	hard	ADJ
ejde-350	77	34	to	to	PART
ejde-350	77	35	obtain	obtain	VERB
ejde-350	77	36	.	.	PUNCT
ejde-350	78	1	to	to	PART
ejde-350	78	2	overcome	overcome	VERB
ejde-350	78	3	this	this	DET
ejde-350	78	4	difficult	difficult	ADJ
ejde-350	78	5	,	,	PUNCT
ejde-350	78	6	by	by	ADP
ejde-350	78	7	using	use	VERB
ejde-350	78	8	the	the	DET
ejde-350	78	9	perturbation	perturbation	NOUN
ejde-350	78	10	method	method	NOUN
ejde-350	78	11	in	in	ADP
ejde-350	78	12	[	[	X
ejde-350	78	13	12	12	NUM
ejde-350	78	14	,	,	PUNCT
ejde-350	78	15	25	25	NUM
ejde-350	78	16	]	]	PUNCT
ejde-350	78	17	,	,	PUNCT
ejde-350	78	18	for	for	ADP
ejde-350	78	19	λ	λ	X
ejde-350	78	20	small	small	ADJ
ejde-350	78	21	enough	enough	ADV
ejde-350	78	22	,	,	PUNCT
ejde-350	78	23	we	we	PRON
ejde-350	78	24	look	look	VERB
ejde-350	78	25	the	the	DET
ejde-350	78	26	system	system	NOUN
ejde-350	78	27	(	(	PUNCT
ejde-350	78	28	1.1	1.1	NUM
ejde-350	78	29	)	)	PUNCT
ejde-350	78	30	as	as	ADP
ejde-350	78	31	a	a	DET
ejde-350	78	32	perturbation	perturbation	NOUN
ejde-350	78	33	of	of	ADP
ejde-350	78	34	the	the	DET
ejde-350	78	35	equation	equation	NOUN
ejde-350	78	36	(	(	PUNCT
ejde-350	78	37	−∆)su−	−∆)su−	PROPN
ejde-350	78	38	µφ(x/|x|	µφ(x/|x|	NOUN
ejde-350	78	39	)	)	PUNCT
ejde-350	78	40	|x|2s	|x|2s	NOUN
ejde-350	78	41	u	u	NOUN
ejde-350	78	42	=	=	PROPN
ejde-350	78	43	|u|2	|u|2	PROPN
ejde-350	78	44	∗	∗	PROPN
ejde-350	78	45	s−2u	s−2u	PROPN
ejde-350	78	46	,	,	PUNCT
ejde-350	78	47	in	in	ADP
ejde-350	78	48	r3	r3	PROPN
ejde-350	78	49	.	.	PUNCT
ejde-350	79	1	(	(	PUNCT
ejde-350	79	2	1.8	1.8	NUM
ejde-350	79	3	)	)	PUNCT
ejde-350	79	4	we	we	PRON
ejde-350	79	5	introduce	introduce	VERB
ejde-350	79	6	the	the	DET
ejde-350	79	7	energy	energy	NOUN
ejde-350	79	8	functional	functional	NOUN
ejde-350	79	9	associated	associate	VERB
ejde-350	79	10	with	with	ADP
ejde-350	79	11	equation	equation	NOUN
ejde-350	79	12	(	(	PUNCT
ejde-350	79	13	1.8	1.8	NUM
ejde-350	79	14	)	)	PUNCT
ejde-350	79	15	by	by	ADP
ejde-350	79	16	i0(u	i0(u	SYM
ejde-350	79	17	)	)	PUNCT
ejde-350	79	18	=	=	SYM
ejde-350	79	19	1	1	NUM
ejde-350	79	20	2	2	X
ejde-350	79	21	‖u‖2φ	‖u‖2φ	NOUN
ejde-350	79	22	−	−	NOUN
ejde-350	79	23	1	1	NUM
ejde-350	79	24	2∗s	2∗s	NUM
ejde-350	79	25	∫	∫	NOUN
ejde-350	79	26	r3	r3	PROPN
ejde-350	79	27	|u|2	|u|2	PROPN
ejde-350	79	28	∗	∗	PROPN
ejde-350	79	29	sdx	sdx	PROPN
ejde-350	79	30	.	.	PUNCT
ejde-350	80	1	for	for	ADP
ejde-350	80	2	λ	λ	PROPN
ejde-350	80	3	small	small	ADJ
ejde-350	80	4	enough	enough	ADV
ejde-350	80	5	,	,	PUNCT
ejde-350	80	6	we	we	PRON
ejde-350	80	7	look	look	VERB
ejde-350	80	8	at	at	ADP
ejde-350	80	9	the	the	DET
ejde-350	80	10	functional	functional	ADJ
ejde-350	80	11	iλ	iλ	NOUN
ejde-350	80	12	as	as	ADP
ejde-350	80	13	a	a	DET
ejde-350	80	14	perturbation	perturbation	NOUN
ejde-350	80	15	of	of	ADP
ejde-350	80	16	functional	functional	ADJ
ejde-350	80	17	i0	i0	PROPN
ejde-350	80	18	,	,	PUNCT
ejde-350	80	19	iλ(u	iλ(u	NUM
ejde-350	80	20	)	)	PUNCT
ejde-350	80	21	:	:	PUNCT
ejde-350	81	1	=	=	SYM
ejde-350	81	2	i0(u	i0(u	NUM
ejde-350	81	3	)	)	PUNCT
ejde-350	81	4	+	+	NOUN
ejde-350	81	5	kλ(u	kλ(u	NUM
ejde-350	81	6	)	)	PUNCT
ejde-350	81	7	,	,	PUNCT
ejde-350	81	8	where	where	SCONJ
ejde-350	81	9	kλ(u	kλ(u	NUM
ejde-350	81	10	)	)	PUNCT
ejde-350	81	11	=	=	SYM
ejde-350	81	12	λ	λ	NOUN
ejde-350	81	13	4	4	NUM
ejde-350	81	14	∫	∫	NOUN
ejde-350	81	15	r3	r3	PROPN
ejde-350	81	16	∫	∫	PROPN
ejde-350	81	17	r3	r3	PROPN
ejde-350	81	18	|u(x)|2|u(y)|2	|u(x)|2|u(y)|2	PROPN
ejde-350	81	19	|x−	|x−	PROPN
ejde-350	81	20	y|3−2	y|3−2	PROPN
ejde-350	81	21	t	t	PROPN
ejde-350	81	22	dxdy	dxdy	PROPN
ejde-350	81	23	.	.	PUNCT
ejde-350	82	1	let	let	VERB
ejde-350	82	2	s	s	PRON
ejde-350	82	3	be	be	AUX
ejde-350	82	4	the	the	DET
ejde-350	82	5	set	set	NOUN
ejde-350	82	6	of	of	ADP
ejde-350	82	7	ground	ground	NOUN
ejde-350	82	8	state	state	NOUN
ejde-350	82	9	critical	critical	ADJ
ejde-350	82	10	points	point	NOUN
ejde-350	82	11	of	of	ADP
ejde-350	82	12	i0	i0	PROPN
ejde-350	82	13	.	.	PUNCT
ejde-350	83	1	the	the	DET
ejde-350	83	2	perturbation	perturbation	NOUN
ejde-350	83	3	method	method	NOUN
ejde-350	83	4	mainly	mainly	ADV
ejde-350	83	5	consists	consist	VERB
ejde-350	83	6	of	of	ADP
ejde-350	83	7	two	two	NUM
ejde-350	83	8	aspects	aspect	NOUN
ejde-350	83	9	:	:	PUNCT
ejde-350	83	10	(	(	PUNCT
ejde-350	83	11	1	1	X
ejde-350	83	12	)	)	PUNCT
ejde-350	83	13	the	the	DET
ejde-350	83	14	mountain	mountain	NOUN
ejde-350	83	15	pass	pass	NOUN
ejde-350	83	16	type	type	NOUN
ejde-350	83	17	critical	critical	ADJ
ejde-350	83	18	point	point	NOUN
ejde-350	83	19	of	of	ADP
ejde-350	83	20	i0	i0	PROPN
ejde-350	83	21	is	be	AUX
ejde-350	83	22	a	a	DET
ejde-350	83	23	ground	ground	NOUN
ejde-350	83	24	state	state	NOUN
ejde-350	83	25	in	in	ADP
ejde-350	83	26	ds,2	ds,2	NOUN
ejde-350	83	27	rad(r3	rad(r3	NOUN
ejde-350	83	28	)	)	PUNCT
ejde-350	83	29	;	;	PUNCT
ejde-350	83	30	(	(	PUNCT
ejde-350	83	31	2	2	X
ejde-350	83	32	)	)	PUNCT
ejde-350	83	33	the	the	DET
ejde-350	83	34	set	set	NOUN
ejde-350	83	35	s	s	PART
ejde-350	83	36	is	be	AUX
ejde-350	83	37	compact	compact	ADJ
ejde-350	83	38	in	in	ADP
ejde-350	83	39	ds,2	ds,2	NOUN
ejde-350	83	40	rad(r3	rad(r3	NOUN
ejde-350	83	41	)	)	PUNCT
ejde-350	83	42	.	.	PUNCT
ejde-350	84	1	if	if	SCONJ
ejde-350	84	2	conditions	condition	NOUN
ejde-350	84	3	(	(	PUNCT
ejde-350	84	4	1	1	NUM
ejde-350	84	5	)	)	PUNCT
ejde-350	84	6	and	and	CCONJ
ejde-350	84	7	(	(	PUNCT
ejde-350	84	8	2	2	X
ejde-350	84	9	)	)	PUNCT
ejde-350	84	10	are	be	AUX
ejde-350	84	11	satisfied	satisfied	ADJ
ejde-350	84	12	,	,	PUNCT
ejde-350	84	13	then	then	ADV
ejde-350	84	14	there	there	PRON
ejde-350	84	15	exists	exist	VERB
ejde-350	84	16	a	a	DET
ejde-350	84	17	palais	palais	ADJ
ejde-350	84	18	-	-	PUNCT
ejde-350	84	19	smale	smale	ADJ
ejde-350	84	20	sequence	sequence	NOUN
ejde-350	84	21	of	of	ADP
ejde-350	84	22	iλ	iλ	NOUN
ejde-350	84	23	near	near	ADP
ejde-350	84	24	the	the	DET
ejde-350	84	25	set	set	NOUN
ejde-350	84	26	s	s	NOUN
ejde-350	84	27	for	for	ADP
ejde-350	84	28	sufficiently	sufficiently	ADV
ejde-350	84	29	small	small	ADJ
ejde-350	84	30	λ	λ	NOUN
ejde-350	84	31	.	.	PUNCT
ejde-350	85	1	since	since	SCONJ
ejde-350	85	2	the	the	DET
ejde-350	85	3	perturbation	perturbation	NOUN
ejde-350	85	4	method	method	NOUN
ejde-350	85	5	is	be	AUX
ejde-350	85	6	based	base	VERB
ejde-350	85	7	on	on	ADP
ejde-350	85	8	the	the	DET
ejde-350	85	9	properties	property	NOUN
ejde-350	85	10	of	of	ADP
ejde-350	85	11	set	set	NOUN
ejde-350	85	12	s	s	PART
ejde-350	85	13	,	,	PUNCT
ejde-350	85	14	we	we	PRON
ejde-350	85	15	have	have	VERB
ejde-350	85	16	to	to	PART
ejde-350	85	17	study	study	VERB
ejde-350	85	18	the	the	DET
ejde-350	85	19	existence	existence	NOUN
ejde-350	85	20	of	of	ADP
ejde-350	85	21	ground	ground	NOUN
ejde-350	85	22	state	state	NOUN
ejde-350	85	23	solution	solution	NOUN
ejde-350	85	24	to	to	ADP
ejde-350	85	25	equation	equation	NOUN
ejde-350	85	26	(	(	PUNCT
ejde-350	85	27	1.8	1.8	NUM
ejde-350	85	28	)	)	PUNCT
ejde-350	85	29	first	first	ADV
ejde-350	85	30	.	.	PUNCT
ejde-350	86	1	the	the	DET
ejde-350	86	2	following	follow	VERB
ejde-350	86	3	is	be	AUX
ejde-350	86	4	our	our	PRON
ejde-350	86	5	first	first	ADJ
ejde-350	86	6	result	result	NOUN
ejde-350	86	7	.	.	PUNCT
ejde-350	87	1	theorem	theorem	VERB
ejde-350	87	2	1.1	1.1	NUM
ejde-350	87	3	.	.	PUNCT
ejde-350	88	1	let	let	VERB
ejde-350	88	2	s	s	PRON
ejde-350	88	3	∈	∈	PROPN
ejde-350	88	4	(	(	PUNCT
ejde-350	88	5	0	0	NUM
ejde-350	88	6	,	,	PUNCT
ejde-350	88	7	3/4	3/4	NUM
ejde-350	88	8	)	)	PUNCT
ejde-350	88	9	and	and	CCONJ
ejde-350	88	10	(	(	PUNCT
ejde-350	88	11	φ1	φ1	PROPN
ejde-350	88	12	)	)	PUNCT
ejde-350	88	13	hold	hold	NOUN
ejde-350	88	14	.	.	PUNCT
ejde-350	89	1	then	then	ADV
ejde-350	89	2	(	(	PUNCT
ejde-350	89	3	1.8	1.8	NUM
ejde-350	89	4	)	)	PUNCT
ejde-350	89	5	has	have	VERB
ejde-350	89	6	a	a	DET
ejde-350	89	7	ground	ground	NOUN
ejde-350	89	8	state	state	NOUN
ejde-350	89	9	solution	solution	NOUN
ejde-350	89	10	v	v	ADP
ejde-350	89	11	∈	∈	PROPN
ejde-350	89	12	ds,2	ds,2	NOUN
ejde-350	89	13	rad(r3	rad(r3	NOUN
ejde-350	89	14	)	)	PUNCT
ejde-350	89	15	.	.	PUNCT
ejde-350	90	1	ejde-2020/01	ejde-2020/01	NOUN
ejde-350	90	2	fractional	fractional	ADJ
ejde-350	90	3	schrödinger	schrödinger	NOUN
ejde-350	90	4	-	-	PUNCT
ejde-350	90	5	poisson	poisson	NOUN
ejde-350	90	6	system	system	NOUN
ejde-350	90	7	5	5	NUM
ejde-350	90	8	there	there	PRON
ejde-350	90	9	is	be	VERB
ejde-350	90	10	a	a	DET
ejde-350	90	11	difficulty	difficulty	NOUN
ejde-350	90	12	in	in	ADP
ejde-350	90	13	the	the	DET
ejde-350	90	14	proof	proof	NOUN
ejde-350	90	15	of	of	ADP
ejde-350	90	16	theorem	theorem	ADJ
ejde-350	90	17	1.1	1.1	NUM
ejde-350	90	18	.	.	PUNCT
ejde-350	91	1	because	because	SCONJ
ejde-350	91	2	of	of	ADP
ejde-350	91	3	the	the	DET
ejde-350	91	4	lack	lack	NOUN
ejde-350	91	5	of	of	ADP
ejde-350	91	6	compactness	compactness	NOUN
ejde-350	91	7	of	of	ADP
ejde-350	91	8	the	the	DET
ejde-350	91	9	sobolev	sobolev	NOUN
ejde-350	91	10	embedding	embed	VERB
ejde-350	91	11	ds,2(r3	ds,2(r3	PUNCT
ejde-350	91	12	)	)	PUNCT
ejde-350	91	13	↪	↪	PROPN
ejde-350	91	14	→	→	SYM
ejde-350	91	15	l2∗	l2∗	NOUN
ejde-350	91	16	s	s	X
ejde-350	91	17	(	(	PUNCT
ejde-350	91	18	r3	r3	PROPN
ejde-350	91	19	)	)	PUNCT
ejde-350	91	20	,	,	PUNCT
ejde-350	91	21	and	and	CCONJ
ejde-350	91	22	the	the	DET
ejde-350	91	23	functional	functional	ADJ
ejde-350	91	24	i0	i0	PROPN
ejde-350	91	25	is	be	AUX
ejde-350	91	26	invariant	invariant	ADJ
ejde-350	91	27	under	under	ADP
ejde-350	91	28	the	the	DET
ejde-350	91	29	weighted	weighted	ADJ
ejde-350	91	30	dilation	dilation	NOUN
ejde-350	91	31	,	,	PUNCT
ejde-350	91	32	it	it	PRON
ejde-350	91	33	is	be	AUX
ejde-350	91	34	hard	hard	ADJ
ejde-350	91	35	to	to	PART
ejde-350	91	36	show	show	VERB
ejde-350	91	37	that	that	SCONJ
ejde-350	91	38	the	the	DET
ejde-350	91	39	palais	palais	PROPN
ejde-350	91	40	-	-	PUNCT
ejde-350	91	41	smale	smale	ADJ
ejde-350	91	42	sequence	sequence	NOUN
ejde-350	91	43	of	of	ADP
ejde-350	91	44	i0	i0	PROPN
ejde-350	91	45	has	have	VERB
ejde-350	91	46	a	a	DET
ejde-350	91	47	convergence	convergence	NOUN
ejde-350	91	48	subsequence	subsequence	NOUN
ejde-350	91	49	.	.	PUNCT
ejde-350	92	1	for	for	ADP
ejde-350	92	2	φ	φ	PROPN
ejde-350	92	3	≡	≡	PROPN
ejde-350	92	4	1	1	NUM
ejde-350	92	5	,	,	PUNCT
ejde-350	92	6	let	let	VERB
ejde-350	92	7	us	we	PRON
ejde-350	92	8	review	review	VERB
ejde-350	92	9	the	the	DET
ejde-350	92	10	method	method	NOUN
ejde-350	92	11	in	in	ADP
ejde-350	92	12	[	[	X
ejde-350	92	13	45	45	NUM
ejde-350	92	14	]	]	PUNCT
ejde-350	92	15	.	.	PUNCT
ejde-350	93	1	applying	apply	VERB
ejde-350	93	2	their	their	PRON
ejde-350	93	3	method	method	NOUN
ejde-350	93	4	,	,	PUNCT
ejde-350	93	5	one	one	PRON
ejde-350	93	6	has	have	VERB
ejde-350	93	7	the	the	DET
ejde-350	93	8	existence	existence	NOUN
ejde-350	93	9	of	of	ADP
ejde-350	93	10	ground	ground	NOUN
ejde-350	93	11	state	state	NOUN
ejde-350	93	12	solution	solution	NOUN
ejde-350	93	13	to	to	ADP
ejde-350	93	14	the	the	DET
ejde-350	93	15	equation	equation	NOUN
ejde-350	93	16	(	(	PUNCT
ejde-350	93	17	−∆)su−	−∆)su−	PROPN
ejde-350	93	18	µ	µ	CCONJ
ejde-350	93	19	u	u	NOUN
ejde-350	93	20	|x|2s	|x|2s	NOUN
ejde-350	93	21	=	=	SYM
ejde-350	93	22	|u|2	|u|2	PROPN
ejde-350	93	23	∗	∗	PROPN
ejde-350	93	24	s−2u	s−2u	PROPN
ejde-350	93	25	,	,	PUNCT
ejde-350	93	26	in	in	ADP
ejde-350	93	27	r3	r3	PROPN
ejde-350	93	28	.	.	PUNCT
ejde-350	94	1	(	(	PUNCT
ejde-350	94	2	1.9	1.9	NUM
ejde-350	94	3	)	)	PUNCT
ejde-350	94	4	similar	similar	ADJ
ejde-350	94	5	to	to	ADP
ejde-350	94	6	section	section	NOUN
ejde-350	94	7	3	3	NUM
ejde-350	94	8	in	in	ADP
ejde-350	94	9	[	[	X
ejde-350	94	10	45	45	NUM
ejde-350	94	11	]	]	PUNCT
ejde-350	94	12	,	,	PUNCT
ejde-350	94	13	there	there	PRON
ejde-350	94	14	exists	exist	VERB
ejde-350	94	15	a	a	DET
ejde-350	94	16	palais	palais	ADJ
ejde-350	94	17	-	-	PUNCT
ejde-350	94	18	smale	smale	ADJ
ejde-350	94	19	sequence	sequence	NOUN
ejde-350	94	20	{	{	PUNCT
ejde-350	94	21	un	un	PROPN
ejde-350	94	22	}	}	PUNCT
ejde-350	94	23	for	for	ADP
ejde-350	94	24	the	the	DET
ejde-350	94	25	energy	energy	NOUN
ejde-350	94	26	functional	functional	ADJ
ejde-350	94	27	corresponding	corresponding	NOUN
ejde-350	94	28	to	to	ADP
ejde-350	94	29	(	(	PUNCT
ejde-350	94	30	1.9	1.9	NUM
ejde-350	94	31	)	)	PUNCT
ejde-350	94	32	such	such	ADJ
ejde-350	94	33	that	that	SCONJ
ejde-350	94	34	un	un	PROPN
ejde-350	94	35	⇀	⇀	PROPN
ejde-350	94	36	u	u	PROPN
ejde-350	94	37	in	in	ADP
ejde-350	94	38	ds,2(r3	ds,2(r3	PROPN
ejde-350	94	39	)	)	PUNCT
ejde-350	94	40	with	with	ADP
ejde-350	94	41	u	u	PRON
ejde-350	94	42	solving	solve	VERB
ejde-350	94	43	(	(	PUNCT
ejde-350	94	44	1.9	1.9	NUM
ejde-350	94	45	)	)	PUNCT
ejde-350	94	46	.	.	PUNCT
ejde-350	95	1	however	however	ADV
ejde-350	95	2	,	,	PUNCT
ejde-350	95	3	it	it	PRON
ejde-350	95	4	may	may	AUX
ejde-350	95	5	occur	occur	VERB
ejde-350	95	6	that	that	SCONJ
ejde-350	95	7	u	u	PROPN
ejde-350	95	8	≡	≡	PROPN
ejde-350	95	9	0	0	PROPN
ejde-350	95	10	.	.	PUNCT
ejde-350	96	1	the	the	DET
ejde-350	96	2	key	key	ADJ
ejde-350	96	3	step	step	NOUN
ejde-350	96	4	of	of	ADP
ejde-350	96	5	[	[	X
ejde-350	96	6	45	45	NUM
ejde-350	96	7	]	]	PUNCT
ejde-350	96	8	was	be	AUX
ejde-350	96	9	to	to	PART
ejde-350	96	10	rule	rule	VERB
ejde-350	96	11	out	out	ADP
ejde-350	96	12	the	the	DET
ejde-350	96	13	”	"	PUNCT
ejde-350	96	14	vanishing	vanishing	NOUN
ejde-350	96	15	”	"	PUNCT
ejde-350	96	16	of	of	ADP
ejde-350	96	17	the	the	DET
ejde-350	96	18	palais	palais	PROPN
ejde-350	96	19	-	-	PUNCT
ejde-350	96	20	smale	smale	ADJ
ejde-350	96	21	sequence	sequence	NOUN
ejde-350	96	22	by	by	ADP
ejde-350	96	23	using	use	VERB
ejde-350	96	24	the	the	DET
ejde-350	96	25	limit	limit	NOUN
ejde-350	96	26	equation	equation	NOUN
ejde-350	96	27	of	of	ADP
ejde-350	96	28	(	(	PUNCT
ejde-350	96	29	1.9	1.9	NUM
ejde-350	96	30	)	)	PUNCT
ejde-350	96	31	.	.	PUNCT
ejde-350	97	1	taking	take	VERB
ejde-350	97	2	vn(x	vn(x	NOUN
ejde-350	97	3	)	)	PUNCT
ejde-350	97	4	=	=	SYM
ejde-350	98	1	λ	λ	X
ejde-350	98	2	3−2s	3−2s	NUM
ejde-350	98	3	2	2	NUM
ejde-350	98	4	n	n	CCONJ
ejde-350	98	5	un(λnx+	un(λnx+	NOUN
ejde-350	98	6	xn	xn	PROPN
ejde-350	98	7	)	)	PUNCT
ejde-350	98	8	where	where	SCONJ
ejde-350	98	9	λn	λn	ADV
ejde-350	98	10	>	>	X
ejde-350	98	11	0	0	PROPN
ejde-350	98	12	,	,	PUNCT
ejde-350	98	13	xn	xn	PROPN
ejde-350	98	14	∈	∈	PROPN
ejde-350	98	15	r3	r3	PROPN
ejde-350	98	16	and	and	CCONJ
ejde-350	98	17	xn	xn	PROPN
ejde-350	98	18	λn	λn	NOUN
ejde-350	98	19	→∞	→∞	NOUN
ejde-350	98	20	as	as	ADP
ejde-350	98	21	n→	n→	ADV
ejde-350	98	22	+	+	PROPN
ejde-350	98	23	∞	∞	PROPN
ejde-350	98	24	,	,	PUNCT
ejde-350	98	25	they	they	PRON
ejde-350	98	26	derived	derive	VERB
ejde-350	98	27	that	that	PRON
ejde-350	98	28	vn	vn	PROPN
ejde-350	98	29	⇀	⇀	NUM
ejde-350	98	30	v	v	NOUN
ejde-350	98	31	in	in	ADP
ejde-350	98	32	ds,2(r3	ds,2(r3	PROPN
ejde-350	98	33	)	)	PUNCT
ejde-350	99	1	and∫	and∫	PROPN
ejde-350	99	2	r3	r3	PROPN
ejde-350	99	3	vkφ	vkφ	PROPN
ejde-350	99	4	|x+	|x+	PROPN
ejde-350	99	5	xk	xk	PROPN
ejde-350	99	6	λk	λk	ADP
ejde-350	99	7	|2s	|2s	ADV
ejde-350	99	8	→	→	SYM
ejde-350	99	9	0	0	PUNCT
ejde-350	99	10	as	as	ADP
ejde-350	99	11	k	k	PROPN
ejde-350	99	12	→	→	PROPN
ejde-350	99	13	+	+	ADJ
ejde-350	99	14	∞	∞	PROPN
ejde-350	99	15	(	(	PUNCT
ejde-350	99	16	1.10	1.10	NUM
ejde-350	99	17	)	)	PUNCT
ejde-350	99	18	for	for	ADP
ejde-350	99	19	any	any	DET
ejde-350	99	20	φ	φ	PROPN
ejde-350	99	21	∈	∈	PROPN
ejde-350	99	22	ds,2(r3	ds,2(r3	PROPN
ejde-350	99	23	)	)	PUNCT
ejde-350	99	24	.	.	PUNCT
ejde-350	100	1	then	then	ADV
ejde-350	100	2	v	v	X
ejde-350	100	3	weakly	weakly	ADJ
ejde-350	100	4	solves	solve	NOUN
ejde-350	100	5	(	(	PUNCT
ejde-350	100	6	−∆)sv	−∆)sv	NOUN
ejde-350	100	7	=	=	SYM
ejde-350	100	8	|v|2	|v|2	PROPN
ejde-350	100	9	∗	∗	NOUN
ejde-350	100	10	s−2v	s−2v	PROPN
ejde-350	100	11	,	,	PUNCT
ejde-350	100	12	in	in	ADP
ejde-350	100	13	r3	r3	PROPN
ejde-350	100	14	.	.	PUNCT
ejde-350	101	1	(	(	PUNCT
ejde-350	101	2	1.11	1.11	NUM
ejde-350	101	3	)	)	PUNCT
ejde-350	101	4	using	use	VERB
ejde-350	101	5	the	the	DET
ejde-350	101	6	limit	limit	NOUN
ejde-350	101	7	equation	equation	NOUN
ejde-350	101	8	(	(	PUNCT
ejde-350	101	9	1.11	1.11	NUM
ejde-350	101	10	)	)	PUNCT
ejde-350	101	11	,	,	PUNCT
ejde-350	101	12	they	they	PRON
ejde-350	101	13	ruled	rule	VERB
ejde-350	101	14	out	out	ADP
ejde-350	101	15	the	the	DET
ejde-350	101	16	“	"	PUNCT
ejde-350	101	17	vanishing	vanishing	NOUN
ejde-350	101	18	”	"	PUNCT
ejde-350	101	19	of	of	ADP
ejde-350	101	20	the	the	DET
ejde-350	101	21	palais	palais	PROPN
ejde-350	101	22	-	-	PUNCT
ejde-350	101	23	smale	smale	ADJ
ejde-350	101	24	sequence	sequence	NOUN
ejde-350	101	25	for	for	ADP
ejde-350	101	26	the	the	DET
ejde-350	101	27	energy	energy	NOUN
ejde-350	101	28	functional	functional	ADJ
ejde-350	101	29	corresponding	corresponding	NOUN
ejde-350	101	30	to	to	ADP
ejde-350	101	31	(	(	PUNCT
ejde-350	101	32	1.9	1.9	NUM
ejde-350	101	33	)	)	PUNCT
ejde-350	101	34	.	.	PUNCT
ejde-350	102	1	naturally	naturally	ADV
ejde-350	102	2	,	,	PUNCT
ejde-350	102	3	we	we	PRON
ejde-350	102	4	would	would	AUX
ejde-350	102	5	hope	hope	VERB
ejde-350	102	6	to	to	PART
ejde-350	102	7	overcome	overcome	VERB
ejde-350	102	8	our	our	PRON
ejde-350	102	9	difficulty	difficulty	NOUN
ejde-350	102	10	by	by	ADP
ejde-350	102	11	using	use	VERB
ejde-350	102	12	the	the	DET
ejde-350	102	13	method	method	NOUN
ejde-350	102	14	in	in	ADP
ejde-350	102	15	[	[	X
ejde-350	102	16	45	45	NUM
ejde-350	102	17	]	]	PUNCT
ejde-350	102	18	,	,	PUNCT
ejde-350	102	19	but	but	CCONJ
ejde-350	102	20	unfortunately	unfortunately	ADV
ejde-350	102	21	,	,	PUNCT
ejde-350	102	22	for	for	ADP
ejde-350	102	23	φ	φ	PROPN
ejde-350	102	24	satisfies	satisfie	NOUN
ejde-350	102	25	condition	condition	NOUN
ejde-350	102	26	(	(	PUNCT
ejde-350	102	27	φ1	φ1	PROPN
ejde-350	102	28	)	)	PUNCT
ejde-350	102	29	,	,	PUNCT
ejde-350	102	30	the	the	DET
ejde-350	102	31	behavior	behavior	NOUN
ejde-350	102	32	of	of	ADP
ejde-350	102	33	lim	lim	PROPN
ejde-350	102	34	n→∞	n→∞	PROPN
ejde-350	102	35	φ	φ	PROPN
ejde-350	102	36	(	(	PUNCT
ejde-350	102	37	x+	x+	PROPN
ejde-350	102	38	xn	xn	PROPN
ejde-350	102	39	λn	λn	PROPN
ejde-350	102	40	|x+	|x+	PROPN
ejde-350	102	41	xn	xn	PROPN
ejde-350	102	42	λn	λn	NOUN
ejde-350	102	43	|	|	ADV
ejde-350	102	44	)	)	PUNCT
ejde-350	102	45	,	,	PUNCT
ejde-350	102	46	as	as	ADP
ejde-350	102	47	xn	xn	PROPN
ejde-350	102	48	λn	λn	PROPN
ejde-350	102	49	→∞	→∞	PROPN
ejde-350	102	50	,	,	PUNCT
ejde-350	102	51	is	be	AUX
ejde-350	102	52	unknown	unknown	ADJ
ejde-350	102	53	,	,	PUNCT
ejde-350	102	54	so	so	SCONJ
ejde-350	102	55	we	we	PRON
ejde-350	102	56	do	do	AUX
ejde-350	102	57	not	not	PART
ejde-350	102	58	have	have	VERB
ejde-350	102	59	any	any	DET
ejde-350	102	60	information	information	NOUN
ejde-350	102	61	of	of	ADP
ejde-350	102	62	the	the	DET
ejde-350	102	63	expression	expression	NOUN
ejde-350	103	1	lim	lim	PROPN
ejde-350	103	2	n→∞	n→∞	NUM
ejde-350	104	1	∫	∫	PROPN
ejde-350	104	2	r3	r3	PROPN
ejde-350	104	3	φ	φ	PROPN
ejde-350	104	4	(	(	PUNCT
ejde-350	104	5	x+	x+	PROPN
ejde-350	104	6	xn	xn	PROPN
ejde-350	104	7	λn	λn	PROPN
ejde-350	104	8	|x+	|x+	PROPN
ejde-350	104	9	xn	xn	PROPN
ejde-350	104	10	λn	λn	NOUN
ejde-350	104	11	|	|	ADV
ejde-350	104	12	)	)	PUNCT
ejde-350	104	13	vnϕ	vnϕ	PROPN
ejde-350	104	14	|x+	|x+	PROPN
ejde-350	104	15	xn	xn	PROPN
ejde-350	104	16	λn	λn	PROPN
ejde-350	104	17	|2s	|2s	X
ejde-350	104	18	dx	dx	PROPN
ejde-350	104	19	.	.	PUNCT
ejde-350	104	20	(	(	PUNCT
ejde-350	104	21	1.12	1.12	NUM
ejde-350	104	22	)	)	PUNCT
ejde-350	104	23	clearly	clearly	ADV
ejde-350	104	24	,	,	PUNCT
ejde-350	104	25	their	their	PRON
ejde-350	104	26	method	method	NOUN
ejde-350	104	27	does	do	AUX
ejde-350	104	28	not	not	PART
ejde-350	104	29	apply	apply	VERB
ejde-350	104	30	to	to	ADP
ejde-350	104	31	our	our	PRON
ejde-350	104	32	case	case	NOUN
ejde-350	104	33	,	,	PUNCT
ejde-350	104	34	since	since	SCONJ
ejde-350	104	35	the	the	DET
ejde-350	104	36	expression	expression	NOUN
ejde-350	104	37	(	(	PUNCT
ejde-350	104	38	1.12	1.12	NUM
ejde-350	104	39	)	)	PUNCT
ejde-350	104	40	is	be	AUX
ejde-350	104	41	not	not	PART
ejde-350	104	42	equal	equal	ADJ
ejde-350	104	43	to	to	ADP
ejde-350	104	44	zero	zero	NUM
ejde-350	104	45	.	.	PUNCT
ejde-350	105	1	for	for	ADP
ejde-350	105	2	the	the	DET
ejde-350	105	3	above	above	ADJ
ejde-350	105	4	reason	reason	NOUN
ejde-350	105	5	,	,	PUNCT
ejde-350	105	6	we	we	PRON
ejde-350	105	7	use	use	VERB
ejde-350	105	8	another	another	DET
ejde-350	105	9	way	way	NOUN
ejde-350	105	10	to	to	PART
ejde-350	105	11	prove	prove	VERB
ejde-350	105	12	theorem	theorem	VERB
ejde-350	105	13	1.1	1.1	NUM
ejde-350	105	14	.	.	PUNCT
ejde-350	106	1	the	the	DET
ejde-350	106	2	crucial	crucial	ADJ
ejde-350	106	3	point	point	NOUN
ejde-350	106	4	is	be	AUX
ejde-350	106	5	the	the	DET
ejde-350	106	6	utilization	utilization	NOUN
ejde-350	106	7	of	of	ADP
ejde-350	106	8	the	the	DET
ejde-350	106	9	uniform	uniform	ADJ
ejde-350	106	10	decay	decay	NOUN
ejde-350	106	11	estimate	estimate	NOUN
ejde-350	106	12	for	for	ADP
ejde-350	106	13	radial	radial	ADJ
ejde-350	106	14	function	function	NOUN
ejde-350	106	15	v	v	ADP
ejde-350	106	16	∈	∈	PROPN
ejde-350	106	17	ds,2	ds,2	NOUN
ejde-350	106	18	rad(r3	rad(r3	NOUN
ejde-350	106	19	)	)	PUNCT
ejde-350	106	20	(	(	PUNCT
ejde-350	106	21	see	see	VERB
ejde-350	106	22	[	[	X
ejde-350	106	23	9	9	NUM
ejde-350	106	24	]	]	SYM
ejde-350	106	25	)	)	PUNCT
ejde-350	107	1	|v(x)|	|v(x)|	PROPN
ejde-350	107	2	6	6	NUM
ejde-350	107	3	c	c	NOUN
ejde-350	107	4	|x|	|x|	PROPN
ejde-350	107	5	3−2s	3−2s	NUM
ejde-350	107	6	2	2	NUM
ejde-350	107	7	‖v‖s	‖v‖s	NOUN
ejde-350	107	8	6	6	NUM
ejde-350	107	9	c	c	NOUN
ejde-350	107	10	|x|	|x|	PROPN
ejde-350	107	11	3−2s	3−2s	NUM
ejde-350	107	12	2	2	NUM
ejde-350	107	13	.	.	PUNCT
ejde-350	108	1	we	we	PRON
ejde-350	108	2	consider	consider	VERB
ejde-350	108	3	the	the	DET
ejde-350	108	4	function	function	NOUN
ejde-350	108	5	i0	i0	PROPN
ejde-350	108	6	:	:	PUNCT
ejde-350	108	7	ds,2	ds,2	NOUN
ejde-350	108	8	rad(r3)→	rad(r3)→	NOUN
ejde-350	108	9	r	r	NOUN
ejde-350	108	10	defined	define	VERB
ejde-350	108	11	by	by	ADP
ejde-350	108	12	j0	j0	PROPN
ejde-350	108	13	=	=	SYM
ejde-350	108	14	i0|ds,2rad(r3	i0|ds,2rad(r3	PROPN
ejde-350	108	15	)	)	PUNCT
ejde-350	108	16	.	.	PUNCT
ejde-350	109	1	the	the	DET
ejde-350	109	2	principle	principle	NOUN
ejde-350	109	3	of	of	ADP
ejde-350	109	4	symmetric	symmetric	ADJ
ejde-350	109	5	criticality	criticality	NOUN
ejde-350	109	6	implies	imply	VERB
ejde-350	109	7	that	that	SCONJ
ejde-350	109	8	the	the	DET
ejde-350	109	9	critical	critical	ADJ
ejde-350	109	10	points	point	NOUN
ejde-350	109	11	of	of	ADP
ejde-350	109	12	j0	j0	PROPN
ejde-350	109	13	are	be	AUX
ejde-350	109	14	also	also	ADV
ejde-350	109	15	critical	critical	ADJ
ejde-350	109	16	points	point	NOUN
ejde-350	109	17	for	for	ADP
ejde-350	109	18	i0	i0	PROPN
ejde-350	109	19	.	.	PUNCT
ejde-350	110	1	moreover	moreover	ADV
ejde-350	110	2	,	,	PUNCT
ejde-350	110	3	in	in	ADP
ejde-350	110	4	theorem	theorem	NOUN
ejde-350	110	5	1.1	1.1	NUM
ejde-350	110	6	we	we	PRON
ejde-350	110	7	have	have	VERB
ejde-350	110	8	the	the	DET
ejde-350	110	9	following	follow	VERB
ejde-350	110	10	results	result	NOUN
ejde-350	110	11	:	:	PUNCT
ejde-350	110	12	(	(	PUNCT
ejde-350	110	13	1	1	X
ejde-350	110	14	)	)	PUNCT
ejde-350	110	15	the	the	DET
ejde-350	110	16	mountain	mountain	NOUN
ejde-350	110	17	pass	pass	NOUN
ejde-350	110	18	type	type	NOUN
ejde-350	110	19	critical	critical	ADJ
ejde-350	110	20	point	point	NOUN
ejde-350	110	21	of	of	ADP
ejde-350	110	22	i0	i0	PROPN
ejde-350	110	23	is	be	AUX
ejde-350	110	24	a	a	DET
ejde-350	110	25	ground	ground	NOUN
ejde-350	110	26	state	state	NOUN
ejde-350	110	27	in	in	ADP
ejde-350	110	28	ds,2	ds,2	NOUN
ejde-350	110	29	rad(r3	rad(r3	NOUN
ejde-350	110	30	)	)	PUNCT
ejde-350	110	31	;	;	PUNCT
ejde-350	110	32	(	(	PUNCT
ejde-350	110	33	2	2	X
ejde-350	110	34	)	)	PUNCT
ejde-350	110	35	the	the	DET
ejde-350	110	36	set	set	NOUN
ejde-350	110	37	s	s	PART
ejde-350	110	38	is	be	AUX
ejde-350	110	39	compact	compact	ADJ
ejde-350	110	40	in	in	ADP
ejde-350	110	41	ds,2	ds,2	NOUN
ejde-350	110	42	rad(r3	rad(r3	NOUN
ejde-350	110	43	)	)	PUNCT
ejde-350	110	44	.	.	PUNCT
ejde-350	111	1	combining	combine	VERB
ejde-350	111	2	the	the	DET
ejde-350	111	3	above	above	ADJ
ejde-350	111	4	results	result	NOUN
ejde-350	111	5	and	and	CCONJ
ejde-350	111	6	the	the	DET
ejde-350	111	7	perturbation	perturbation	NOUN
ejde-350	111	8	method	method	NOUN
ejde-350	111	9	,	,	PUNCT
ejde-350	111	10	we	we	PRON
ejde-350	111	11	give	give	VERB
ejde-350	111	12	our	our	PRON
ejde-350	111	13	second	second	ADJ
ejde-350	111	14	result	result	NOUN
ejde-350	111	15	as	as	SCONJ
ejde-350	111	16	follows	follow	VERB
ejde-350	111	17	.	.	PUNCT
ejde-350	112	1	6	6	NUM
ejde-350	112	2	y.	y.	PROPN
ejde-350	112	3	su	su	PROPN
ejde-350	112	4	,	,	PUNCT
ejde-350	112	5	h.	h.	PROPN
ejde-350	112	6	chen	chen	PROPN
ejde-350	112	7	,	,	PUNCT
ejde-350	112	8	s.	s.	PROPN
ejde-350	112	9	liu	liu	PROPN
ejde-350	112	10	,	,	PUNCT
ejde-350	112	11	x.	x.	PROPN
ejde-350	112	12	fang	fang	PROPN
ejde-350	112	13	ejde-2020/01	ejde-2020/01	PROPN
ejde-350	112	14	theorem	theorem	VERB
ejde-350	112	15	1.2	1.2	NUM
ejde-350	112	16	.	.	PUNCT
ejde-350	113	1	let	let	VERB
ejde-350	113	2	s	s	PRON
ejde-350	113	3	∈	∈	PROPN
ejde-350	113	4	(	(	PUNCT
ejde-350	113	5	0	0	NUM
ejde-350	113	6	,	,	PUNCT
ejde-350	113	7	3/4	3/4	NUM
ejde-350	113	8	)	)	PUNCT
ejde-350	113	9	,	,	PUNCT
ejde-350	113	10	t	t	PROPN
ejde-350	113	11	∈	∈	PROPN
ejde-350	113	12	(	(	PUNCT
ejde-350	113	13	0	0	NUM
ejde-350	113	14	,	,	PUNCT
ejde-350	113	15	1	1	NUM
ejde-350	113	16	)	)	PUNCT
ejde-350	113	17	,	,	PUNCT
ejde-350	113	18	2t+	2t+	NUM
ejde-350	113	19	4s	4s	NUM
ejde-350	113	20	=	=	SYM
ejde-350	113	21	3	3	NUM
ejde-350	113	22	and	and	CCONJ
ejde-350	113	23	(	(	PUNCT
ejde-350	113	24	φ1	φ1	PROPN
ejde-350	113	25	)	)	PUNCT
ejde-350	113	26	hold	hold	NOUN
ejde-350	113	27	.	.	PUNCT
ejde-350	114	1	then	then	ADV
ejde-350	114	2	there	there	PRON
ejde-350	114	3	exists	exist	VERB
ejde-350	114	4	λ0	λ0	NOUN
ejde-350	114	5	such	such	ADJ
ejde-350	114	6	that	that	DET
ejde-350	114	7	system	system	NOUN
ejde-350	114	8	(	(	PUNCT
ejde-350	114	9	1.1	1.1	NUM
ejde-350	114	10	)	)	PUNCT
ejde-350	114	11	has	have	VERB
ejde-350	114	12	a	a	DET
ejde-350	114	13	radially	radially	ADV
ejde-350	114	14	symmetric	symmetric	ADJ
ejde-350	114	15	solution	solution	NOUN
ejde-350	114	16	for	for	ADP
ejde-350	114	17	all	all	DET
ejde-350	114	18	λ	λ	X
ejde-350	114	19	∈	∈	PROPN
ejde-350	114	20	(	(	PUNCT
ejde-350	114	21	0	0	NUM
ejde-350	114	22	,	,	PUNCT
ejde-350	114	23	λ0	λ0	NOUN
ejde-350	114	24	)	)	PUNCT
ejde-350	114	25	.	.	PUNCT
ejde-350	115	1	this	this	DET
ejde-350	115	2	article	article	NOUN
ejde-350	115	3	is	be	AUX
ejde-350	115	4	organized	organize	VERB
ejde-350	115	5	as	as	SCONJ
ejde-350	115	6	follows	follow	VERB
ejde-350	115	7	.	.	PUNCT
ejde-350	116	1	in	in	ADP
ejde-350	116	2	section	section	NOUN
ejde-350	116	3	2	2	NUM
ejde-350	116	4	,	,	PUNCT
ejde-350	116	5	we	we	PRON
ejde-350	116	6	present	present	VERB
ejde-350	116	7	some	some	DET
ejde-350	116	8	notations	notation	NOUN
ejde-350	116	9	.	.	PUNCT
ejde-350	117	1	in	in	ADP
ejde-350	117	2	section	section	NOUN
ejde-350	117	3	3	3	NUM
ejde-350	117	4	,	,	PUNCT
ejde-350	117	5	we	we	PRON
ejde-350	117	6	give	give	VERB
ejde-350	117	7	the	the	DET
ejde-350	117	8	proof	proof	NOUN
ejde-350	117	9	of	of	ADP
ejde-350	117	10	theorem	theorem	ADJ
ejde-350	117	11	1.1	1.1	NUM
ejde-350	117	12	.	.	PUNCT
ejde-350	118	1	in	in	ADP
ejde-350	118	2	section	section	NOUN
ejde-350	118	3	4	4	NUM
ejde-350	118	4	,	,	PUNCT
ejde-350	118	5	we	we	PRON
ejde-350	118	6	show	show	VERB
ejde-350	118	7	the	the	DET
ejde-350	118	8	proof	proof	NOUN
ejde-350	118	9	of	of	ADP
ejde-350	118	10	theorem	theorem	ADJ
ejde-350	118	11	1.2	1.2	NUM
ejde-350	118	12	.	.	NOUN
ejde-350	118	13	2	2	NUM
ejde-350	118	14	.	.	NUM
ejde-350	118	15	preliminaries	preliminary	NOUN
ejde-350	118	16	for	for	ADP
ejde-350	118	17	s	s	PROPN
ejde-350	118	18	∈	∈	PROPN
ejde-350	118	19	(	(	PUNCT
ejde-350	118	20	0	0	NUM
ejde-350	118	21	,	,	PUNCT
ejde-350	118	22	1	1	NUM
ejde-350	118	23	)	)	PUNCT
ejde-350	118	24	,	,	PUNCT
ejde-350	118	25	the	the	DET
ejde-350	118	26	space	space	NOUN
ejde-350	118	27	ds,2(r3	ds,2(r3	PROPN
ejde-350	118	28	)	)	PUNCT
ejde-350	118	29	is	be	AUX
ejde-350	118	30	the	the	DET
ejde-350	118	31	completion	completion	NOUN
ejde-350	118	32	of	of	ADP
ejde-350	118	33	c∞0	c∞0	PROPN
ejde-350	118	34	(	(	PUNCT
ejde-350	118	35	r3	r3	PROPN
ejde-350	118	36	)	)	PUNCT
ejde-350	118	37	with	with	ADP
ejde-350	118	38	respect	respect	NOUN
ejde-350	118	39	to	to	ADP
ejde-350	118	40	the	the	DET
ejde-350	118	41	norm	norm	NOUN
ejde-350	118	42	‖u‖2s	‖u‖2s	PUNCT
ejde-350	119	1	=	=	SYM
ejde-350	119	2	∫	∫	PROPN
ejde-350	119	3	r3	r3	PROPN
ejde-350	119	4	∫	∫	PROPN
ejde-350	119	5	r3	r3	PROPN
ejde-350	119	6	|u(x)−	|u(x)−	PROPN
ejde-350	119	7	u(y)|2	u(y)|2	PROPN
ejde-350	119	8	|x−	|x−	PROPN
ejde-350	120	1	y|3	y|3	PROPN
ejde-350	120	2	+	+	PROPN
ejde-350	120	3	2s	2s	PROPN
ejde-350	120	4	dxdy	dxdy	NOUN
ejde-350	120	5	.	.	PUNCT
ejde-350	121	1	we	we	PRON
ejde-350	121	2	denote	denote	VERB
ejde-350	121	3	by	by	ADP
ejde-350	121	4	ds,2	ds,2	NOUN
ejde-350	121	5	rad(r3	rad(r3	NOUN
ejde-350	121	6	)	)	PUNCT
ejde-350	121	7	the	the	DET
ejde-350	121	8	space	space	NOUN
ejde-350	121	9	of	of	ADP
ejde-350	121	10	radial	radial	ADJ
ejde-350	121	11	functions	function	NOUN
ejde-350	121	12	in	in	ADP
ejde-350	121	13	ds,2(r3	ds,2(r3	PROPN
ejde-350	121	14	)	)	PUNCT
ejde-350	121	15	.	.	PUNCT
ejde-350	122	1	we	we	PRON
ejde-350	122	2	could	could	AUX
ejde-350	122	3	define	define	VERB
ejde-350	122	4	the	the	DET
ejde-350	122	5	best	good	ADJ
ejde-350	122	6	constants	constant	NOUN
ejde-350	122	7	ss	ss	INTJ
ejde-350	122	8	:	:	PUNCT
ejde-350	122	9	=	=	NUM
ejde-350	122	10	inf	inf	PROPN
ejde-350	122	11	u∈ds,2(r3)\{0	u∈ds,2(r3)\{0	PROPN
ejde-350	122	12	}	}	PUNCT
ejde-350	122	13	‖u‖2s	‖u‖2s	PUNCT
ejde-350	122	14	(	(	PUNCT
ejde-350	122	15	∫	∫	PROPN
ejde-350	122	16	r3	r3	PROPN
ejde-350	122	17	|u|2∗	|u|2∗	NOUN
ejde-350	122	18	sdx	sdx	PROPN
ejde-350	122	19	)	)	PUNCT
ejde-350	122	20	2	2	NUM
ejde-350	122	21	2∗s	2∗s	NUM
ejde-350	122	22	.	.	PUNCT
ejde-350	123	1	(	(	PUNCT
ejde-350	123	2	2.1	2.1	NUM
ejde-350	123	3	)	)	PUNCT
ejde-350	123	4	we	we	PRON
ejde-350	123	5	know	know	VERB
ejde-350	123	6	that	that	SCONJ
ejde-350	123	7	ss	ss	PROPN
ejde-350	123	8	can	can	AUX
ejde-350	123	9	be	be	AUX
ejde-350	123	10	attained	attain	VERB
ejde-350	123	11	in	in	ADP
ejde-350	123	12	r3	r3	PROPN
ejde-350	123	13	(	(	PUNCT
ejde-350	123	14	see	see	VERB
ejde-350	123	15	[	[	X
ejde-350	123	16	33	33	NUM
ejde-350	123	17	]	]	NUM
ejde-350	123	18	)	)	PUNCT
ejde-350	123	19	.	.	PUNCT
ejde-350	124	1	for	for	ADP
ejde-350	124	2	u	u	PROPN
ejde-350	124	3	∈	∈	PROPN
ejde-350	124	4	ds,2(r3	ds,2(r3	PROPN
ejde-350	124	5	)	)	PUNCT
ejde-350	124	6	,	,	PUNCT
ejde-350	124	7	we	we	PRON
ejde-350	124	8	have	have	VERB
ejde-350	124	9	the	the	DET
ejde-350	124	10	hardy	hardy	ADJ
ejde-350	124	11	inequality	inequality	NOUN
ejde-350	124	12	(	(	PUNCT
ejde-350	124	13	see	see	VERB
ejde-350	124	14	[	[	X
ejde-350	124	15	22	22	NUM
ejde-350	124	16	]	]	PUNCT
ejde-350	124	17	):	):	PUNCT
ejde-350	125	1	cs,2	cs,2	PROPN
ejde-350	125	2	∫	∫	PROPN
ejde-350	125	3	r3	r3	PROPN
ejde-350	125	4	|u|2	|u|2	PROPN
ejde-350	125	5	|x|2s	|x|2s	PROPN
ejde-350	125	6	dx	dx	PROPN
ejde-350	125	7	6	6	NUM
ejde-350	125	8	∫	∫	PROPN
ejde-350	125	9	r3	r3	PROPN
ejde-350	125	10	∫	∫	PROPN
ejde-350	125	11	r3	r3	PROPN
ejde-350	125	12	|u(x)−	|u(x)−	PROPN
ejde-350	125	13	u(y)|2	u(y)|2	PROPN
ejde-350	125	14	|x−	|x−	PROPN
ejde-350	126	1	y|3	y|3	PROPN
ejde-350	126	2	+	+	PROPN
ejde-350	126	3	2s	2s	PROPN
ejde-350	126	4	dxdy	dxdy	NOUN
ejde-350	126	5	,	,	PUNCT
ejde-350	126	6	(	(	PUNCT
ejde-350	126	7	2.2	2.2	NUM
ejde-350	126	8	)	)	PUNCT
ejde-350	126	9	with	with	ADP
ejde-350	126	10	cs,2	cs,2	PROPN
ejde-350	126	11	:	:	PUNCT
ejde-350	126	12	=	=	SYM
ejde-350	126	13	2	2	NUM
ejde-350	126	14	∫	∫	NOUN
ejde-350	126	15	1	1	NUM
ejde-350	126	16	0	0	NUM
ejde-350	126	17	r2s−1|1−	r2s−1|1−	NOUN
ejde-350	126	18	r	r	NOUN
ejde-350	126	19	3−2s	3−2s	NUM
ejde-350	126	20	2	2	NUM
ejde-350	126	21	|2φs,2(r)dr	|2φs,2(r)dr	NOUN
ejde-350	126	22	.	.	PUNCT
ejde-350	127	1	we	we	PRON
ejde-350	127	2	introduce	introduce	VERB
ejde-350	127	3	the	the	DET
ejde-350	127	4	measure	measure	NOUN
ejde-350	127	5	dϑ	dϑ	NOUN
ejde-350	127	6	induced	induce	VERB
ejde-350	127	7	by	by	ADP
ejde-350	127	8	lebesgues	lebesgue	NOUN
ejde-350	127	9	measure	measure	NOUN
ejde-350	127	10	on	on	ADP
ejde-350	127	11	the	the	DET
ejde-350	127	12	unit	unit	NOUN
ejde-350	127	13	sphere	sphere	PROPN
ejde-350	127	14	s2	s2	PROPN
ejde-350	127	15	⊂	⊂	PROPN
ejde-350	127	16	r3	r3	PROPN
ejde-350	127	17	.	.	PUNCT
ejde-350	128	1	we	we	PRON
ejde-350	128	2	denote	denote	VERB
ejde-350	128	3	by	by	ADP
ejde-350	128	4	‖	‖	PROPN
ejde-350	128	5	·	·	SYM
ejde-350	128	6	‖lq(s2	‖lq(s2	PROPN
ejde-350	128	7	)	)	PUNCT
ejde-350	128	8	the	the	DET
ejde-350	128	9	quantity	quantity	NOUN
ejde-350	128	10	‖φ‖qlq(s2	‖φ‖qlq(s2	NUM
ejde-350	128	11	)	)	PUNCT
ejde-350	128	12	=	=	SYM
ejde-350	128	13	∫	∫	PROPN
ejde-350	128	14	s2	s2	VERB
ejde-350	128	15	|φ(ϑ)|qdϑ.	|φ(ϑ)|qdϑ.	NUM
ejde-350	128	16	lemma	lemma	PROPN
ejde-350	128	17	2.1	2.1	NUM
ejde-350	128	18	(	(	PUNCT
ejde-350	128	19	[	[	X
ejde-350	128	20	24	24	NUM
ejde-350	128	21	]	]	PUNCT
ejde-350	128	22	)	)	PUNCT
ejde-350	128	23	.	.	PUNCT
ejde-350	129	1	let	let	VERB
ejde-350	129	2	s	s	PRON
ejde-350	129	3	∈	∈	PROPN
ejde-350	129	4	(	(	PUNCT
ejde-350	129	5	0	0	NUM
ejde-350	129	6	,	,	PUNCT
ejde-350	129	7	1	1	NUM
ejde-350	129	8	)	)	PUNCT
ejde-350	129	9	and	and	CCONJ
ejde-350	129	10	0	0	NUM
ejde-350	129	11	6	6	NUM
ejde-350	129	12	φ	φ	NUM
ejde-350	129	13	∈	∈	PROPN
ejde-350	129	14	l	l	NOUN
ejde-350	129	15	3	3	NUM
ejde-350	129	16	2s	2s	PROPN
ejde-350	129	17	(	(	PUNCT
ejde-350	129	18	s2	s2	PROPN
ejde-350	129	19	)	)	PUNCT
ejde-350	129	20	.	.	PUNCT
ejde-350	130	1	then∫	then∫	PROPN
ejde-350	130	2	r3	r3	PROPN
ejde-350	130	3	∫	∫	PROPN
ejde-350	130	4	r3	r3	PROPN
ejde-350	130	5	|u(x)−	|u(x)−	PROPN
ejde-350	130	6	u(y)|2	u(y)|2	PROPN
ejde-350	130	7	|x−	|x−	PROPN
ejde-350	131	1	y|3	y|3	PROPN
ejde-350	131	2	+	+	PROPN
ejde-350	131	3	2s	2s	PROPN
ejde-350	131	4	dxdy	dxdy	PROPN
ejde-350	131	5	>	>	X
ejde-350	131	6	λ(φ	λ(φ	PROPN
ejde-350	131	7	)	)	PUNCT
ejde-350	131	8	∫	∫	PROPN
ejde-350	131	9	r3	r3	PROPN
ejde-350	131	10	φ(x/|x|)|u|2	φ(x/|x|)|u|2	PROPN
ejde-350	131	11	|x|2s	|x|2s	ADJ
ejde-350	131	12	dx	dx	PROPN
ejde-350	131	13	,	,	PUNCT
ejde-350	131	14	where	where	SCONJ
ejde-350	131	15	u	u	PROPN
ejde-350	131	16	∈	∈	PROPN
ejde-350	131	17	ds,2(r3	ds,2(r3	PROPN
ejde-350	131	18	)	)	PUNCT
ejde-350	131	19	and	and	CCONJ
ejde-350	131	20	λ(φ	λ(φ	PROPN
ejde-350	131	21	)	)	PUNCT
ejde-350	131	22	=	=	PUNCT
ejde-350	131	23	cs,2|s2|	cs,2|s2|	NOUN
ejde-350	132	1	2s	2s	NOUN
ejde-350	132	2	3	3	NUM
ejde-350	132	3	‖φ‖−1	‖φ‖−1	NOUN
ejde-350	132	4	l	l	NOUN
ejde-350	132	5	3	3	NUM
ejde-350	132	6	2s	2s	PROPN
ejde-350	132	7	(	(	PUNCT
ejde-350	132	8	s2	s2	PROPN
ejde-350	132	9	)	)	PUNCT
ejde-350	132	10	.	.	PUNCT
ejde-350	133	1	by	by	ADP
ejde-350	133	2	using	use	VERB
ejde-350	133	3	lemma	lemma	PROPN
ejde-350	133	4	2.1	2.1	NUM
ejde-350	133	5	and	and	CCONJ
ejde-350	133	6	µ	µ	PRON
ejde-350	133	7	∈	∈	NOUN
ejde-350	133	8	(	(	PUNCT
ejde-350	133	9	0,λ(φ	0,λ(φ	NUM
ejde-350	133	10	)	)	PUNCT
ejde-350	133	11	)	)	PUNCT
ejde-350	133	12	,	,	PUNCT
ejde-350	133	13	‖u‖φ	‖u‖φ	NOUN
ejde-350	133	14	=	=	SYM
ejde-350	133	15	(	(	PUNCT
ejde-350	133	16	∫	∫	PROPN
ejde-350	133	17	r3	r3	PROPN
ejde-350	133	18	∫	∫	PROPN
ejde-350	133	19	r3	r3	PROPN
ejde-350	133	20	|u(x)−	|u(x)−	PROPN
ejde-350	133	21	u(y)|2	u(y)|2	PROPN
ejde-350	133	22	|x−	|x−	PROPN
ejde-350	133	23	y|3	y|3	PROPN
ejde-350	133	24	+	+	PROPN
ejde-350	133	25	2s	2s	PROPN
ejde-350	133	26	dxdy	dxdy	PROPN
ejde-350	133	27	−	−	PROPN
ejde-350	133	28	µ	µ	PROPN
ejde-350	133	29	∫	∫	PROPN
ejde-350	133	30	r3	r3	PROPN
ejde-350	133	31	φ(x/|x|)|u|2	φ(x/|x|)|u|2	PROPN
ejde-350	133	32	|x|2s	|x|2s	PROPN
ejde-350	133	33	dx	dx	PROPN
ejde-350	133	34	)	)	PUNCT
ejde-350	133	35	1/2	1/2	NUM
ejde-350	133	36	is	be	AUX
ejde-350	133	37	an	an	DET
ejde-350	133	38	equivalent	equivalent	ADJ
ejde-350	133	39	norm	norm	NOUN
ejde-350	133	40	in	in	ADP
ejde-350	133	41	ds,2(rn	ds,2(rn	PROPN
ejde-350	133	42	)	)	PUNCT
ejde-350	133	43	.	.	PUNCT
ejde-350	134	1	lemma	lemma	PROPN
ejde-350	134	2	2.2	2.2	NUM
ejde-350	134	3	(	(	PUNCT
ejde-350	134	4	[	[	X
ejde-350	134	5	29	29	NUM
ejde-350	134	6	]	]	PUNCT
ejde-350	134	7	)	)	PUNCT
ejde-350	134	8	.	.	PUNCT
ejde-350	135	1	let	let	VERB
ejde-350	135	2	t	t	NOUN
ejde-350	135	3	,	,	PUNCT
ejde-350	135	4	r	r	NOUN
ejde-350	135	5	>	>	X
ejde-350	135	6	1	1	NUM
ejde-350	135	7	and	and	CCONJ
ejde-350	135	8	0	0	NUM
ejde-350	135	9	<	<	X
ejde-350	135	10	α	α	X
ejde-350	135	11	<	<	X
ejde-350	135	12	3	3	NUM
ejde-350	135	13	with	with	ADP
ejde-350	135	14	1	1	NUM
ejde-350	135	15	t	t	NOUN
ejde-350	135	16	+	+	CCONJ
ejde-350	135	17	1	1	NUM
ejde-350	135	18	r	r	NOUN
ejde-350	135	19	+	+	NUM
ejde-350	135	20	3−α	3−α	NUM
ejde-350	135	21	3	3	NUM
ejde-350	135	22	=	=	SYM
ejde-350	135	23	2	2	NUM
ejde-350	135	24	,	,	PUNCT
ejde-350	135	25	f	f	PROPN
ejde-350	135	26	∈	∈	PROPN
ejde-350	135	27	lt(r3	lt(r3	PROPN
ejde-350	135	28	)	)	PUNCT
ejde-350	135	29	and	and	CCONJ
ejde-350	135	30	h	h	NOUN
ejde-350	135	31	∈	∈	PROPN
ejde-350	135	32	lr(r3	lr(r3	PROPN
ejde-350	135	33	)	)	PUNCT
ejde-350	135	34	.	.	PUNCT
ejde-350	136	1	there	there	PRON
ejde-350	136	2	exists	exist	VERB
ejde-350	136	3	a	a	DET
ejde-350	136	4	sharp	sharp	ADJ
ejde-350	136	5	constant	constant	ADJ
ejde-350	136	6	c(α	c(α	PROPN
ejde-350	136	7	,	,	PUNCT
ejde-350	136	8	t	t	PROPN
ejde-350	136	9	,	,	PUNCT
ejde-350	136	10	r	r	NOUN
ejde-350	136	11	)	)	PUNCT
ejde-350	136	12	>	>	X
ejde-350	136	13	0	0	NUM
ejde-350	136	14	,	,	PUNCT
ejde-350	136	15	independent	independent	ADJ
ejde-350	136	16	of	of	ADP
ejde-350	136	17	f	f	PROPN
ejde-350	136	18	,	,	PUNCT
ejde-350	136	19	h	h	PROPN
ejde-350	136	20	such	such	ADJ
ejde-350	136	21	that	that	SCONJ
ejde-350	136	22	∫	∫	PROPN
ejde-350	136	23	r3	r3	PROPN
ejde-350	136	24	∫	∫	PROPN
ejde-350	136	25	r3	r3	PROPN
ejde-350	136	26	|f(x)||h(y)|	|f(x)||h(y)|	PROPN
ejde-350	136	27	|x−	|x−	PROPN
ejde-350	136	28	y|3−α	y|3−α	PROPN
ejde-350	136	29	dxdy	dxdy	PROPN
ejde-350	136	30	6	6	NUM
ejde-350	136	31	c(α	c(α	PROPN
ejde-350	136	32	,	,	PUNCT
ejde-350	136	33	t	t	PROPN
ejde-350	136	34	,	,	PUNCT
ejde-350	136	35	r)‖f‖t‖h‖r	r)‖f‖t‖h‖r	PROPN
ejde-350	136	36	.	.	PUNCT
ejde-350	137	1	if	if	SCONJ
ejde-350	137	2	t	t	NOUN
ejde-350	137	3	=	=	SYM
ejde-350	137	4	r	r	NOUN
ejde-350	137	5	=	=	SYM
ejde-350	137	6	6	6	NUM
ejde-350	137	7	3+α	3+α	NUM
ejde-350	137	8	,	,	PUNCT
ejde-350	137	9	then	then	ADV
ejde-350	137	10	c(α	c(α	PROPN
ejde-350	137	11	,	,	PUNCT
ejde-350	137	12	t	t	PROPN
ejde-350	137	13	,	,	PUNCT
ejde-350	137	14	r	r	NOUN
ejde-350	137	15	)	)	PUNCT
ejde-350	137	16	=	=	SYM
ejde-350	137	17	c(α	c(α	NOUN
ejde-350	137	18	)	)	PUNCT
ejde-350	137	19	=	=	PUNCT
ejde-350	137	20	π	π	NOUN
ejde-350	137	21	3−α	3−α	NUM
ejde-350	137	22	2	2	NUM
ejde-350	137	23	γ(α2	γ(α2	NOUN
ejde-350	137	24	)	)	PUNCT
ejde-350	138	1	γ(3	γ(3	PROPN
ejde-350	139	1	+	+	PUNCT
ejde-350	139	2	α	α	PROPN
ejde-350	139	3	2	2	NUM
ejde-350	139	4	)	)	PUNCT
ejde-350	139	5	{	{	PUNCT
ejde-350	139	6	γ	γ	X
ejde-350	139	7	(	(	PUNCT
ejde-350	139	8	3	3	NUM
ejde-350	139	9	2	2	NUM
ejde-350	139	10	)	)	PUNCT
ejde-350	139	11	γ(3	γ(3	PROPN
ejde-350	139	12	)	)	PUNCT
ejde-350	139	13	}	}	PUNCT
ejde-350	139	14	−α/3	−α/3	PROPN
ejde-350	139	15	.	.	PUNCT
ejde-350	140	1	ejde-2020/01	ejde-2020/01	NOUN
ejde-350	140	2	fractional	fractional	ADJ
ejde-350	140	3	schrödinger	schrödinger	NOUN
ejde-350	140	4	-	-	PUNCT
ejde-350	140	5	poisson	poisson	NOUN
ejde-350	140	6	system	system	NOUN
ejde-350	140	7	7	7	NUM
ejde-350	140	8	a	a	DET
ejde-350	140	9	measurable	measurable	ADJ
ejde-350	140	10	function	function	NOUN
ejde-350	140	11	u	u	NOUN
ejde-350	140	12	:	:	PUNCT
ejde-350	140	13	r3	r3	PROPN
ejde-350	140	14	→	→	SYM
ejde-350	140	15	r	r	NOUN
ejde-350	140	16	belongs	belong	VERB
ejde-350	140	17	to	to	ADP
ejde-350	140	18	the	the	DET
ejde-350	140	19	morrey	morrey	PROPN
ejde-350	140	20	space	space	NOUN
ejde-350	140	21	lq,$(r3	lq,$(r3	ADV
ejde-350	140	22	)	)	PUNCT
ejde-350	140	23	with	with	ADP
ejde-350	140	24	q	q	PROPN
ejde-350	140	25	∈	∈	PROPN
ejde-350	141	1	[	[	X
ejde-350	141	2	1,∞	1,∞	NUM
ejde-350	141	3	)	)	PUNCT
ejde-350	141	4	and	and	CCONJ
ejde-350	141	5	$	$	SYM
ejde-350	141	6	∈	∈	NOUN
ejde-350	141	7	(	(	PUNCT
ejde-350	141	8	0	0	NUM
ejde-350	141	9	,	,	PUNCT
ejde-350	141	10	n	n	CCONJ
ejde-350	141	11	]	]	PUNCT
ejde-350	141	12	if	if	SCONJ
ejde-350	141	13	‖u‖qlq,$(r3	‖u‖qlq,$(r3	PROPN
ejde-350	141	14	)	)	PUNCT
ejde-350	141	15	=	=	SYM
ejde-350	141	16	sup	sup	NOUN
ejde-350	141	17	r>0,x∈r3	r>0,x∈r3	PROPN
ejde-350	142	1	r$−3	r$−3	PROPN
ejde-350	142	2	∫	∫	PROPN
ejde-350	142	3	b(x	b(x	PROPN
ejde-350	142	4	,	,	PUNCT
ejde-350	142	5	r	r	NOUN
ejde-350	142	6	)	)	PUNCT
ejde-350	142	7	|u(y)|qdy	|u(y)|qdy	ADP
ejde-350	142	8	<	<	X
ejde-350	142	9	∞.	∞.	PROPN
ejde-350	142	10	lemma	lemma	PROPN
ejde-350	142	11	2.3	2.3	NUM
ejde-350	142	12	(	(	PUNCT
ejde-350	142	13	[	[	X
ejde-350	142	14	35	35	NUM
ejde-350	142	15	]	]	SYM
ejde-350	142	16	)	)	PUNCT
ejde-350	142	17	.	.	PUNCT
ejde-350	143	1	for	for	ADP
ejde-350	143	2	s	s	PROPN
ejde-350	143	3	∈	∈	PROPN
ejde-350	143	4	(	(	PUNCT
ejde-350	143	5	0	0	NUM
ejde-350	143	6	,	,	PUNCT
ejde-350	143	7	1	1	NUM
ejde-350	143	8	)	)	PUNCT
ejde-350	143	9	,	,	PUNCT
ejde-350	143	10	there	there	PRON
ejde-350	143	11	exists	exist	VERB
ejde-350	143	12	c	c	NOUN
ejde-350	143	13	>	>	X
ejde-350	143	14	0	0	NUM
ejde-350	144	1	such	such	ADJ
ejde-350	144	2	that	that	PRON
ejde-350	144	3	for	for	ADP
ejde-350	144	4	ι	ι	PROPN
ejde-350	144	5	and	and	CCONJ
ejde-350	144	6	ϑ	ϑ	AUX
ejde-350	144	7	satisfying	satisfy	VERB
ejde-350	144	8	2	2	NUM
ejde-350	144	9	2∗	2∗	NUM
ejde-350	144	10	s	s	PART
ejde-350	144	11	6	6	NUM
ejde-350	144	12	ι	ι	SYM
ejde-350	144	13	<	<	X
ejde-350	144	14	1	1	NUM
ejde-350	144	15	,	,	PUNCT
ejde-350	144	16	1	1	NUM
ejde-350	144	17	6	6	NUM
ejde-350	144	18	ϑ	ϑ	X
ejde-350	144	19	<	<	X
ejde-350	144	20	2∗s	2∗s	NUM
ejde-350	144	21	,	,	PUNCT
ejde-350	144	22	we	we	PRON
ejde-350	144	23	have	have	VERB
ejde-350	144	24	(	(	PUNCT
ejde-350	144	25	∫	∫	PROPN
ejde-350	144	26	r3	r3	PROPN
ejde-350	144	27	|u|2	|u|2	PROPN
ejde-350	144	28	∗	∗	PROPN
ejde-350	144	29	sdx	sdx	PROPN
ejde-350	144	30	)	)	PUNCT
ejde-350	144	31	1/(2∗	1/(2∗	NUM
ejde-350	144	32	s	s	NOUN
ejde-350	144	33	)	)	PUNCT
ejde-350	144	34	6	6	NUM
ejde-350	144	35	c‖u‖ιs‖u‖1−ι	c‖u‖ιs‖u‖1−ι	NOUN
ejde-350	144	36	lϑ	lϑ	PROPN
ejde-350	144	37	,	,	PUNCT
ejde-350	144	38	ϑ(n−2s	ϑ(n−2s	PROPN
ejde-350	144	39	)	)	PUNCT
ejde-350	144	40	2	2	NUM
ejde-350	144	41	(	(	PUNCT
ejde-350	144	42	r3	r3	PROPN
ejde-350	144	43	)	)	PUNCT
ejde-350	144	44	,	,	PUNCT
ejde-350	144	45	for	for	ADP
ejde-350	144	46	any	any	DET
ejde-350	144	47	u	u	PROPN
ejde-350	144	48	∈	∈	PROPN
ejde-350	144	49	ds,2(r3	ds,2(r3	PROPN
ejde-350	144	50	)	)	PUNCT
ejde-350	144	51	.	.	PUNCT
ejde-350	145	1	2.1	2.1	NUM
ejde-350	145	2	.	.	PUNCT
ejde-350	145	3	formulation	formulation	NOUN
ejde-350	145	4	of	of	ADP
ejde-350	145	5	system	system	NOUN
ejde-350	145	6	(	(	PUNCT
ejde-350	145	7	1.1	1.1	NUM
ejde-350	145	8	)	)	PUNCT
ejde-350	145	9	.	.	PUNCT
ejde-350	146	1	considering	consider	VERB
ejde-350	146	2	u	u	PROPN
ejde-350	146	3	∈	∈	PROPN
ejde-350	146	4	ds,2(r3	ds,2(r3	PROPN
ejde-350	146	5	)	)	PUNCT
ejde-350	146	6	,	,	PUNCT
ejde-350	146	7	we	we	PRON
ejde-350	146	8	define	define	VERB
ejde-350	146	9	the	the	DET
ejde-350	146	10	linear	linear	ADJ
ejde-350	146	11	functional	functional	ADJ
ejde-350	146	12	fu(v	fu(v	NOUN
ejde-350	146	13	)	)	PUNCT
ejde-350	146	14	:	:	PUNCT
ejde-350	147	1	dt,2(r3)→	dt,2(r3)→	ADP
ejde-350	147	2	r	r	NOUN
ejde-350	147	3	by	by	ADP
ejde-350	147	4	fu(v	fu(v	NOUN
ejde-350	147	5	)	)	PUNCT
ejde-350	147	6	=	=	SYM
ejde-350	147	7	∫	∫	PROPN
ejde-350	147	8	r3	r3	PROPN
ejde-350	147	9	u2vdx	u2vdx	PROPN
ejde-350	147	10	.	.	PUNCT
ejde-350	148	1	using	use	VERB
ejde-350	148	2	2t+	2t+	NUM
ejde-350	148	3	4s	4s	NUM
ejde-350	148	4	=	=	SYM
ejde-350	148	5	3	3	NUM
ejde-350	148	6	,	,	PUNCT
ejde-350	148	7	holder	holder	NOUN
ejde-350	148	8	’s	’s	PART
ejde-350	148	9	inequality	inequality	NOUN
ejde-350	148	10	,	,	PUNCT
ejde-350	148	11	and	and	CCONJ
ejde-350	148	12	(	(	PUNCT
ejde-350	148	13	1.9	1.9	NUM
ejde-350	148	14	)	)	PUNCT
ejde-350	148	15	,	,	PUNCT
ejde-350	148	16	we	we	PRON
ejde-350	148	17	obtain	obtain	VERB
ejde-350	148	18	|fu(v)|	|fu(v)|	NOUN
ejde-350	148	19	6	6	NUM
ejde-350	148	20	∫	∫	PROPN
ejde-350	148	21	r3	r3	PROPN
ejde-350	148	22	|u|	|u|	PROPN
ejde-350	148	23	6−4s	6−4s	NUM
ejde-350	148	24	3−2s	3−2s	NUM
ejde-350	148	25	|v|dx	|v|dx	NOUN
ejde-350	148	26	=	=	SYM
ejde-350	148	27	∫	∫	PROPN
ejde-350	148	28	r3	r3	PROPN
ejde-350	148	29	|u|	|u|	PROPN
ejde-350	148	30	3	3	NUM
ejde-350	148	31	+	+	SYM
ejde-350	148	32	2	2	NUM
ejde-350	148	33	t	t	NOUN
ejde-350	148	34	3−2s	3−2s	NUM
ejde-350	148	35	|v|dx	|v|dx	NOUN
ejde-350	148	36	6	6	NUM
ejde-350	148	37	(	(	PUNCT
ejde-350	148	38	∫	∫	PROPN
ejde-350	148	39	r3	r3	PROPN
ejde-350	148	40	|u|	|u|	PROPN
ejde-350	148	41	3	3	NUM
ejde-350	148	42	+	+	SYM
ejde-350	148	43	2	2	NUM
ejde-350	148	44	t	t	NOUN
ejde-350	148	45	3−2s	3−2s	NUM
ejde-350	148	46	·	·	PUNCT
ejde-350	148	47	6	6	NUM
ejde-350	148	48	3	3	NUM
ejde-350	148	49	+	+	SYM
ejde-350	148	50	2	2	NUM
ejde-350	148	51	t	t	NOUN
ejde-350	148	52	dx	dx	PROPN
ejde-350	148	53	)	)	PUNCT
ejde-350	149	1	3	3	NUM
ejde-350	149	2	+	+	SYM
ejde-350	149	3	2	2	NUM
ejde-350	149	4	t	t	NOUN
ejde-350	149	5	6	6	NUM
ejde-350	149	6	(	(	PUNCT
ejde-350	149	7	∫	∫	PROPN
ejde-350	149	8	r3	r3	PROPN
ejde-350	149	9	|v|	|v|	NUM
ejde-350	149	10	6	6	NUM
ejde-350	149	11	3−2	3−2	NUM
ejde-350	149	12	t	t	NOUN
ejde-350	149	13	dx	dx	PROPN
ejde-350	149	14	)	)	PUNCT
ejde-350	149	15	3−2	3−2	NUM
ejde-350	149	16	t	t	NOUN
ejde-350	149	17	6	6	NUM
ejde-350	149	18	6	6	NUM
ejde-350	149	19	(	(	PUNCT
ejde-350	149	20	1	1	NUM
ejde-350	149	21	ss	ss	NOUN
ejde-350	149	22	‖u‖2s	‖u‖2s	PROPN
ejde-350	149	23	)	)	PUNCT
ejde-350	149	24	3	3	NUM
ejde-350	150	1	+	+	SYM
ejde-350	150	2	2	2	NUM
ejde-350	150	3	t	t	NOUN
ejde-350	150	4	6	6	NUM
ejde-350	150	5	(	(	PUNCT
ejde-350	150	6	1	1	NUM
ejde-350	150	7	st	st	PROPN
ejde-350	150	8	‖v‖2	‖v‖2	PROPN
ejde-350	150	9	t	t	NOUN
ejde-350	150	10	)	)	PUNCT
ejde-350	150	11	3−2	3−2	NUM
ejde-350	150	12	t	t	NOUN
ejde-350	150	13	6	6	NUM
ejde-350	150	14	,	,	PUNCT
ejde-350	150	15	which	which	PRON
ejde-350	150	16	implies	imply	VERB
ejde-350	150	17	that	that	SCONJ
ejde-350	150	18	fu	fu	NOUN
ejde-350	150	19	is	be	AUX
ejde-350	150	20	well	well	ADV
ejde-350	150	21	defined	define	VERB
ejde-350	150	22	and	and	CCONJ
ejde-350	150	23	continuous	continuous	ADJ
ejde-350	150	24	in	in	ADP
ejde-350	150	25	dt,2(r3	dt,2(r3	PROPN
ejde-350	150	26	)	)	PUNCT
ejde-350	150	27	.	.	PUNCT
ejde-350	151	1	from	from	ADP
ejde-350	151	2	the	the	DET
ejde-350	151	3	lax	lax	PROPN
ejde-350	151	4	-	-	PUNCT
ejde-350	151	5	milgram	milgram	NOUN
ejde-350	151	6	theorem	theorem	NOUN
ejde-350	151	7	it	it	PRON
ejde-350	151	8	follows	follow	VERB
ejde-350	151	9	that	that	SCONJ
ejde-350	151	10	,	,	PUNCT
ejde-350	151	11	for	for	ADP
ejde-350	151	12	every	every	DET
ejde-350	151	13	u	u	PROPN
ejde-350	151	14	∈	∈	PROPN
ejde-350	151	15	ds,2(r3	ds,2(r3	PROPN
ejde-350	151	16	)	)	PUNCT
ejde-350	151	17	,	,	PUNCT
ejde-350	151	18	there	there	PRON
ejde-350	151	19	exists	exist	VERB
ejde-350	151	20	a	a	DET
ejde-350	151	21	unique	unique	ADJ
ejde-350	151	22	φu	φu	NOUN
ejde-350	151	23	,	,	PUNCT
ejde-350	151	24	t	t	PROPN
ejde-350	151	25	∈	∈	PROPN
ejde-350	151	26	dt,2(r3	dt,2(r3	PROPN
ejde-350	151	27	)	)	PUNCT
ejde-350	151	28	such	such	ADJ
ejde-350	151	29	that∫	that∫	NOUN
ejde-350	151	30	r3	r3	PROPN
ejde-350	151	31	(	(	PUNCT
ejde-350	151	32	−∆)t/2φu	−∆)t/2φu	PROPN
ejde-350	151	33	,	,	PUNCT
ejde-350	151	34	t(−∆)t/2vdx	t(−∆)t/2vdx	PROPN
ejde-350	151	35	=	=	SYM
ejde-350	151	36	∫	∫	PROPN
ejde-350	151	37	r3	r3	PROPN
ejde-350	151	38	u2vdx	u2vdx	PROPN
ejde-350	151	39	,	,	PUNCT
ejde-350	151	40	which	which	PRON
ejde-350	151	41	implies	imply	VERB
ejde-350	151	42	that	that	SCONJ
ejde-350	151	43	φu	φu	PROPN
ejde-350	151	44	,	,	PUNCT
ejde-350	151	45	t	t	PROPN
ejde-350	151	46	is	be	AUX
ejde-350	151	47	a	a	DET
ejde-350	151	48	weak	weak	ADJ
ejde-350	151	49	solution	solution	NOUN
ejde-350	151	50	of	of	ADP
ejde-350	151	51	(	(	PUNCT
ejde-350	151	52	−∆)tφu	−∆)tφu	PROPN
ejde-350	151	53	,	,	PUNCT
ejde-350	151	54	t	t	NOUN
ejde-350	151	55	=	=	SYM
ejde-350	151	56	u2	u2	PROPN
ejde-350	151	57	,	,	PUNCT
ejde-350	151	58	and	and	CCONJ
ejde-350	151	59	the	the	DET
ejde-350	151	60	representation	representation	NOUN
ejde-350	151	61	formula	formula	NOUN
ejde-350	151	62	holds	hold	VERB
ejde-350	151	63	,	,	PUNCT
ejde-350	151	64	φu	φu	NOUN
ejde-350	151	65	,	,	PUNCT
ejde-350	151	66	t	t	PROPN
ejde-350	151	67	=	=	SYM
ejde-350	151	68	∫	∫	PROPN
ejde-350	151	69	r3	r3	PROPN
ejde-350	151	70	|u(y)|2	|u(y)|2	X
ejde-350	151	71	|x−	|x−	NOUN
ejde-350	151	72	y|3−2	y|3−2	PROPN
ejde-350	151	73	t	t	PROPN
ejde-350	151	74	dy	dy	X
ejde-350	151	75	.	.	PUNCT
ejde-350	152	1	(	(	PUNCT
ejde-350	152	2	2.3	2.3	NUM
ejde-350	152	3	)	)	PUNCT
ejde-350	152	4	it	it	PRON
ejde-350	152	5	follows	follow	VERB
ejde-350	152	6	from	from	ADP
ejde-350	152	7	(	(	PUNCT
ejde-350	152	8	2.3	2.3	NUM
ejde-350	152	9	)	)	PUNCT
ejde-350	152	10	that	that	DET
ejde-350	152	11	system	system	NOUN
ejde-350	152	12	(	(	PUNCT
ejde-350	152	13	1.1	1.1	NUM
ejde-350	152	14	)	)	PUNCT
ejde-350	152	15	can	can	AUX
ejde-350	152	16	be	be	AUX
ejde-350	152	17	rewritten	rewrite	VERB
ejde-350	152	18	as	as	ADP
ejde-350	152	19	the	the	DET
ejde-350	152	20	equivalent	equivalent	ADJ
ejde-350	152	21	form	form	NOUN
ejde-350	152	22	(	(	PUNCT
ejde-350	152	23	−∆)su−	−∆)su−	PROPN
ejde-350	152	24	µφ(x/|x|	µφ(x/|x|	NOUN
ejde-350	152	25	)	)	PUNCT
ejde-350	152	26	|x|2s	|x|2s	ADJ
ejde-350	152	27	u+	u+	ADJ
ejde-350	152	28	λ	λ	PROPN
ejde-350	152	29	(	(	PUNCT
ejde-350	152	30	i2	i2	PROPN
ejde-350	152	31	t	t	PROPN
ejde-350	152	32	∗	∗	NOUN
ejde-350	152	33	|u|2	|u|2	PROPN
ejde-350	152	34	)	)	PUNCT
ejde-350	152	35	u	u	NOUN
ejde-350	152	36	=	=	PROPN
ejde-350	152	37	|u|2	|u|2	PROPN
ejde-350	152	38	∗	∗	VERB
ejde-350	152	39	s−2u	s−2u	PROPN
ejde-350	152	40	in	in	ADP
ejde-350	152	41	r3	r3	PROPN
ejde-350	152	42	.	.	PROPN
ejde-350	153	1	8	8	NUM
ejde-350	153	2	y.	y.	PROPN
ejde-350	153	3	su	su	PROPN
ejde-350	153	4	,	,	PUNCT
ejde-350	153	5	h.	h.	PROPN
ejde-350	153	6	chen	chen	PROPN
ejde-350	153	7	,	,	PUNCT
ejde-350	153	8	s.	s.	PROPN
ejde-350	153	9	liu	liu	PROPN
ejde-350	153	10	,	,	PUNCT
ejde-350	153	11	x.	x.	PROPN
ejde-350	153	12	fang	fang	PROPN
ejde-350	153	13	ejde-2020/01	ejde-2020/01	NOUN
ejde-350	153	14	3	3	X
ejde-350	153	15	.	.	NUM
ejde-350	153	16	perturbed	perturb	VERB
ejde-350	153	17	equation	equation	NOUN
ejde-350	153	18	we	we	PRON
ejde-350	153	19	look	look	VERB
ejde-350	153	20	at	at	ADP
ejde-350	153	21	equation	equation	NOUN
ejde-350	153	22	(	(	PUNCT
ejde-350	153	23	1.1	1.1	NUM
ejde-350	153	24	)	)	PUNCT
ejde-350	153	25	as	as	ADP
ejde-350	153	26	a	a	DET
ejde-350	153	27	perturbation	perturbation	NOUN
ejde-350	153	28	of	of	ADP
ejde-350	153	29	the	the	DET
ejde-350	153	30	equation	equation	NOUN
ejde-350	153	31	(	(	PUNCT
ejde-350	153	32	−∆)su−	−∆)su−	PROPN
ejde-350	153	33	µφ(x/|x|	µφ(x/|x|	NOUN
ejde-350	153	34	)	)	PUNCT
ejde-350	153	35	|x|2s	|x|2s	NOUN
ejde-350	153	36	u	u	NOUN
ejde-350	153	37	=	=	PROPN
ejde-350	153	38	|u|2	|u|2	PROPN
ejde-350	153	39	∗	∗	PROPN
ejde-350	153	40	s−2u	s−2u	PROPN
ejde-350	153	41	,	,	PUNCT
ejde-350	153	42	in	in	ADP
ejde-350	153	43	r3	r3	PROPN
ejde-350	153	44	.	.	PUNCT
ejde-350	154	1	(	(	PUNCT
ejde-350	154	2	3.1	3.1	NUM
ejde-350	154	3	)	)	PUNCT
ejde-350	154	4	we	we	PRON
ejde-350	154	5	introduce	introduce	VERB
ejde-350	154	6	the	the	DET
ejde-350	154	7	energy	energy	NOUN
ejde-350	154	8	functional	functional	NOUN
ejde-350	154	9	associated	associate	VERB
ejde-350	154	10	with	with	ADP
ejde-350	154	11	(	(	PUNCT
ejde-350	154	12	1.8	1.8	NUM
ejde-350	154	13	)	)	PUNCT
ejde-350	154	14	by	by	ADP
ejde-350	154	15	i0(u	i0(u	SYM
ejde-350	154	16	)	)	PUNCT
ejde-350	154	17	=	=	SYM
ejde-350	154	18	1	1	NUM
ejde-350	154	19	2	2	X
ejde-350	154	20	‖u‖2φ	‖u‖2φ	NOUN
ejde-350	154	21	−	−	NOUN
ejde-350	154	22	1	1	NUM
ejde-350	154	23	2∗s	2∗s	NUM
ejde-350	154	24	∫	∫	NOUN
ejde-350	154	25	r3	r3	PROPN
ejde-350	154	26	|u|2	|u|2	PROPN
ejde-350	154	27	∗	∗	PROPN
ejde-350	154	28	sdx	sdx	PROPN
ejde-350	154	29	.	.	PUNCT
ejde-350	155	1	define	define	VERB
ejde-350	155	2	j0	j0	PROPN
ejde-350	155	3	=	=	SYM
ejde-350	155	4	i0|ds,2rad(r3	i0|ds,2rad(r3	PROPN
ejde-350	155	5	)	)	PUNCT
ejde-350	155	6	.	.	PUNCT
ejde-350	156	1	3.1	3.1	NUM
ejde-350	156	2	.	.	PUNCT
ejde-350	156	3	mountain	mountain	NOUN
ejde-350	156	4	pass	pass	NOUN
ejde-350	156	5	geometry	geometry	NOUN
ejde-350	156	6	and	and	CCONJ
ejde-350	156	7	nehari	nehari	PROPN
ejde-350	156	8	manifold	manifold	NOUN
ejde-350	156	9	.	.	PUNCT
ejde-350	157	1	lemma	lemma	PROPN
ejde-350	157	2	3.1	3.1	NUM
ejde-350	157	3	.	.	PUNCT
ejde-350	158	1	under	under	ADP
ejde-350	158	2	the	the	DET
ejde-350	158	3	assumptions	assumption	NOUN
ejde-350	158	4	of	of	ADP
ejde-350	158	5	theorem	theorem	NOUN
ejde-350	158	6	1.1	1.1	NUM
ejde-350	158	7	,	,	PUNCT
ejde-350	158	8	the	the	DET
ejde-350	158	9	functional	functional	ADJ
ejde-350	158	10	j0	j0	PROPN
ejde-350	158	11	possesses	possess	VERB
ejde-350	158	12	the	the	DET
ejde-350	158	13	mountain	mountain	NOUN
ejde-350	158	14	pass	pass	NOUN
ejde-350	158	15	geometry	geometry	NOUN
ejde-350	158	16	.	.	PUNCT
ejde-350	159	1	proof	proof	NOUN
ejde-350	159	2	.	.	PUNCT
ejde-350	160	1	we	we	PRON
ejde-350	160	2	prove	prove	VERB
ejde-350	160	3	that	that	SCONJ
ejde-350	160	4	j0	j0	PROPN
ejde-350	160	5	satisfies	satisfy	VERB
ejde-350	160	6	all	all	DET
ejde-350	160	7	the	the	DET
ejde-350	160	8	conditions	condition	NOUN
ejde-350	160	9	in	in	ADP
ejde-350	160	10	mountain	mountain	NOUN
ejde-350	160	11	pass	pass	NOUN
ejde-350	160	12	theorem	theorem	NOUN
ejde-350	160	13	.	.	PUNCT
ejde-350	161	1	(	(	PUNCT
ejde-350	161	2	i	i	NOUN
ejde-350	161	3	)	)	PUNCT
ejde-350	161	4	for	for	ADP
ejde-350	161	5	any	any	DET
ejde-350	161	6	u	u	PROPN
ejde-350	161	7	∈	∈	PROPN
ejde-350	161	8	ds,2	ds,2	NOUN
ejde-350	161	9	rad(r3	rad(r3	NOUN
ejde-350	161	10	)	)	PUNCT
ejde-350	161	11	\	\	NOUN
ejde-350	161	12	{	{	PUNCT
ejde-350	161	13	0	0	NUM
ejde-350	161	14	}	}	PUNCT
ejde-350	161	15	,	,	PUNCT
ejde-350	161	16	we	we	PRON
ejde-350	161	17	have	have	VERB
ejde-350	161	18	j0(u	j0(u	VERB
ejde-350	161	19	)	)	PUNCT
ejde-350	161	20	>	>	X
ejde-350	161	21	1	1	NUM
ejde-350	161	22	2	2	X
ejde-350	161	23	‖u‖2φ	‖u‖2φ	NOUN
ejde-350	161	24	−	−	NOUN
ejde-350	161	25	1	1	NUM
ejde-350	161	26	2∗s	2∗s	NUM
ejde-350	161	27	·	·	PUNCT
ejde-350	161	28	s	s	VERB
ejde-350	161	29	2∗	2∗	NUM
ejde-350	161	30	s	s	PART
ejde-350	161	31	s	s	X
ejde-350	161	32	‖u‖2	‖u‖2	PROPN
ejde-350	161	33	∗	∗	PROPN
ejde-350	161	34	s	s	NOUN
ejde-350	161	35	φ	φ	NOUN
ejde-350	161	36	.	.	PUNCT
ejde-350	162	1	because	because	SCONJ
ejde-350	162	2	of	of	ADP
ejde-350	162	3	2	2	NUM
ejde-350	162	4	<	<	NOUN
ejde-350	162	5	2∗s	2∗s	NUM
ejde-350	162	6	,	,	PUNCT
ejde-350	162	7	there	there	PRON
ejde-350	162	8	exists	exist	VERB
ejde-350	162	9	a	a	DET
ejde-350	162	10	sufficiently	sufficiently	ADV
ejde-350	162	11	small	small	ADJ
ejde-350	162	12	positive	positive	ADJ
ejde-350	162	13	number	number	NOUN
ejde-350	162	14	ρ	ρ	NOUN
ejde-350	162	15	such	such	ADJ
ejde-350	162	16	that	that	SCONJ
ejde-350	162	17	ς	ς	PROPN
ejde-350	162	18	:	:	PUNCT
ejde-350	162	19	=	=	NUM
ejde-350	162	20	inf	inf	ADJ
ejde-350	162	21	‖u‖s	‖u‖s	NOUN
ejde-350	162	22	=	=	PROPN
ejde-350	162	23	ρ	ρ	PROPN
ejde-350	162	24	j0(u	j0(u	PROPN
ejde-350	162	25	)	)	PUNCT
ejde-350	162	26	>	>	X
ejde-350	162	27	0	0	PUNCT
ejde-350	163	1	=	=	SYM
ejde-350	163	2	j0(0	j0(0	PROPN
ejde-350	163	3	)	)	PUNCT
ejde-350	163	4	.	.	PUNCT
ejde-350	164	1	(	(	PUNCT
ejde-350	164	2	ii	ii	NOUN
ejde-350	164	3	)	)	PUNCT
ejde-350	164	4	given	give	VERB
ejde-350	164	5	u	u	NOUN
ejde-350	164	6	∈	∈	PROPN
ejde-350	164	7	ds,2	ds,2	NOUN
ejde-350	164	8	rad(r3	rad(r3	NOUN
ejde-350	164	9	)	)	PUNCT
ejde-350	164	10	\	\	NOUN
ejde-350	164	11	{	{	PUNCT
ejde-350	164	12	0	0	NUM
ejde-350	164	13	}	}	PUNCT
ejde-350	164	14	,	,	PUNCT
ejde-350	164	15	we	we	PRON
ejde-350	164	16	have	have	VERB
ejde-350	164	17	j0(tu	j0(tu	PROPN
ejde-350	164	18	)	)	PUNCT
ejde-350	164	19	=	=	SYM
ejde-350	164	20	t2	t2	NOUN
ejde-350	164	21	2	2	NUM
ejde-350	164	22	‖u‖2φ	‖u‖2φ	PROPN
ejde-350	164	23	−	−	PROPN
ejde-350	164	24	t2	t2	PROPN
ejde-350	164	25	∗	∗	NOUN
ejde-350	164	26	s	s	PART
ejde-350	164	27	2∗s	2∗s	NUM
ejde-350	164	28	∫	∫	NOUN
ejde-350	164	29	r3	r3	PROPN
ejde-350	164	30	|u|2	|u|2	PROPN
ejde-350	164	31	∗	∗	PROPN
ejde-350	164	32	sdx	sdx	PROPN
ejde-350	164	33	<	<	X
ejde-350	164	34	0	0	PROPN
ejde-350	164	35	,	,	PUNCT
ejde-350	164	36	for	for	ADP
ejde-350	164	37	t	t	NOUN
ejde-350	164	38	large	large	ADJ
ejde-350	164	39	enough	enough	ADV
ejde-350	164	40	.	.	PUNCT
ejde-350	165	1	we	we	PRON
ejde-350	165	2	choose	choose	VERB
ejde-350	165	3	tu	tu	PROPN
ejde-350	165	4	>	>	X
ejde-350	165	5	0	0	PUNCT
ejde-350	166	1	corresponding	correspond	VERB
ejde-350	166	2	to	to	ADP
ejde-350	166	3	u	u	PRON
ejde-350	166	4	such	such	ADJ
ejde-350	166	5	that	that	PRON
ejde-350	166	6	j0(tu	j0(tu	PROPN
ejde-350	166	7	)	)	PUNCT
ejde-350	166	8	<	<	X
ejde-350	166	9	0	0	NUM
ejde-350	166	10	for	for	ADP
ejde-350	166	11	all	all	DET
ejde-350	166	12	t	t	PROPN
ejde-350	166	13	>	>	X
ejde-350	166	14	tu	tu	PROPN
ejde-350	166	15	and	and	CCONJ
ejde-350	166	16	‖tuu‖s	‖tuu‖s	PROPN
ejde-350	166	17	>	>	X
ejde-350	166	18	ρ	ρ	PROPN
ejde-350	166	19	.	.	PUNCT
ejde-350	166	20	�	�	PROPN
ejde-350	166	21	define	define	VERB
ejde-350	166	22	c0	c0	PROPN
ejde-350	166	23	=	=	PROPN
ejde-350	166	24	inf	inf	PROPN
ejde-350	166	25	υ∈γ0	υ∈γ0	NOUN
ejde-350	166	26	max	max	PROPN
ejde-350	166	27	t∈[0,1	t∈[0,1	PROPN
ejde-350	166	28	]	]	X
ejde-350	166	29	j0(υ(t	j0(υ(t	NOUN
ejde-350	166	30	)	)	PUNCT
ejde-350	166	31	)	)	PUNCT
ejde-350	166	32	,	,	PUNCT
ejde-350	166	33	where	where	SCONJ
ejde-350	166	34	γ0	γ0	NOUN
ejde-350	166	35	=	=	SYM
ejde-350	166	36	{	{	PUNCT
ejde-350	166	37	υ	υ	PROPN
ejde-350	166	38	∈	∈	PROPN
ejde-350	166	39	c([0	c([0	NOUN
ejde-350	166	40	,	,	PUNCT
ejde-350	166	41	1	1	NUM
ejde-350	166	42	]	]	PUNCT
ejde-350	166	43	,	,	PUNCT
ejde-350	166	44	ds,2	ds,2	PROPN
ejde-350	166	45	rad(r3))|υ(0	rad(r3))|υ(0	PROPN
ejde-350	166	46	)	)	PUNCT
ejde-350	166	47	=	=	SYM
ejde-350	166	48	0	0	NUM
ejde-350	166	49	,	,	PUNCT
ejde-350	166	50	j0(υ(1	j0(υ(1	PROPN
ejde-350	166	51	)	)	PUNCT
ejde-350	166	52	)	)	PUNCT
ejde-350	166	53	<	<	X
ejde-350	166	54	0	0	NUM
ejde-350	166	55	}	}	PUNCT
ejde-350	166	56	.	.	PUNCT
ejde-350	167	1	by	by	ADP
ejde-350	167	2	lemma	lemma	PROPN
ejde-350	167	3	3.1	3.1	NUM
ejde-350	167	4	,	,	PUNCT
ejde-350	167	5	we	we	PRON
ejde-350	167	6	obtain	obtain	VERB
ejde-350	167	7	that	that	PRON
ejde-350	167	8	for	for	ADP
ejde-350	167	9	all	all	DET
ejde-350	167	10	λ	λ	PROPN
ejde-350	167	11	>	>	X
ejde-350	167	12	0	0	NUM
ejde-350	167	13	,	,	PUNCT
ejde-350	167	14	there	there	PRON
ejde-350	167	15	exists	exist	VERB
ejde-350	167	16	{	{	PUNCT
ejde-350	167	17	un	un	ADJ
ejde-350	167	18	}	}	PUNCT
ejde-350	167	19	⊂	⊂	PROPN
ejde-350	167	20	ds,2	ds,2	NOUN
ejde-350	167	21	rad(r3	rad(r3	NOUN
ejde-350	167	22	)	)	PUNCT
ejde-350	167	23	such	such	ADJ
ejde-350	167	24	that	that	SCONJ
ejde-350	167	25	j0(un)→	j0(un)→	PROPN
ejde-350	167	26	c0	c0	PROPN
ejde-350	167	27	>	>	X
ejde-350	167	28	0	0	PUNCT
ejde-350	168	1	and	and	CCONJ
ejde-350	168	2	j	j	PROPN
ejde-350	168	3	′0(un)→	′0(un)→	ADV
ejde-350	168	4	0	0	PUNCT
ejde-350	168	5	as	as	ADP
ejde-350	168	6	n→∞.	n→∞.	NUM
ejde-350	168	7	it	it	PRON
ejde-350	168	8	is	be	AUX
ejde-350	168	9	also	also	ADV
ejde-350	168	10	easy	easy	ADJ
ejde-350	168	11	to	to	PART
ejde-350	168	12	see	see	VERB
ejde-350	168	13	that	that	SCONJ
ejde-350	168	14	{	{	PUNCT
ejde-350	168	15	un	un	PROPN
ejde-350	168	16	}	}	PUNCT
ejde-350	168	17	is	be	AUX
ejde-350	168	18	uniformly	uniformly	ADV
ejde-350	168	19	bounded	bound	VERB
ejde-350	168	20	in	in	ADP
ejde-350	168	21	ds,2	ds,2	NOUN
ejde-350	168	22	rad(r3	rad(r3	NOUN
ejde-350	168	23	)	)	PUNCT
ejde-350	168	24	.	.	PUNCT
ejde-350	169	1	the	the	DET
ejde-350	169	2	nehari	nehari	NOUN
ejde-350	169	3	manifold	manifold	ADJ
ejde-350	169	4	on	on	ADP
ejde-350	169	5	ds,2	ds,2	NOUN
ejde-350	169	6	rad(r3	rad(r3	NOUN
ejde-350	169	7	)	)	PUNCT
ejde-350	169	8	is	be	AUX
ejde-350	169	9	defined	define	VERB
ejde-350	169	10	by	by	ADP
ejde-350	169	11	n	n	NOUN
ejde-350	169	12	=	=	PUNCT
ejde-350	169	13	{	{	PUNCT
ejde-350	169	14	u	u	NOUN
ejde-350	169	15	∈	∈	PROPN
ejde-350	169	16	ds,2	ds,2	NOUN
ejde-350	169	17	rad(r3)|〈j	rad(r3)|〈j	VERB
ejde-350	169	18	′0(u	′0(u	NOUN
ejde-350	169	19	)	)	PUNCT
ejde-350	169	20	,	,	PUNCT
ejde-350	169	21	u	u	NOUN
ejde-350	169	22	〉	〉	NOUN
ejde-350	169	23	=	=	SYM
ejde-350	169	24	0	0	NUM
ejde-350	169	25	,	,	PUNCT
ejde-350	169	26	u	u	NOUN
ejde-350	169	27	6=	6=	PROPN
ejde-350	169	28	0	0	NUM
ejde-350	169	29	}	}	PUNCT
ejde-350	169	30	,	,	PUNCT
ejde-350	169	31	¯̄c0	¯̄c0	PROPN
ejde-350	169	32	=	=	PUNCT
ejde-350	169	33	inf	inf	PROPN
ejde-350	169	34	u∈n	u∈n	PROPN
ejde-350	169	35	j0(u	j0(u	PROPN
ejde-350	169	36	)	)	PUNCT
ejde-350	169	37	,	,	PUNCT
ejde-350	169	38	c̄0	c̄0	PUNCT
ejde-350	170	1	=	=	SYM
ejde-350	170	2	inf	inf	PROPN
ejde-350	170	3	u∈ds,2rad(r3	u∈ds,2rad(r3	PROPN
ejde-350	170	4	)	)	PUNCT
ejde-350	170	5	max	max	PROPN
ejde-350	170	6	t>0	t>0	PROPN
ejde-350	170	7	j0(tu	j0(tu	PROPN
ejde-350	170	8	)	)	PUNCT
ejde-350	170	9	.	.	PUNCT
ejde-350	171	1	with	with	ADP
ejde-350	171	2	minor	minor	ADJ
ejde-350	171	3	changes	change	NOUN
ejde-350	171	4	in	in	ADP
ejde-350	171	5	the	the	DET
ejde-350	171	6	proof	proof	NOUN
ejde-350	171	7	of	of	ADP
ejde-350	171	8	[	[	X
ejde-350	171	9	44	44	NUM
ejde-350	171	10	,	,	PUNCT
ejde-350	171	11	theorem	theorem	VERB
ejde-350	171	12	4.2	4.2	NUM
ejde-350	171	13	]	]	PUNCT
ejde-350	171	14	,	,	PUNCT
ejde-350	171	15	we	we	PRON
ejde-350	171	16	can	can	AUX
ejde-350	171	17	show	show	VERB
ejde-350	171	18	that	that	SCONJ
ejde-350	171	19	¯̄c0	¯̄c0	PROPN
ejde-350	171	20	=	=	PUNCT
ejde-350	171	21	c̄0	c̄0	PROPN
ejde-350	171	22	=	=	SYM
ejde-350	171	23	c0	c0	PROPN
ejde-350	171	24	.	.	PUNCT
ejde-350	171	25	ejde-2020/01	ejde-2020/01	PROPN
ejde-350	171	26	fractional	fractional	ADJ
ejde-350	171	27	schrödinger	schrödinger	NOUN
ejde-350	171	28	-	-	PUNCT
ejde-350	171	29	poisson	poisson	NOUN
ejde-350	171	30	system	system	NOUN
ejde-350	171	31	9	9	NUM
ejde-350	171	32	the	the	DET
ejde-350	171	33	following	following	ADJ
ejde-350	171	34	result	result	NOUN
ejde-350	171	35	implies	imply	VERB
ejde-350	171	36	the	the	DET
ejde-350	171	37	non	non	ADJ
ejde-350	171	38	-	-	ADJ
ejde-350	171	39	vanishing	vanishing	ADJ
ejde-350	171	40	property	property	NOUN
ejde-350	171	41	of	of	ADP
ejde-350	171	42	(	(	PUNCT
ejde-350	171	43	ps)c0	ps)c0	PROPN
ejde-350	171	44	sequence	sequence	NOUN
ejde-350	171	45	.	.	PUNCT
ejde-350	172	1	lemma	lemma	PROPN
ejde-350	172	2	3.2	3.2	NUM
ejde-350	172	3	.	.	PUNCT
ejde-350	173	1	assume	assume	VERB
ejde-350	173	2	that	that	SCONJ
ejde-350	173	3	the	the	DET
ejde-350	173	4	assumptions	assumption	NOUN
ejde-350	173	5	of	of	ADP
ejde-350	173	6	theorem	theorem	ADJ
ejde-350	173	7	1.1	1.1	NUM
ejde-350	173	8	hold	hold	NOUN
ejde-350	173	9	.	.	PUNCT
ejde-350	174	1	let	let	VERB
ejde-350	174	2	{	{	PUNCT
ejde-350	174	3	un	un	AUX
ejde-350	174	4	}	}	PUNCT
ejde-350	174	5	be	be	AUX
ejde-350	174	6	a	a	DET
ejde-350	174	7	(	(	PUNCT
ejde-350	174	8	ps)c0	ps)c0	NOUN
ejde-350	174	9	sequence	sequence	NOUN
ejde-350	174	10	of	of	ADP
ejde-350	174	11	j0	j0	PROPN
ejde-350	174	12	with	with	ADP
ejde-350	174	13	c0	c0	PROPN
ejde-350	174	14	>	>	X
ejde-350	174	15	0	0	X
ejde-350	174	16	.	.	PUNCT
ejde-350	175	1	then	then	ADV
ejde-350	175	2	lim	lim	PROPN
ejde-350	175	3	n→∞	n→∞	NUM
ejde-350	175	4	∫	∫	PROPN
ejde-350	175	5	r3	r3	PROPN
ejde-350	175	6	|un|2	|un|2	PROPN
ejde-350	175	7	∗	∗	PROPN
ejde-350	175	8	sdx	sdx	PROPN
ejde-350	175	9	>	>	X
ejde-350	175	10	0	0	PROPN
ejde-350	175	11	.	.	PUNCT
ejde-350	175	12	proof	proof	NOUN
ejde-350	175	13	.	.	PUNCT
ejde-350	176	1	it	it	PRON
ejde-350	176	2	is	be	AUX
ejde-350	176	3	easy	easy	ADJ
ejde-350	176	4	to	to	PART
ejde-350	176	5	see	see	VERB
ejde-350	176	6	that	that	SCONJ
ejde-350	176	7	{	{	PUNCT
ejde-350	176	8	un	un	PROPN
ejde-350	176	9	}	}	PUNCT
ejde-350	176	10	is	be	AUX
ejde-350	176	11	uniformly	uniformly	ADV
ejde-350	176	12	bounded	bound	VERB
ejde-350	176	13	in	in	ADP
ejde-350	176	14	ds,2	ds,2	NOUN
ejde-350	176	15	rad(r3	rad(r3	NOUN
ejde-350	176	16	)	)	PUNCT
ejde-350	176	17	.	.	PUNCT
ejde-350	177	1	then	then	ADV
ejde-350	177	2	there	there	PRON
ejde-350	177	3	exists	exist	VERB
ejde-350	177	4	a	a	DET
ejde-350	177	5	constant	constant	ADJ
ejde-350	177	6	0	0	NUM
ejde-350	177	7	<	<	X
ejde-350	177	8	c	c	X
ejde-350	177	9	<	<	X
ejde-350	177	10	∞	∞	NUM
ejde-350	177	11	such	such	ADJ
ejde-350	177	12	that	that	SCONJ
ejde-350	177	13	‖un‖φ	‖un‖φ	PROPN
ejde-350	177	14	6	6	NUM
ejde-350	177	15	c.	c.	NOUN
ejde-350	177	16	suppose	suppose	VERB
ejde-350	177	17	on	on	ADP
ejde-350	177	18	the	the	DET
ejde-350	177	19	contrary	contrary	NOUN
ejde-350	177	20	that	that	PRON
ejde-350	177	21	lim	lim	PROPN
ejde-350	177	22	n→∞	n→∞	PRON
ejde-350	177	23	∫	∫	PROPN
ejde-350	177	24	r3	r3	PROPN
ejde-350	177	25	|un|2	|un|2	PROPN
ejde-350	177	26	∗	∗	NOUN
ejde-350	177	27	sdx	sdx	NOUN
ejde-350	177	28	=	=	SYM
ejde-350	177	29	0	0	PROPN
ejde-350	177	30	.	.	PUNCT
ejde-350	178	1	(	(	PUNCT
ejde-350	178	2	3.2	3.2	NUM
ejde-350	178	3	)	)	PUNCT
ejde-350	178	4	according	accord	VERB
ejde-350	178	5	to	to	ADP
ejde-350	178	6	(	(	PUNCT
ejde-350	178	7	3.2	3.2	NUM
ejde-350	178	8	)	)	PUNCT
ejde-350	178	9	and	and	CCONJ
ejde-350	178	10	the	the	DET
ejde-350	178	11	definition	definition	NOUN
ejde-350	178	12	of	of	ADP
ejde-350	178	13	(	(	PUNCT
ejde-350	178	14	ps)c0	ps)c0	PROPN
ejde-350	178	15	sequence	sequence	NOUN
ejde-350	178	16	,	,	PUNCT
ejde-350	178	17	we	we	PRON
ejde-350	178	18	obtain	obtain	VERB
ejde-350	178	19	c0	c0	NOUN
ejde-350	178	20	+	+	X
ejde-350	178	21	o(1	o(1	PROPN
ejde-350	178	22	)	)	PUNCT
ejde-350	178	23	=	=	SYM
ejde-350	178	24	1	1	NUM
ejde-350	178	25	2	2	NUM
ejde-350	178	26	‖un‖2φ	‖un‖2φ	X
ejde-350	178	27	and	and	CCONJ
ejde-350	178	28	‖un‖2φ	‖un‖2φ	NOUN
ejde-350	178	29	=	=	SYM
ejde-350	178	30	o(1	o(1	PROPN
ejde-350	178	31	)	)	PUNCT
ejde-350	178	32	;	;	PUNCT
ejde-350	178	33	these	these	PRON
ejde-350	178	34	imply	imply	VERB
ejde-350	178	35	that	that	SCONJ
ejde-350	178	36	c0	c0	NOUN
ejde-350	178	37	=	=	PUNCT
ejde-350	178	38	0	0	PROPN
ejde-350	178	39	,	,	PUNCT
ejde-350	178	40	which	which	PRON
ejde-350	178	41	contradicts	contradict	VERB
ejde-350	178	42	with	with	ADP
ejde-350	178	43	0	0	NUM
ejde-350	178	44	<	<	X
ejde-350	178	45	c0	c0	X
ejde-350	178	46	.	.	PUNCT
ejde-350	179	1	�	�	PROPN
ejde-350	179	2	3.2	3.2	NUM
ejde-350	179	3	.	.	PUNCT
ejde-350	180	1	ground	ground	NOUN
ejde-350	180	2	state	state	NOUN
ejde-350	180	3	solution	solution	NOUN
ejde-350	180	4	.	.	PUNCT
ejde-350	181	1	proof	proof	NOUN
ejde-350	181	2	of	of	ADP
ejde-350	181	3	theorem	theorem	ADJ
ejde-350	181	4	1.1	1.1	NUM
ejde-350	181	5	.	.	PUNCT
ejde-350	182	1	we	we	PRON
ejde-350	182	2	divide	divide	VERB
ejde-350	182	3	the	the	DET
ejde-350	182	4	proof	proof	NOUN
ejde-350	182	5	of	of	ADP
ejde-350	182	6	theorem	theorem	ADJ
ejde-350	182	7	1.1	1.1	NUM
ejde-350	182	8	into	into	ADP
ejde-350	182	9	two	two	NUM
ejde-350	182	10	steps	step	NOUN
ejde-350	182	11	.	.	PUNCT
ejde-350	183	1	step	step	NOUN
ejde-350	183	2	1	1	NUM
ejde-350	183	3	.	.	PUNCT
ejde-350	184	1	since	since	SCONJ
ejde-350	184	2	{	{	PUNCT
ejde-350	184	3	un	un	VERB
ejde-350	184	4	}	}	PUNCT
ejde-350	184	5	is	be	AUX
ejde-350	184	6	a	a	DET
ejde-350	184	7	bounded	bounded	ADJ
ejde-350	184	8	sequence	sequence	NOUN
ejde-350	184	9	in	in	ADP
ejde-350	184	10	ds,2	ds,2	NOUN
ejde-350	184	11	rad(r3	rad(r3	NOUN
ejde-350	184	12	)	)	PUNCT
ejde-350	184	13	,	,	PUNCT
ejde-350	184	14	up	up	ADP
ejde-350	184	15	to	to	ADP
ejde-350	184	16	a	a	DET
ejde-350	184	17	subsequence	subsequence	NOUN
ejde-350	184	18	,	,	PUNCT
ejde-350	184	19	we	we	PRON
ejde-350	184	20	assume	assume	VERB
ejde-350	184	21	that	that	SCONJ
ejde-350	184	22	un	un	PROPN
ejde-350	184	23	⇀	⇀	PROPN
ejde-350	184	24	u	u	NOUN
ejde-350	184	25	in	in	ADP
ejde-350	184	26	ds,2	ds,2	NOUN
ejde-350	184	27	rad(r3	rad(r3	NOUN
ejde-350	184	28	)	)	PUNCT
ejde-350	184	29	,	,	PUNCT
ejde-350	184	30	un	un	PROPN
ejde-350	184	31	→	→	SYM
ejde-350	184	32	u	u	PROPN
ejde-350	184	33	a.e	a.e	PROPN
ejde-350	184	34	.	.	PROPN
ejde-350	184	35	in	in	ADP
ejde-350	184	36	r3	r3	PROPN
ejde-350	184	37	,	,	PUNCT
ejde-350	184	38	un	un	PROPN
ejde-350	184	39	→	→	SYM
ejde-350	184	40	u	u	PROPN
ejde-350	184	41	in	in	ADP
ejde-350	184	42	lrloc(r3	lrloc(r3	NOUN
ejde-350	184	43	)	)	PUNCT
ejde-350	184	44	for	for	ADP
ejde-350	184	45	all	all	DET
ejde-350	184	46	r	r	NOUN
ejde-350	184	47	∈	∈	PROPN
ejde-350	185	1	[	[	X
ejde-350	185	2	2	2	NUM
ejde-350	185	3	,	,	PUNCT
ejde-350	185	4	2∗s	2∗s	NUM
ejde-350	185	5	)	)	PUNCT
ejde-350	185	6	.	.	PUNCT
ejde-350	186	1	according	accord	VERB
ejde-350	186	2	to	to	ADP
ejde-350	186	3	lemmas	lemmas	PROPN
ejde-350	186	4	2.3	2.3	NUM
ejde-350	186	5	and	and	CCONJ
ejde-350	186	6	3.2	3.2	NUM
ejde-350	186	7	,	,	PUNCT
ejde-350	186	8	there	there	PRON
ejde-350	186	9	exists	exist	VERB
ejde-350	186	10	c	c	NOUN
ejde-350	186	11	>	>	X
ejde-350	186	12	0	0	NUM
ejde-350	187	1	such	such	ADJ
ejde-350	187	2	that	that	PRON
ejde-350	187	3	for	for	ADP
ejde-350	187	4	any	any	DET
ejde-350	187	5	n	n	CCONJ
ejde-350	187	6	,	,	PUNCT
ejde-350	187	7	we	we	PRON
ejde-350	187	8	obtain	obtain	VERB
ejde-350	187	9	‖un‖l2,3−2s(r3	‖un‖l2,3−2s(r3	ADP
ejde-350	187	10	)	)	PUNCT
ejde-350	187	11	>	>	X
ejde-350	188	1	c	c	X
ejde-350	188	2	>	>	X
ejde-350	188	3	0	0	X
ejde-350	188	4	.	.	PUNCT
ejde-350	189	1	on	on	ADP
ejde-350	189	2	the	the	DET
ejde-350	189	3	other	other	ADJ
ejde-350	189	4	hand	hand	NOUN
ejde-350	189	5	,	,	PUNCT
ejde-350	189	6	since	since	SCONJ
ejde-350	189	7	{	{	PUNCT
ejde-350	189	8	un	un	VERB
ejde-350	189	9	}	}	PUNCT
ejde-350	189	10	is	be	AUX
ejde-350	189	11	bounded	bound	VERB
ejde-350	189	12	in	in	ADP
ejde-350	189	13	ds,2	ds,2	NOUN
ejde-350	189	14	rad(r3	rad(r3	NOUN
ejde-350	189	15	)	)	PUNCT
ejde-350	189	16	and	and	CCONJ
ejde-350	189	17	ds,2	ds,2	NOUN
ejde-350	189	18	rad(r3	rad(r3	NOUN
ejde-350	189	19	)	)	PUNCT
ejde-350	189	20	↪	↪	PROPN
ejde-350	189	21	→	→	SYM
ejde-350	189	22	ds,2(r3	ds,2(r3	PROPN
ejde-350	189	23	)	)	PUNCT
ejde-350	189	24	↪	↪	PROPN
ejde-350	189	25	→	→	SYM
ejde-350	189	26	l2∗	l2∗	NOUN
ejde-350	189	27	s	s	X
ejde-350	189	28	(	(	PUNCT
ejde-350	189	29	r3	r3	PROPN
ejde-350	189	30	)	)	PUNCT
ejde-350	189	31	↪	↪	PROPN
ejde-350	189	32	→	→	SYM
ejde-350	189	33	l2,3−2s(r3	l2,3−2s(r3	PROPN
ejde-350	189	34	)	)	PUNCT
ejde-350	189	35	,	,	PUNCT
ejde-350	189	36	we	we	PRON
ejde-350	189	37	have	have	AUX
ejde-350	189	38	‖un‖l2,3−2s(r3	‖un‖l2,3−2s(r3	VERB
ejde-350	189	39	)	)	PUNCT
ejde-350	190	1	6	6	NUM
ejde-350	190	2	c	c	NOUN
ejde-350	190	3	,	,	PUNCT
ejde-350	190	4	for	for	ADP
ejde-350	190	5	some	some	DET
ejde-350	190	6	c	c	PROPN
ejde-350	190	7	>	>	X
ejde-350	190	8	0	0	PROPN
ejde-350	190	9	independent	independent	NOUN
ejde-350	190	10	of	of	ADP
ejde-350	190	11	n.	n.	NOUN
ejde-350	190	12	hence	hence	ADV
ejde-350	190	13	,	,	PUNCT
ejde-350	190	14	there	there	PRON
ejde-350	190	15	exists	exist	VERB
ejde-350	190	16	a	a	DET
ejde-350	190	17	positive	positive	ADJ
ejde-350	190	18	constant	constant	NOUN
ejde-350	190	19	which	which	PRON
ejde-350	190	20	we	we	PRON
ejde-350	190	21	denote	denote	VERB
ejde-350	190	22	again	again	ADV
ejde-350	190	23	by	by	ADP
ejde-350	190	24	c	c	PROPN
ejde-350	190	25	such	such	ADJ
ejde-350	190	26	that	that	PRON
ejde-350	190	27	for	for	ADP
ejde-350	190	28	any	any	DET
ejde-350	190	29	n	n	CCONJ
ejde-350	190	30	,	,	PUNCT
ejde-350	190	31	we	we	PRON
ejde-350	190	32	obtain	obtain	VERB
ejde-350	190	33	c	c	NOUN
ejde-350	190	34	6	6	NUM
ejde-350	190	35	‖un‖l2,3−2s(r3	‖un‖l2,3−2s(r3	ADJ
ejde-350	190	36	)	)	PUNCT
ejde-350	190	37	6	6	NUM
ejde-350	190	38	c	c	NOUN
ejde-350	190	39	−1	−1	NOUN
ejde-350	190	40	.	.	PUNCT
ejde-350	191	1	combining	combine	VERB
ejde-350	191	2	the	the	DET
ejde-350	191	3	definition	definition	NOUN
ejde-350	191	4	of	of	ADP
ejde-350	191	5	morrey	morrey	PROPN
ejde-350	191	6	space	space	NOUN
ejde-350	191	7	and	and	CCONJ
ejde-350	191	8	above	above	ADP
ejde-350	191	9	inequality	inequality	NOUN
ejde-350	191	10	,	,	PUNCT
ejde-350	191	11	we	we	PRON
ejde-350	191	12	deduce	deduce	VERB
ejde-350	191	13	that	that	SCONJ
ejde-350	191	14	for	for	ADP
ejde-350	191	15	any	any	DET
ejde-350	191	16	n	n	PRON
ejde-350	191	17	∈	∈	NOUN
ejde-350	191	18	n	n	AUX
ejde-350	191	19	there	there	PRON
ejde-350	191	20	exist	exist	VERB
ejde-350	191	21	σn	σn	NOUN
ejde-350	191	22	>	>	X
ejde-350	191	23	0	0	PUNCT
ejde-350	192	1	and	and	CCONJ
ejde-350	192	2	xn	xn	PROPN
ejde-350	192	3	∈	∈	PROPN
ejde-350	192	4	r3	r3	PROPN
ejde-350	192	5	such	such	ADJ
ejde-350	192	6	that	that	SCONJ
ejde-350	192	7	1	1	NUM
ejde-350	192	8	σ2s	σ2s	NUM
ejde-350	192	9	n	n	NUM
ejde-350	192	10	∫	∫	PROPN
ejde-350	192	11	b(xn	b(xn	PROPN
ejde-350	192	12	,	,	PUNCT
ejde-350	192	13	σn	σn	NOUN
ejde-350	192	14	)	)	PUNCT
ejde-350	192	15	|un(y)|2dy	|un(y)|2dy	NOUN
ejde-350	192	16	>	>	X
ejde-350	192	17	‖un‖2l2,3−2s(r3	‖un‖2l2,3−2s(r3	PROPN
ejde-350	192	18	)	)	PUNCT
ejde-350	192	19	−	−	PROPN
ejde-350	192	20	c	c	NOUN
ejde-350	192	21	2n	2n	NUM
ejde-350	192	22	>	>	X
ejde-350	192	23	c1	c1	PROPN
ejde-350	192	24	>	>	X
ejde-350	192	25	0	0	X
ejde-350	192	26	.	.	PUNCT
ejde-350	193	1	let	let	VERB
ejde-350	193	2	vn(x	vn(x	PRON
ejde-350	193	3	)	)	PUNCT
ejde-350	194	1	=	=	PUNCT
ejde-350	194	2	σ	σ	NOUN
ejde-350	195	1	3−2s	3−2s	NUM
ejde-350	195	2	2	2	NUM
ejde-350	195	3	n	n	PRON
ejde-350	195	4	un(σnx	un(σnx	NOUN
ejde-350	195	5	)	)	PUNCT
ejde-350	195	6	.	.	PUNCT
ejde-350	196	1	we	we	PRON
ejde-350	196	2	know	know	VERB
ejde-350	196	3	that	that	SCONJ
ejde-350	196	4	j0(vn	j0(vn	PROPN
ejde-350	196	5	)	)	PUNCT
ejde-350	196	6	=	=	PUNCT
ejde-350	197	1	j0(un)→	j0(un)→	PROPN
ejde-350	197	2	c0	c0	PROPN
ejde-350	197	3	and	and	CCONJ
ejde-350	197	4	j	j	PROPN
ejde-350	197	5	′0(vn)→	′0(vn)→	NOUN
ejde-350	197	6	0	0	NUM
ejde-350	198	1	as	as	ADP
ejde-350	198	2	n→∞.	n→∞.	ADJ
ejde-350	198	3	thus	thus	ADV
ejde-350	198	4	there	there	PRON
ejde-350	198	5	exists	exist	VERB
ejde-350	198	6	v	v	ADP
ejde-350	198	7	such	such	ADJ
ejde-350	198	8	that	that	PRON
ejde-350	198	9	vn	vn	PROPN
ejde-350	198	10	⇀	⇀	NUM
ejde-350	198	11	v	v	NOUN
ejde-350	198	12	in	in	ADP
ejde-350	198	13	ds,2	ds,2	NOUN
ejde-350	198	14	rad(r3	rad(r3	NOUN
ejde-350	198	15	)	)	PUNCT
ejde-350	198	16	,	,	PUNCT
ejde-350	198	17	vn	vn	PROPN
ejde-350	198	18	→	→	SYM
ejde-350	198	19	v	v	X
ejde-350	198	20	a.e	a.e	PROPN
ejde-350	198	21	.	.	PROPN
ejde-350	199	1	in	in	ADP
ejde-350	199	2	r3	r3	PROPN
ejde-350	199	3	,	,	PUNCT
ejde-350	199	4	vn	vn	PROPN
ejde-350	199	5	→	→	SYM
ejde-350	199	6	v	v	PROPN
ejde-350	199	7	in	in	ADP
ejde-350	199	8	lrloc(r3	lrloc(r3	NOUN
ejde-350	199	9	)	)	PUNCT
ejde-350	199	10	for	for	ADP
ejde-350	199	11	all	all	DET
ejde-350	199	12	r	r	NOUN
ejde-350	199	13	∈	∈	PROPN
ejde-350	200	1	[	[	X
ejde-350	200	2	2	2	NUM
ejde-350	200	3	,	,	PUNCT
ejde-350	200	4	2∗s	2∗s	NUM
ejde-350	200	5	)	)	PUNCT
ejde-350	200	6	.	.	PUNCT
ejde-350	201	1	then∫	then∫	NOUN
ejde-350	201	2	b	b	PROPN
ejde-350	201	3	(	(	PUNCT
ejde-350	201	4	xnσn	xnσn	NOUN
ejde-350	201	5	,	,	PUNCT
ejde-350	201	6	1	1	NUM
ejde-350	201	7	)	)	PUNCT
ejde-350	201	8	|vn(y)|2dy	|vn(y)|2dy	X
ejde-350	202	1	=	=	NOUN
ejde-350	202	2	1	1	NUM
ejde-350	202	3	σ2s	σ2s	NUM
ejde-350	202	4	n	n	NUM
ejde-350	202	5	∫	∫	PROPN
ejde-350	202	6	b(xn	b(xn	PROPN
ejde-350	202	7	,	,	PUNCT
ejde-350	202	8	σn	σn	NOUN
ejde-350	202	9	)	)	PUNCT
ejde-350	202	10	|un(y)|2dy	|un(y)|2dy	X
ejde-350	202	11	>	>	X
ejde-350	202	12	c1	c1	PROPN
ejde-350	202	13	>	>	X
ejde-350	202	14	0	0	PROPN
ejde-350	202	15	.	.	PUNCT
ejde-350	203	1	(	(	PUNCT
ejde-350	203	2	3.3	3.3	NUM
ejde-350	203	3	)	)	PUNCT
ejde-350	203	4	10	10	NUM
ejde-350	203	5	y.	y.	PROPN
ejde-350	203	6	su	su	PROPN
ejde-350	203	7	,	,	PUNCT
ejde-350	203	8	h.	h.	PROPN
ejde-350	203	9	chen	chen	PROPN
ejde-350	203	10	,	,	PUNCT
ejde-350	203	11	s.	s.	PROPN
ejde-350	203	12	liu	liu	PROPN
ejde-350	203	13	,	,	PUNCT
ejde-350	203	14	x.	x.	PROPN
ejde-350	203	15	fang	fang	PROPN
ejde-350	203	16	ejde-2020/01	ejde-2020/01	NOUN
ejde-350	203	17	step	step	NOUN
ejde-350	203	18	2	2	NUM
ejde-350	203	19	.	.	PUNCT
ejde-350	204	1	we	we	PRON
ejde-350	204	2	will	will	AUX
ejde-350	204	3	show	show	VERB
ejde-350	204	4	that	that	SCONJ
ejde-350	204	5	{	{	PUNCT
ejde-350	204	6	xnσn	xnσn	NOUN
ejde-350	204	7	}	}	PUNCT
ejde-350	204	8	is	be	AUX
ejde-350	204	9	bounded	bound	VERB
ejde-350	204	10	.	.	PUNCT
ejde-350	205	1	suppose	suppose	VERB
ejde-350	205	2	on	on	ADP
ejde-350	205	3	the	the	DET
ejde-350	205	4	contrary	contrary	NOUN
ejde-350	205	5	that	that	PRON
ejde-350	205	6	xn	xn	PROPN
ejde-350	205	7	σn	σn	PROPN
ejde-350	205	8	→∞	→∞	PROPN
ejde-350	205	9	as	as	ADP
ejde-350	205	10	n	n	PROPN
ejde-350	205	11	→	→	PUNCT
ejde-350	205	12	∞.	∞.	PROPN
ejde-350	205	13	by	by	ADP
ejde-350	205	14	using	use	VERB
ejde-350	205	15	the	the	DET
ejde-350	205	16	boundedness	boundedness	NOUN
ejde-350	205	17	of	of	ADP
ejde-350	205	18	{	{	PUNCT
ejde-350	205	19	un	un	PROPN
ejde-350	205	20	}	}	PUNCT
ejde-350	205	21	in	in	ADP
ejde-350	205	22	ds,2	ds,2	NOUN
ejde-350	205	23	rad(r3	rad(r3	NOUN
ejde-350	205	24	)	)	PUNCT
ejde-350	205	25	,	,	PUNCT
ejde-350	205	26	we	we	PRON
ejde-350	205	27	have	have	VERB
ejde-350	205	28	‖vn‖s	‖vn‖s	PROPN
ejde-350	205	29	=	=	SYM
ejde-350	206	1	‖un‖s	‖un‖s	PROPN
ejde-350	206	2	6	6	NUM
ejde-350	206	3	c2	c2	PROPN
ejde-350	206	4	.	.	PUNCT
ejde-350	207	1	applying	apply	VERB
ejde-350	207	2	the	the	DET
ejde-350	207	3	uniform	uniform	ADJ
ejde-350	207	4	decay	decay	NOUN
ejde-350	207	5	estimates	estimate	NOUN
ejde-350	207	6	of	of	ADP
ejde-350	207	7	radial	radial	ADJ
ejde-350	207	8	functions	function	NOUN
ejde-350	207	9	,	,	PUNCT
ejde-350	207	10	we	we	PRON
ejde-350	207	11	have	have	AUX
ejde-350	207	12	|vn(x)|	|vn(x)|	VERB
ejde-350	207	13	6	6	NUM
ejde-350	207	14	c	c	NOUN
ejde-350	207	15	|x|	|x|	PROPN
ejde-350	207	16	3−2s	3−2s	NUM
ejde-350	207	17	2	2	NUM
ejde-350	207	18	‖vn‖s	‖vn‖s	PROPN
ejde-350	207	19	6	6	NUM
ejde-350	207	20	c3	c3	NOUN
ejde-350	207	21	|x|	|x|	PROPN
ejde-350	207	22	3−2s	3−2s	NUM
ejde-350	207	23	2	2	NUM
ejde-350	207	24	,	,	PUNCT
ejde-350	207	25	where	where	SCONJ
ejde-350	207	26	c3	c3	PROPN
ejde-350	207	27	=	=	PROPN
ejde-350	207	28	cc2	cc2	PROPN
ejde-350	207	29	.	.	PUNCT
ejde-350	208	1	for	for	ADP
ejde-350	208	2	any	any	DET
ejde-350	208	3	√	√	PROPN
ejde-350	208	4	c1	c1	PROPN
ejde-350	208	5	|b(0,1)|	|b(0,1)|	NUM
ejde-350	208	6	>	>	X
ejde-350	208	7	ε	ε	PROPN
ejde-350	208	8	>	>	X
ejde-350	208	9	0	0	PROPN
ejde-350	208	10	,	,	PUNCT
ejde-350	208	11	there	there	PRON
ejde-350	208	12	exists	exist	VERB
ejde-350	208	13	m	m	VERB
ejde-350	208	14	>	>	X
ejde-350	208	15	0	0	NUM
ejde-350	208	16	,	,	PUNCT
ejde-350	208	17	such	such	ADJ
ejde-350	208	18	that	that	PRON
ejde-350	208	19	for	for	ADP
ejde-350	208	20	n	n	PROPN
ejde-350	208	21	>	>	X
ejde-350	208	22	m	m	VERB
ejde-350	208	23	,	,	PUNCT
ejde-350	208	24	we	we	PRON
ejde-350	208	25	have	have	AUX
ejde-350	208	26	|vn(x)|	|vn(x)|	VERB
ejde-350	208	27	6	6	NUM
ejde-350	208	28	c3	c3	NOUN
ejde-350	208	29	|xnσn	|xnσn	NOUN
ejde-350	208	30	−	−	PROPN
ejde-350	208	31	1|	1|	NUM
ejde-350	208	32	3−2s	3−2s	NUM
ejde-350	208	33	2	2	NUM
ejde-350	208	34	6	6	NUM
ejde-350	208	35	ε	ε	PROPN
ejde-350	208	36	,	,	PUNCT
ejde-350	208	37	for	for	ADP
ejde-350	208	38	all	all	DET
ejde-350	208	39	x	x	SYM
ejde-350	208	40	∈	∈	PROPN
ejde-350	208	41	bc(0	bc(0	PROPN
ejde-350	208	42	,	,	PUNCT
ejde-350	208	43	|xn	|xn	X
ejde-350	208	44	σn	σn	PROPN
ejde-350	208	45	−	−	PROPN
ejde-350	208	46	1|	1|	NUM
ejde-350	208	47	)	)	PUNCT
ejde-350	208	48	.	.	PUNCT
ejde-350	209	1	since	since	SCONJ
ejde-350	209	2	b(xnσn	b(xnσn	NOUN
ejde-350	209	3	,	,	PUNCT
ejde-350	209	4	1	1	X
ejde-350	209	5	)	)	PUNCT
ejde-350	209	6	⊂	⊂	PROPN
ejde-350	209	7	bc(0	bc(0	PROPN
ejde-350	209	8	,	,	PUNCT
ejde-350	209	9	|xnσn	|xnσn	NOUN
ejde-350	209	10	−	−	NOUN
ejde-350	209	11	1|	1|	NUM
ejde-350	209	12	)	)	PUNCT
ejde-350	209	13	,	,	PUNCT
ejde-350	209	14	we	we	PRON
ejde-350	209	15	obtain∫	obtain∫	VERB
ejde-350	209	16	b	b	X
ejde-350	209	17	(	(	PUNCT
ejde-350	209	18	xnσn	xnσn	NOUN
ejde-350	209	19	,	,	PUNCT
ejde-350	209	20	1	1	NUM
ejde-350	209	21	)	)	PUNCT
ejde-350	209	22	|vn(y)|2dy	|vn(y)|2dy	NUM
ejde-350	209	23	6	6	NUM
ejde-350	209	24	ε2	ε2	ADJ
ejde-350	209	25	∫	∫	PROPN
ejde-350	209	26	b	b	PROPN
ejde-350	209	27	(	(	PUNCT
ejde-350	209	28	xnσn	xnσn	NOUN
ejde-350	209	29	,	,	PUNCT
ejde-350	209	30	1	1	X
ejde-350	209	31	)	)	PUNCT
ejde-350	209	32	dy	dy	NOUN
ejde-350	209	33	=	=	SYM
ejde-350	209	34	ε2|b	ε2|b	PROPN
ejde-350	209	35	(	(	PUNCT
ejde-350	209	36	xn	xn	PROPN
ejde-350	209	37	σn	σn	PROPN
ejde-350	209	38	,	,	PUNCT
ejde-350	209	39	1)|	1)|	NUM
ejde-350	209	40	=	=	SYM
ejde-350	209	41	ε2|b(0	ε2|b(0	NOUN
ejde-350	209	42	,	,	PUNCT
ejde-350	209	43	1)|	1)|	NUM
ejde-350	209	44	<	<	X
ejde-350	209	45	c1	c1	PROPN
ejde-350	209	46	.	.	PUNCT
ejde-350	210	1	this	this	PRON
ejde-350	210	2	contradicts	contradict	VERB
ejde-350	210	3	(	(	PUNCT
ejde-350	210	4	3.3	3.3	NUM
ejde-350	210	5	)	)	PUNCT
ejde-350	210	6	.	.	PUNCT
ejde-350	211	1	hence	hence	ADV
ejde-350	211	2	,	,	PUNCT
ejde-350	211	3	{	{	PUNCT
ejde-350	211	4	xnσn	xnσn	NOUN
ejde-350	211	5	}	}	PUNCT
ejde-350	211	6	is	be	AUX
ejde-350	211	7	bounded	bound	VERB
ejde-350	211	8	,	,	PUNCT
ejde-350	211	9	and	and	CCONJ
ejde-350	211	10	there	there	PRON
ejde-350	211	11	exists	exist	VERB
ejde-350	211	12	r	r	NOUN
ejde-350	211	13	>	>	X
ejde-350	211	14	0	0	NUM
ejde-350	211	15	such	such	ADJ
ejde-350	211	16	that∫	that∫	NOUN
ejde-350	211	17	b(0,r	b(0,r	CCONJ
ejde-350	211	18	)	)	PUNCT
ejde-350	212	1	|vn(y)|2dy	|vn(y)|2dy	X
ejde-350	212	2	>	>	X
ejde-350	212	3	∫	∫	PROPN
ejde-350	212	4	b	b	PROPN
ejde-350	212	5	(	(	PUNCT
ejde-350	212	6	xnσn	xnσn	NOUN
ejde-350	212	7	,	,	PUNCT
ejde-350	212	8	1	1	NUM
ejde-350	212	9	)	)	PUNCT
ejde-350	212	10	|vn(y)|2dy	|vn(y)|2dy	X
ejde-350	212	11	>	>	X
ejde-350	212	12	c1	c1	PROPN
ejde-350	212	13	>	>	X
ejde-350	212	14	0	0	X
ejde-350	212	15	.	.	PUNCT
ejde-350	213	1	since	since	SCONJ
ejde-350	213	2	the	the	DET
ejde-350	213	3	embedding	embed	VERB
ejde-350	213	4	ds,2	ds,2	NOUN
ejde-350	213	5	rad(r3	rad(r3	NOUN
ejde-350	213	6	)	)	PUNCT
ejde-350	213	7	↪	↪	PROPN
ejde-350	213	8	→	→	SYM
ejde-350	213	9	lrloc(r3	lrloc(r3	NOUN
ejde-350	213	10	)	)	PUNCT
ejde-350	213	11	,	,	PUNCT
ejde-350	213	12	r	r	NOUN
ejde-350	213	13	∈	∈	PROPN
ejde-350	214	1	[	[	X
ejde-350	214	2	2	2	NUM
ejde-350	214	3	,	,	PUNCT
ejde-350	214	4	2∗s	2∗s	NUM
ejde-350	214	5	)	)	PUNCT
ejde-350	214	6	is	be	AUX
ejde-350	214	7	compact	compact	ADJ
ejde-350	214	8	,	,	PUNCT
ejde-350	214	9	we	we	PRON
ejde-350	214	10	deduce	deduce	VERB
ejde-350	214	11	that∫	that∫	NOUN
ejde-350	214	12	b(0,r	b(0,r	CCONJ
ejde-350	214	13	)	)	PUNCT
ejde-350	214	14	|v(y)|2dy	|v(y)|2dy	ADP
ejde-350	214	15	>	>	X
ejde-350	214	16	c1	c1	PROPN
ejde-350	214	17	>	>	X
ejde-350	214	18	0	0	X
ejde-350	214	19	.	.	PUNCT
ejde-350	215	1	hence	hence	ADV
ejde-350	215	2	,	,	PUNCT
ejde-350	215	3	v	v	ADP
ejde-350	215	4	6≡	6≡	NUM
ejde-350	215	5	0	0	NUM
ejde-350	215	6	.	.	PUNCT
ejde-350	216	1	from	from	ADP
ejde-350	216	2	vn	vn	PROPN
ejde-350	216	3	⇀	⇀	NUM
ejde-350	216	4	v	v	ADP
ejde-350	216	5	weakly	weakly	ADJ
ejde-350	216	6	in	in	ADP
ejde-350	216	7	ds,2	ds,2	NOUN
ejde-350	216	8	rad(r3	rad(r3	NOUN
ejde-350	216	9	)	)	PUNCT
ejde-350	216	10	and	and	CCONJ
ejde-350	216	11	limn→∞〈j	limn→∞〈j	VERB
ejde-350	216	12	′0(vn	′0(vn	PROPN
ejde-350	216	13	)	)	PUNCT
ejde-350	216	14	,	,	PUNCT
ejde-350	216	15	ϕ	ϕ	NOUN
ejde-350	216	16	〉	〉	NOUN
ejde-350	216	17	=	=	SYM
ejde-350	216	18	o(1	o(1	PROPN
ejde-350	216	19	)	)	PUNCT
ejde-350	216	20	,	,	PUNCT
ejde-350	216	21	we	we	PRON
ejde-350	216	22	obtain	obtain	VERB
ejde-350	216	23	〈	〈	PROPN
ejde-350	216	24	j	j	PROPN
ejde-350	216	25	′λ(v	′λ(v	PROPN
ejde-350	216	26	)	)	PUNCT
ejde-350	216	27	,	,	PUNCT
ejde-350	216	28	ϕ	ϕ	NOUN
ejde-350	216	29	〉	〉	NOUN
ejde-350	216	30	=	=	SYM
ejde-350	216	31	0	0	X
ejde-350	216	32	.	.	PUNCT
ejde-350	217	1	since	since	SCONJ
ejde-350	217	2	v	v	NUM
ejde-350	217	3	6≡	6≡	NUM
ejde-350	217	4	0	0	NUM
ejde-350	217	5	,	,	PUNCT
ejde-350	217	6	we	we	PRON
ejde-350	217	7	know	know	VERB
ejde-350	217	8	that	that	SCONJ
ejde-350	217	9	v	v	ADP
ejde-350	217	10	∈	∈	PROPN
ejde-350	217	11	n	n	NOUN
ejde-350	217	12	.	.	PUNCT
ejde-350	218	1	now	now	ADV
ejde-350	218	2	,	,	PUNCT
ejde-350	218	3	we	we	PRON
ejde-350	218	4	show	show	VERB
ejde-350	218	5	that	that	SCONJ
ejde-350	218	6	vn	vn	PROPN
ejde-350	218	7	→	→	SYM
ejde-350	218	8	v	v	NOUN
ejde-350	218	9	strongly	strongly	ADV
ejde-350	218	10	in	in	ADP
ejde-350	218	11	ds,2	ds,2	NOUN
ejde-350	218	12	rad(r3	rad(r3	NOUN
ejde-350	218	13	)	)	PUNCT
ejde-350	218	14	.	.	PUNCT
ejde-350	219	1	applying	apply	VERB
ejde-350	219	2	the	the	DET
ejde-350	219	3	brézis	brézi	NOUN
ejde-350	219	4	-	-	PUNCT
ejde-350	219	5	lieb	lieb	ADJ
ejde-350	219	6	lemma	lemma	PROPN
ejde-350	220	1	[	[	X
ejde-350	220	2	10	10	NUM
ejde-350	220	3	]	]	PUNCT
ejde-350	220	4	,	,	PUNCT
ejde-350	220	5	we	we	PRON
ejde-350	220	6	obtain	obtain	VERB
ejde-350	220	7	c0	c0	NOUN
ejde-350	220	8	=	=	PROPN
ejde-350	220	9	lim	lim	PROPN
ejde-350	220	10	n→∞	n→∞	PROPN
ejde-350	221	1	j0(vn)−	j0(vn)−	PROPN
ejde-350	221	2	lim	lim	PROPN
ejde-350	221	3	n→∞	n→∞	NUM
ejde-350	221	4	1	1	NUM
ejde-350	221	5	2∗s	2∗s	NUM
ejde-350	221	6	〈	〈	PROPN
ejde-350	221	7	j	j	PROPN
ejde-350	221	8	′0(vn	′0(vn	PROPN
ejde-350	221	9	)	)	PUNCT
ejde-350	221	10	,	,	PUNCT
ejde-350	221	11	vn	vn	VERB
ejde-350	221	12	〉	〉	PROPN
ejde-350	221	13	=	=	SYM
ejde-350	221	14	lim	lim	PROPN
ejde-350	221	15	n→∞	n→∞	X
ejde-350	221	16	(	(	PUNCT
ejde-350	221	17	1	1	NUM
ejde-350	221	18	2	2	NUM
ejde-350	221	19	−	−	NUM
ejde-350	221	20	1	1	NUM
ejde-350	221	21	2∗s	2∗s	NUM
ejde-350	221	22	)	)	PUNCT
ejde-350	222	1	‖vn‖2φ	‖vn‖2φ	X
ejde-350	222	2	>	>	PUNCT
ejde-350	223	1	(	(	PUNCT
ejde-350	223	2	1	1	NUM
ejde-350	223	3	2	2	NUM
ejde-350	223	4	−	−	NUM
ejde-350	223	5	1	1	NUM
ejde-350	223	6	2∗s	2∗s	NUM
ejde-350	223	7	)	)	PUNCT
ejde-350	223	8	‖v‖2φ	‖v‖2φ	PROPN
ejde-350	223	9	=	=	SYM
ejde-350	223	10	j0(v	j0(v	PROPN
ejde-350	223	11	)	)	PUNCT
ejde-350	223	12	>	>	X
ejde-350	224	1	¯̄c0	¯̄c0	PROPN
ejde-350	224	2	=	=	PROPN
ejde-350	224	3	c0	c0	PROPN
ejde-350	224	4	.	.	PUNCT
ejde-350	225	1	(	(	PUNCT
ejde-350	225	2	3.4	3.4	NUM
ejde-350	225	3	)	)	PUNCT
ejde-350	225	4	thus	thus	ADV
ejde-350	225	5	,	,	PUNCT
ejde-350	225	6	the	the	DET
ejde-350	225	7	inequalities	inequality	NOUN
ejde-350	225	8	above	above	ADV
ejde-350	225	9	have	have	VERB
ejde-350	225	10	to	to	PART
ejde-350	225	11	be	be	AUX
ejde-350	225	12	equalities	equality	NOUN
ejde-350	225	13	.	.	PUNCT
ejde-350	226	1	we	we	PRON
ejde-350	226	2	know	know	VERB
ejde-350	226	3	that	that	SCONJ
ejde-350	226	4	lim	lim	PROPN
ejde-350	226	5	n→∞	n→∞	NUM
ejde-350	226	6	‖vn‖2φ	‖vn‖2φ	PROPN
ejde-350	226	7	=	=	PUNCT
ejde-350	226	8	‖v‖2φ	‖v‖2φ	PROPN
ejde-350	226	9	.	.	PUNCT
ejde-350	226	10	by	by	ADP
ejde-350	226	11	using	use	VERB
ejde-350	226	12	brézis	brézi	NOUN
ejde-350	226	13	-	-	PUNCT
ejde-350	226	14	lieb	lieb	ADJ
ejde-350	226	15	lemma	lemma	PROPN
ejde-350	227	1	[	[	X
ejde-350	227	2	10	10	NUM
ejde-350	227	3	]	]	PUNCT
ejde-350	227	4	again	again	ADV
ejde-350	227	5	,	,	PUNCT
ejde-350	227	6	we	we	PRON
ejde-350	227	7	have	have	VERB
ejde-350	227	8	lim	lim	PROPN
ejde-350	227	9	n→∞	n→∞	NUM
ejde-350	228	1	‖vn‖2φ	‖vn‖2φ	PROPN
ejde-350	228	2	−	−	PROPN
ejde-350	228	3	lim	lim	PROPN
ejde-350	228	4	n→∞	n→∞	X
ejde-350	229	1	‖vn	‖vn	PROPN
ejde-350	229	2	−	−	PROPN
ejde-350	229	3	v‖2φ	v‖2φ	NOUN
ejde-350	229	4	=	=	SYM
ejde-350	229	5	‖v‖2φ	‖v‖2φ	PROPN
ejde-350	229	6	,	,	PUNCT
ejde-350	229	7	which	which	PRON
ejde-350	229	8	implies	imply	VERB
ejde-350	229	9	that	that	SCONJ
ejde-350	229	10	lim	lim	PROPN
ejde-350	229	11	n→∞	n→∞	X
ejde-350	230	1	‖vn	‖vn	PROPN
ejde-350	230	2	−	−	PROPN
ejde-350	230	3	v‖2φ	v‖2φ	X
ejde-350	230	4	=	=	SYM
ejde-350	230	5	0	0	PROPN
ejde-350	230	6	.	.	PUNCT
ejde-350	230	7	ejde-2020/01	ejde-2020/01	NOUN
ejde-350	230	8	fractional	fractional	ADJ
ejde-350	230	9	schrödinger	schrödinger	NOUN
ejde-350	230	10	-	-	PUNCT
ejde-350	230	11	poisson	poisson	NOUN
ejde-350	230	12	system	system	NOUN
ejde-350	230	13	11	11	NUM
ejde-350	230	14	using	use	VERB
ejde-350	230	15	(	(	PUNCT
ejde-350	230	16	3.4	3.4	NUM
ejde-350	230	17	)	)	PUNCT
ejde-350	230	18	again	again	ADV
ejde-350	230	19	,	,	PUNCT
ejde-350	230	20	we	we	PRON
ejde-350	230	21	know	know	VERB
ejde-350	230	22	that	that	SCONJ
ejde-350	230	23	j0(v	j0(v	PROPN
ejde-350	230	24	)	)	PUNCT
ejde-350	230	25	=	=	SYM
ejde-350	230	26	c0	c0	NOUN
ejde-350	230	27	.	.	PUNCT
ejde-350	231	1	this	this	PRON
ejde-350	231	2	implies	imply	VERB
ejde-350	231	3	that	that	SCONJ
ejde-350	231	4	v	v	PART
ejde-350	231	5	attain	attain	VERB
ejde-350	231	6	the	the	DET
ejde-350	231	7	minimum	minimum	NOUN
ejde-350	231	8	of	of	ADP
ejde-350	231	9	j0	j0	PROPN
ejde-350	231	10	at	at	ADP
ejde-350	231	11	c0	c0	PROPN
ejde-350	231	12	.	.	PUNCT
ejde-350	232	1	�	�	PROPN
ejde-350	232	2	4	4	NUM
ejde-350	232	3	.	.	PUNCT
ejde-350	232	4	proof	proof	NOUN
ejde-350	232	5	of	of	ADP
ejde-350	232	6	theorem	theorem	ADJ
ejde-350	232	7	1.2	1.2	NUM
ejde-350	232	8	first	first	ADV
ejde-350	232	9	,	,	PUNCT
ejde-350	232	10	we	we	PRON
ejde-350	232	11	summarize	summarize	VERB
ejde-350	232	12	the	the	DET
ejde-350	232	13	proof	proof	NOUN
ejde-350	232	14	of	of	ADP
ejde-350	232	15	theorem	theorem	ADJ
ejde-350	232	16	1.1	1.1	NUM
ejde-350	232	17	as	as	SCONJ
ejde-350	232	18	follows	follow	VERB
ejde-350	232	19	.	.	PUNCT
ejde-350	233	1	lemma	lemma	PROPN
ejde-350	233	2	4.1	4.1	NUM
ejde-350	233	3	.	.	PUNCT
ejde-350	234	1	the	the	DET
ejde-350	234	2	energy	energy	NOUN
ejde-350	234	3	functional	functional	ADJ
ejde-350	234	4	j0	j0	PROPN
ejde-350	234	5	satisfies	satisfy	VERB
ejde-350	234	6	the	the	DET
ejde-350	234	7	following	follow	VERB
ejde-350	234	8	properties	property	NOUN
ejde-350	234	9	:	:	PUNCT
ejde-350	234	10	(	(	PUNCT
ejde-350	234	11	1	1	X
ejde-350	234	12	)	)	PUNCT
ejde-350	234	13	there	there	PRON
ejde-350	234	14	exist	exist	VERB
ejde-350	234	15	ρ	ρ	NOUN
ejde-350	234	16	,	,	PUNCT
ejde-350	234	17	ς	ς	PROPN
ejde-350	234	18	>	>	X
ejde-350	234	19	0	0	NUM
ejde-350	234	20	such	such	ADJ
ejde-350	234	21	that	that	SCONJ
ejde-350	234	22	if	if	SCONJ
ejde-350	234	23	‖u‖s	‖u‖s	PROPN
ejde-350	234	24	=	=	SYM
ejde-350	234	25	ρ	ρ	PROPN
ejde-350	234	26	,	,	PUNCT
ejde-350	234	27	then	then	ADV
ejde-350	234	28	j0(u	j0(u	PROPN
ejde-350	234	29	)	)	PUNCT
ejde-350	234	30	>	>	X
ejde-350	234	31	ς	ς	PROPN
ejde-350	234	32	,	,	PUNCT
ejde-350	234	33	and	and	CCONJ
ejde-350	234	34	e	e	PROPN
ejde-350	234	35	∈	∈	PROPN
ejde-350	234	36	ds,2	ds,2	NOUN
ejde-350	234	37	rad(r3	rad(r3	NOUN
ejde-350	234	38	)	)	PUNCT
ejde-350	234	39	exists	exist	VERB
ejde-350	234	40	such	such	ADJ
ejde-350	234	41	that	that	SCONJ
ejde-350	234	42	‖e‖s	‖e‖s	PROPN
ejde-350	234	43	>	>	X
ejde-350	234	44	ρ	ρ	PROPN
ejde-350	234	45	and	and	CCONJ
ejde-350	234	46	j0(e	j0(e	PROPN
ejde-350	234	47	)	)	PUNCT
ejde-350	234	48	<	<	X
ejde-350	234	49	0	0	NUM
ejde-350	234	50	;	;	PUNCT
ejde-350	234	51	(	(	PUNCT
ejde-350	234	52	2	2	X
ejde-350	234	53	)	)	PUNCT
ejde-350	234	54	there	there	PRON
ejde-350	234	55	exists	exist	VERB
ejde-350	234	56	a	a	DET
ejde-350	234	57	critical	critical	ADJ
ejde-350	234	58	point	point	NOUN
ejde-350	234	59	v	v	NOUN
ejde-350	234	60	of	of	ADP
ejde-350	234	61	j0	j0	PROPN
ejde-350	234	62	such	such	ADJ
ejde-350	234	63	that	that	SCONJ
ejde-350	234	64	j0(v	j0(v	PROPN
ejde-350	234	65	)	)	PUNCT
ejde-350	234	66	=	=	SYM
ejde-350	234	67	c0	c0	NOUN
ejde-350	234	68	:	:	PUNCT
ejde-350	234	69	=	=	SYM
ejde-350	234	70	min	min	PROPN
ejde-350	234	71	υ∈γ0	υ∈γ0	PROPN
ejde-350	234	72	max	max	PROPN
ejde-350	234	73	t∈[0,1	t∈[0,1	PROPN
ejde-350	234	74	]	]	X
ejde-350	234	75	j0(υ(t	j0(υ(t	NOUN
ejde-350	234	76	)	)	PUNCT
ejde-350	234	77	)	)	PUNCT
ejde-350	234	78	,	,	PUNCT
ejde-350	234	79	where	where	SCONJ
ejde-350	234	80	γ0	γ0	NOUN
ejde-350	234	81	=	=	SYM
ejde-350	234	82	{	{	PUNCT
ejde-350	234	83	υ	υ	PROPN
ejde-350	234	84	∈	∈	PROPN
ejde-350	234	85	c([0	c([0	NOUN
ejde-350	234	86	,	,	PUNCT
ejde-350	234	87	1	1	NUM
ejde-350	234	88	]	]	PUNCT
ejde-350	234	89	,	,	PUNCT
ejde-350	234	90	ds,2	ds,2	PROPN
ejde-350	234	91	rad(r3))|υ(0	rad(r3))|υ(0	PROPN
ejde-350	234	92	)	)	PUNCT
ejde-350	234	93	=	=	SYM
ejde-350	234	94	0	0	NUM
ejde-350	234	95	,	,	PUNCT
ejde-350	234	96	j0(υ(1	j0(υ(1	PROPN
ejde-350	234	97	)	)	PUNCT
ejde-350	234	98	)	)	PUNCT
ejde-350	234	99	<	<	X
ejde-350	235	1	0	0	NUM
ejde-350	235	2	}	}	PUNCT
ejde-350	235	3	;	;	PUNCT
ejde-350	235	4	(	(	PUNCT
ejde-350	235	5	3	3	X
ejde-350	235	6	)	)	PUNCT
ejde-350	235	7	c0	c0	NOUN
ejde-350	235	8	:	:	PUNCT
ejde-350	235	9	=	=	SYM
ejde-350	235	10	inf{j0(u)|j	inf{j0(u)|j	PROPN
ejde-350	235	11	′0(u	′0(u	PROPN
ejde-350	235	12	)	)	PUNCT
ejde-350	235	13	=	=	SYM
ejde-350	235	14	0	0	NUM
ejde-350	235	15	,	,	PUNCT
ejde-350	235	16	u	u	PROPN
ejde-350	235	17	∈	∈	PROPN
ejde-350	235	18	ds,2	ds,2	NOUN
ejde-350	235	19	rad(r3	rad(r3	NOUN
ejde-350	235	20	)	)	PUNCT
ejde-350	235	21	\	\	NOUN
ejde-350	235	22	{	{	PUNCT
ejde-350	235	23	0	0	NUM
ejde-350	235	24	}	}	PUNCT
ejde-350	235	25	}	}	PUNCT
ejde-350	235	26	;	;	PUNCT
ejde-350	235	27	(	(	PUNCT
ejde-350	235	28	4	4	X
ejde-350	235	29	)	)	PUNCT
ejde-350	235	30	there	there	PRON
ejde-350	235	31	exists	exist	VERB
ejde-350	235	32	a	a	DET
ejde-350	235	33	path	path	NOUN
ejde-350	235	34	υ0(t	υ0(t	NOUN
ejde-350	235	35	)	)	PUNCT
ejde-350	235	36	∈	∈	PROPN
ejde-350	235	37	γ0	γ0	NOUN
ejde-350	235	38	passing	pass	VERB
ejde-350	235	39	through	through	ADP
ejde-350	235	40	v	v	NOUN
ejde-350	235	41	at	at	ADP
ejde-350	235	42	t	t	PROPN
ejde-350	235	43	=	=	SYM
ejde-350	235	44	t0	t0	PROPN
ejde-350	235	45	and	and	CCONJ
ejde-350	235	46	satisfying	satisfy	VERB
ejde-350	235	47	j0(v	j0(v	PROPN
ejde-350	235	48	)	)	PUNCT
ejde-350	235	49	>	>	X
ejde-350	235	50	j0(υ0(t	j0(υ0(t	PROPN
ejde-350	235	51	)	)	PUNCT
ejde-350	235	52	)	)	PUNCT
ejde-350	235	53	for	for	ADP
ejde-350	235	54	all	all	DET
ejde-350	235	55	t	t	PROPN
ejde-350	235	56	6=	6=	PROPN
ejde-350	235	57	t0	t0	PROPN
ejde-350	235	58	;	;	PUNCT
ejde-350	235	59	(	(	PUNCT
ejde-350	235	60	5	5	X
ejde-350	235	61	)	)	PUNCT
ejde-350	235	62	the	the	DET
ejde-350	235	63	set	set	NOUN
ejde-350	235	64	s	s	VERB
ejde-350	235	65	:	:	PUNCT
ejde-350	235	66	=	=	SYM
ejde-350	235	67	{	{	PUNCT
ejde-350	235	68	u	u	NOUN
ejde-350	235	69	∈	∈	PROPN
ejde-350	235	70	ds,2	ds,2	PROPN
ejde-350	235	71	rad(r3)|j	rad(r3)|j	NOUN
ejde-350	235	72	′0(u	′0(u	PROPN
ejde-350	235	73	)	)	PUNCT
ejde-350	235	74	=	=	SYM
ejde-350	235	75	0	0	NUM
ejde-350	235	76	,	,	PUNCT
ejde-350	235	77	j0(u	j0(u	NOUN
ejde-350	235	78	)	)	PUNCT
ejde-350	235	79	=	=	SYM
ejde-350	235	80	c0	c0	NOUN
ejde-350	235	81	}	}	PUNCT
ejde-350	235	82	is	be	AUX
ejde-350	235	83	compact	compact	ADJ
ejde-350	235	84	in	in	ADP
ejde-350	235	85	ds,2	ds,2	NOUN
ejde-350	235	86	rad(r3	rad(r3	NOUN
ejde-350	235	87	)	)	PUNCT
ejde-350	235	88	endowed	endow	VERB
ejde-350	235	89	with	with	ADP
ejde-350	235	90	the	the	DET
ejde-350	235	91	strong	strong	ADJ
ejde-350	235	92	topology	topology	NOUN
ejde-350	235	93	up	up	ADP
ejde-350	235	94	to	to	ADP
ejde-350	235	95	dilations	dilation	NOUN
ejde-350	235	96	in	in	ADP
ejde-350	235	97	r3	r3	PROPN
ejde-350	235	98	.	.	PUNCT
ejde-350	236	1	proof	proof	NOUN
ejde-350	236	2	.	.	PUNCT
ejde-350	237	1	it	it	PRON
ejde-350	237	2	is	be	AUX
ejde-350	237	3	easy	easy	ADJ
ejde-350	237	4	to	to	PART
ejde-350	237	5	see	see	VERB
ejde-350	237	6	that	that	SCONJ
ejde-350	237	7	j0	j0	PROPN
ejde-350	237	8	is	be	AUX
ejde-350	237	9	invariant	invariant	ADJ
ejde-350	237	10	by	by	ADP
ejde-350	237	11	dilations	dilation	NOUN
ejde-350	237	12	.	.	PUNCT
ejde-350	238	1	as	as	ADP
ejde-350	238	2	a	a	DET
ejde-350	238	3	byproduct	byproduct	NOUN
ejde-350	238	4	of	of	ADP
ejde-350	238	5	the	the	DET
ejde-350	238	6	proof	proof	NOUN
ejde-350	238	7	of	of	ADP
ejde-350	238	8	theorem	theorem	ADJ
ejde-350	238	9	1.1	1.1	NUM
ejde-350	238	10	,	,	PUNCT
ejde-350	238	11	the	the	DET
ejde-350	238	12	weak	weak	ADJ
ejde-350	238	13	convergence	convergence	NOUN
ejde-350	238	14	of	of	ADP
ejde-350	238	15	the	the	DET
ejde-350	238	16	dilated	dilate	VERB
ejde-350	238	17	subsequence	subsequence	NOUN
ejde-350	238	18	can	can	AUX
ejde-350	238	19	be	be	AUX
ejde-350	238	20	upgraded	upgrade	VERB
ejde-350	238	21	into	into	ADP
ejde-350	238	22	strong	strong	ADJ
ejde-350	238	23	convergence	convergence	NOUN
ejde-350	238	24	.	.	PUNCT
ejde-350	239	1	as	as	ADP
ejde-350	239	2	a	a	DET
ejde-350	239	3	direct	direct	ADJ
ejde-350	239	4	consequence	consequence	NOUN
ejde-350	239	5	,	,	PUNCT
ejde-350	239	6	we	we	PRON
ejde-350	239	7	show	show	VERB
ejde-350	239	8	that	that	SCONJ
ejde-350	239	9	the	the	DET
ejde-350	239	10	set	set	NOUN
ejde-350	239	11	s	s	PART
ejde-350	239	12	is	be	AUX
ejde-350	239	13	compact	compact	ADJ
ejde-350	239	14	in	in	ADP
ejde-350	239	15	ds,2	ds,2	NOUN
ejde-350	239	16	rad(r3	rad(r3	NOUN
ejde-350	239	17	)	)	PUNCT
ejde-350	239	18	endowed	endow	VERB
ejde-350	239	19	with	with	ADP
ejde-350	239	20	the	the	DET
ejde-350	239	21	strong	strong	ADJ
ejde-350	239	22	topology	topology	NOUN
ejde-350	239	23	up	up	ADP
ejde-350	239	24	to	to	ADP
ejde-350	239	25	dilations	dilation	NOUN
ejde-350	239	26	in	in	ADP
ejde-350	239	27	r3	r3	PROPN
ejde-350	239	28	.	.	PUNCT
ejde-350	240	1	the	the	DET
ejde-350	240	2	proof	proof	NOUN
ejde-350	240	3	is	be	AUX
ejde-350	240	4	completed	complete	VERB
ejde-350	240	5	.	.	PUNCT
ejde-350	241	1	�	�	NOUN
ejde-350	241	2	we	we	PRON
ejde-350	241	3	introduce	introduce	VERB
ejde-350	241	4	the	the	DET
ejde-350	241	5	energy	energy	NOUN
ejde-350	241	6	functional	functional	NOUN
ejde-350	241	7	associated	associate	VERB
ejde-350	241	8	with	with	ADP
ejde-350	241	9	system	system	NOUN
ejde-350	241	10	(	(	PUNCT
ejde-350	241	11	1.1	1.1	NUM
ejde-350	241	12	)	)	PUNCT
ejde-350	241	13	by	by	ADP
ejde-350	241	14	iλ(u	iλ(u	NOUN
ejde-350	241	15	)	)	PUNCT
ejde-350	241	16	=	=	SYM
ejde-350	241	17	1	1	NUM
ejde-350	241	18	2	2	X
ejde-350	241	19	‖u‖2φ	‖u‖2φ	NOUN
ejde-350	241	20	+	+	CCONJ
ejde-350	241	21	λ	λ	PROPN
ejde-350	241	22	4	4	NUM
ejde-350	241	23	∫	∫	NOUN
ejde-350	241	24	r3	r3	PROPN
ejde-350	241	25	∫	∫	PROPN
ejde-350	241	26	r3	r3	PROPN
ejde-350	241	27	|u(x)|2|u(y)|2	|u(x)|2|u(y)|2	PROPN
ejde-350	241	28	|x−	|x−	PROPN
ejde-350	241	29	y|3−2	y|3−2	PROPN
ejde-350	241	30	t	t	PROPN
ejde-350	241	31	dxdy	dxdy	PROPN
ejde-350	241	32	−	−	PROPN
ejde-350	241	33	1	1	NUM
ejde-350	241	34	2∗s	2∗s	NUM
ejde-350	241	35	∫	∫	NOUN
ejde-350	241	36	r3	r3	PROPN
ejde-350	241	37	|u|2	|u|2	PROPN
ejde-350	241	38	∗	∗	PROPN
ejde-350	241	39	sdx	sdx	PROPN
ejde-350	241	40	.	.	PUNCT
ejde-350	242	1	define	define	VERB
ejde-350	242	2	jλ	jλ	PROPN
ejde-350	242	3	=	=	NOUN
ejde-350	242	4	iλ|ds,2rad(r3	iλ|ds,2rad(r3	PRON
ejde-350	242	5	)	)	PUNCT
ejde-350	242	6	.	.	PUNCT
ejde-350	243	1	as	as	ADP
ejde-350	243	2	in	in	ADP
ejde-350	243	3	[	[	X
ejde-350	243	4	12	12	NUM
ejde-350	243	5	,	,	PUNCT
ejde-350	243	6	25	25	NUM
ejde-350	243	7	]	]	PUNCT
ejde-350	243	8	,	,	PUNCT
ejde-350	243	9	we	we	PRON
ejde-350	243	10	define	define	VERB
ejde-350	243	11	a	a	DET
ejde-350	243	12	modified	modify	VERB
ejde-350	243	13	mountain	mountain	NOUN
ejde-350	243	14	pass	pass	NOUN
ejde-350	243	15	energy	energy	NOUN
ejde-350	243	16	level	level	NOUN
ejde-350	243	17	of	of	ADP
ejde-350	243	18	jλ	jλ	ADP
ejde-350	243	19	cλ	cλ	X
ejde-350	243	20	:	:	PUNCT
ejde-350	243	21	=	=	NUM
ejde-350	243	22	min	min	NOUN
ejde-350	243	23	υ∈υm	υ∈υm	PROPN
ejde-350	243	24	max	max	PROPN
ejde-350	243	25	t∈[0,1	t∈[0,1	PROPN
ejde-350	243	26	]	]	PUNCT
ejde-350	243	27	jλ(υ(t	jλ(υ(t	NOUN
ejde-350	243	28	)	)	PUNCT
ejde-350	243	29	)	)	PUNCT
ejde-350	243	30	,	,	PUNCT
ejde-350	243	31	where	where	SCONJ
ejde-350	243	32	υm	υm	PROPN
ejde-350	243	33	=	=	PRON
ejde-350	243	34	{	{	PUNCT
ejde-350	243	35	υ	υ	NOUN
ejde-350	243	36	∈	∈	PROPN
ejde-350	243	37	γ0|	γ0|	NOUN
ejde-350	243	38	sup	sup	NOUN
ejde-350	243	39	t∈[0,1	t∈[0,1	NOUN
ejde-350	243	40	]	]	PUNCT
ejde-350	243	41	‖υ(t)‖s	‖υ(t)‖s	PROPN
ejde-350	243	42	6	6	NUM
ejde-350	243	43	m	m	NOUN
ejde-350	243	44	}	}	PUNCT
ejde-350	243	45	,	,	PUNCT
ejde-350	243	46	m	m	VERB
ejde-350	243	47	=	=	SYM
ejde-350	243	48	2{sup	2{sup	PROPN
ejde-350	243	49	u∈s	u∈s	ADJ
ejde-350	243	50	‖u‖s	‖u‖s	NOUN
ejde-350	243	51	,	,	PUNCT
ejde-350	243	52	sup	sup	NOUN
ejde-350	243	53	t∈[0,1	t∈[0,1	NOUN
ejde-350	243	54	]	]	PUNCT
ejde-350	243	55	‖υ(t)‖s	‖υ(t)‖s	PROPN
ejde-350	243	56	}	}	PUNCT
ejde-350	243	57	.	.	PUNCT
ejde-350	244	1	clearly	clearly	ADV
ejde-350	244	2	,	,	PUNCT
ejde-350	244	3	by	by	ADP
ejde-350	244	4	the	the	DET
ejde-350	244	5	choice	choice	NOUN
ejde-350	244	6	of	of	ADP
ejde-350	244	7	m	m	PROPN
ejde-350	244	8	,	,	PUNCT
ejde-350	244	9	υ0	υ0	PROPN
ejde-350	244	10	∈	∈	PROPN
ejde-350	244	11	γm	γm	NOUN
ejde-350	244	12	and	and	CCONJ
ejde-350	244	13	thus	thus	ADV
ejde-350	244	14	,	,	PUNCT
ejde-350	244	15	c0	c0	PROPN
ejde-350	244	16	=	=	SYM
ejde-350	244	17	min	min	PROPN
ejde-350	244	18	υ∈γm	υ∈γm	PROPN
ejde-350	244	19	max	max	PROPN
ejde-350	244	20	t∈[0,1	t∈[0,1	PROPN
ejde-350	244	21	]	]	X
ejde-350	244	22	j0(υ(t	j0(υ(t	NOUN
ejde-350	244	23	)	)	PUNCT
ejde-350	244	24	)	)	PUNCT
ejde-350	244	25	.	.	PUNCT
ejde-350	245	1	however	however	ADV
ejde-350	245	2	,	,	PUNCT
ejde-350	245	3	since	since	SCONJ
ejde-350	245	4	γm	γm	PROPN
ejde-350	245	5	(	(	PUNCT
ejde-350	245	6	γ0	γ0	NOUN
ejde-350	245	7	,	,	PUNCT
ejde-350	245	8	the	the	DET
ejde-350	245	9	standard	standard	ADJ
ejde-350	245	10	mountain	mountain	NOUN
ejde-350	245	11	pass	pass	NOUN
ejde-350	245	12	theorem	theorem	NOUN
ejde-350	245	13	can	can	AUX
ejde-350	245	14	not	not	PART
ejde-350	245	15	be	be	AUX
ejde-350	245	16	applied	apply	VERB
ejde-350	245	17	,	,	PUNCT
ejde-350	245	18	so	so	SCONJ
ejde-350	245	19	other	other	ADJ
ejde-350	245	20	arguments	argument	NOUN
ejde-350	245	21	are	be	AUX
ejde-350	245	22	needed	need	VERB
ejde-350	245	23	to	to	PART
ejde-350	245	24	prove	prove	VERB
ejde-350	245	25	that	that	SCONJ
ejde-350	245	26	cλ	cλ	PROPN
ejde-350	245	27	is	be	AUX
ejde-350	245	28	a	a	DET
ejde-350	245	29	critical	critical	ADJ
ejde-350	245	30	value	value	NOUN
ejde-350	245	31	.	.	PUNCT
ejde-350	246	1	lemma	lemma	PROPN
ejde-350	246	2	4.2	4.2	NUM
ejde-350	246	3	.	.	PUNCT
ejde-350	247	1	let	let	VERB
ejde-350	247	2	λ	λ	INTJ
ejde-350	247	3	>	>	X
ejde-350	247	4	0	0	PROPN
ejde-350	247	5	.	.	PUNCT
ejde-350	248	1	then	then	ADV
ejde-350	248	2	limλ→0	limλ→0	PROPN
ejde-350	248	3	cλ	cλ	PROPN
ejde-350	248	4	=	=	SYM
ejde-350	248	5	c0	c0	NOUN
ejde-350	248	6	.	.	PROPN
ejde-350	249	1	12	12	NUM
ejde-350	249	2	y.	y.	PROPN
ejde-350	249	3	su	su	PROPN
ejde-350	249	4	,	,	PUNCT
ejde-350	249	5	h.	h.	PROPN
ejde-350	249	6	chen	chen	PROPN
ejde-350	249	7	,	,	PUNCT
ejde-350	249	8	s.	s.	PROPN
ejde-350	249	9	liu	liu	PROPN
ejde-350	249	10	,	,	PUNCT
ejde-350	249	11	x.	x.	NOUN
ejde-350	249	12	fang	fang	PROPN
ejde-350	249	13	ejde-2020/01	ejde-2020/01	NOUN
ejde-350	249	14	proof	proof	NOUN
ejde-350	249	15	.	.	PUNCT
ejde-350	250	1	since	since	SCONJ
ejde-350	250	2	λ	λ	PROPN
ejde-350	250	3	>	>	X
ejde-350	250	4	0	0	NUM
ejde-350	250	5	,	,	PUNCT
ejde-350	250	6	it	it	PRON
ejde-350	250	7	is	be	AUX
ejde-350	250	8	easy	easy	ADJ
ejde-350	250	9	to	to	PART
ejde-350	250	10	see	see	VERB
ejde-350	250	11	that	that	DET
ejde-350	250	12	cλ	cλ	PROPN
ejde-350	250	13	>	>	X
ejde-350	250	14	c0	c0	PROPN
ejde-350	250	15	.	.	PUNCT
ejde-350	251	1	on	on	ADP
ejde-350	251	2	the	the	DET
ejde-350	251	3	other	other	ADJ
ejde-350	251	4	hand	hand	NOUN
ejde-350	251	5	,	,	PUNCT
ejde-350	251	6	we	we	PRON
ejde-350	251	7	can	can	AUX
ejde-350	251	8	take	take	VERB
ejde-350	251	9	e	e	NOUN
ejde-350	251	10	=	=	NOUN
ejde-350	251	11	tv	tv	NOUN
ejde-350	251	12	in	in	ADP
ejde-350	251	13	property	property	NOUN
ejde-350	251	14	(	(	PUNCT
ejde-350	251	15	1	1	NUM
ejde-350	251	16	)	)	PUNCT
ejde-350	251	17	,	,	PUNCT
ejde-350	251	18	where	where	SCONJ
ejde-350	251	19	t	t	PROPN
ejde-350	251	20	>	>	X
ejde-350	251	21	(	(	PUNCT
ejde-350	251	22	2∗s	2∗s	NUM
ejde-350	251	23	2	2	NUM
ejde-350	251	24	)	)	PUNCT
ejde-350	251	25	1	1	NUM
ejde-350	251	26	2∗s−2	2∗s−2	NOUN
ejde-350	251	27	.	.	PUNCT
ejde-350	252	1	then	then	ADV
ejde-350	252	2	υ0(t	υ0(t	X
ejde-350	252	3	)	)	PUNCT
ejde-350	252	4	∈	∈	PROPN
ejde-350	252	5	c([0	c([0	NOUN
ejde-350	252	6	,	,	PUNCT
ejde-350	252	7	1	1	NUM
ejde-350	252	8	]	]	PUNCT
ejde-350	252	9	,	,	PUNCT
ejde-350	252	10	ds,2(r3	ds,2(r3	PROPN
ejde-350	252	11	)	)	PUNCT
ejde-350	252	12	)	)	PUNCT
ejde-350	252	13	is	be	AUX
ejde-350	252	14	defined	define	VERB
ejde-350	252	15	as	as	ADP
ejde-350	252	16	υ0(t	υ0(t	NOUN
ejde-350	252	17	)	)	PUNCT
ejde-350	252	18	=	=	SYM
ejde-350	252	19	te	te	PROPN
ejde-350	252	20	=	=	SYM
ejde-350	252	21	ttv	ttv	PROPN
ejde-350	252	22	,	,	PUNCT
ejde-350	252	23	and	and	CCONJ
ejde-350	252	24	t0	t0	NOUN
ejde-350	252	25	=	=	SYM
ejde-350	252	26	1	1	NUM
ejde-350	252	27	t	t	NOUN
ejde-350	252	28	in	in	ADP
ejde-350	252	29	property	property	NOUN
ejde-350	252	30	(	(	PUNCT
ejde-350	252	31	4	4	NUM
ejde-350	252	32	)	)	PUNCT
ejde-350	252	33	.	.	PUNCT
ejde-350	253	1	we	we	PRON
ejde-350	253	2	know	know	VERB
ejde-350	253	3	that	that	SCONJ
ejde-350	253	4	lim	lim	PROPN
ejde-350	253	5	λ→0	λ→0	PROPN
ejde-350	253	6	cλ	cλ	PROPN
ejde-350	253	7	=	=	SYM
ejde-350	253	8	lim	lim	PROPN
ejde-350	253	9	λ→0	λ→0	PUNCT
ejde-350	253	10	jλ(υ0(t	jλ(υ0(t	PROPN
ejde-350	253	11	)	)	PUNCT
ejde-350	253	12	)	)	PUNCT
ejde-350	253	13	6j0(υ0(t	6j0(υ0(t	NUM
ejde-350	253	14	)	)	PUNCT
ejde-350	253	15	)	)	PUNCT
ejde-350	254	1	+	+	CCONJ
ejde-350	254	2	lim	lim	PROPN
ejde-350	254	3	λ→0	λ→0	PROPN
ejde-350	254	4	λ	λ	PROPN
ejde-350	254	5	4	4	NUM
ejde-350	254	6	∫	∫	NOUN
ejde-350	254	7	r3	r3	PROPN
ejde-350	254	8	∫	∫	PROPN
ejde-350	254	9	r3	r3	PROPN
ejde-350	254	10	|tv(y)|2|tv(x)|2	|tv(y)|2|tv(x)|2	PROPN
ejde-350	254	11	|x−	|x−	PROPN
ejde-350	254	12	y|3−2	y|3−2	PROPN
ejde-350	254	13	t	t	PROPN
ejde-350	254	14	dxdy	dxdy	PROPN
ejde-350	254	15	=	=	PROPN
ejde-350	254	16	j0(v	j0(v	PROPN
ejde-350	254	17	)	)	PUNCT
ejde-350	254	18	=	=	SYM
ejde-350	254	19	c0	c0	NOUN
ejde-350	254	20	.	.	PUNCT
ejde-350	255	1	the	the	DET
ejde-350	255	2	proof	proof	NOUN
ejde-350	255	3	is	be	AUX
ejde-350	255	4	complete	complete	ADJ
ejde-350	255	5	.	.	PUNCT
ejde-350	256	1	�	�	PROPN
ejde-350	256	2	for	for	ADP
ejde-350	256	3	any	any	DET
ejde-350	256	4	positive	positive	ADJ
ejde-350	256	5	number	number	NOUN
ejde-350	256	6	d	d	NOUN
ejde-350	256	7	,	,	PUNCT
ejde-350	256	8	we	we	PRON
ejde-350	256	9	denote	denote	VERB
ejde-350	256	10	bd(u	bd(u	PUNCT
ejde-350	256	11	)	)	PUNCT
ejde-350	256	12	:	:	PUNCT
ejde-350	257	1	=	=	SYM
ejde-350	257	2	{	{	PUNCT
ejde-350	257	3	v	v	NUM
ejde-350	257	4	∈	∈	NOUN
ejde-350	257	5	ds,2	ds,2	NOUN
ejde-350	257	6	rad(r3)|‖u−	rad(r3)|‖u−	VERB
ejde-350	257	7	v‖s	v‖s	NOUN
ejde-350	257	8	6	6	NUM
ejde-350	257	9	d	d	NOUN
ejde-350	257	10	}	}	PUNCT
ejde-350	257	11	,	,	PUNCT
ejde-350	257	12	and	and	CCONJ
ejde-350	257	13	for	for	ADP
ejde-350	257	14	any	any	DET
ejde-350	257	15	subset	subset	NOUN
ejde-350	257	16	a	a	PRON
ejde-350	257	17	of	of	ADP
ejde-350	257	18	ds,2	ds,2	NOUN
ejde-350	257	19	rad(r3	rad(r3	NOUN
ejde-350	257	20	)	)	PUNCT
ejde-350	257	21	,	,	PUNCT
ejde-350	257	22	we	we	PRON
ejde-350	257	23	set	set	VERB
ejde-350	257	24	ad	ad	NOUN
ejde-350	257	25	:	:	PUNCT
ejde-350	257	26	=	=	SYM
ejde-350	257	27	∪u∈abd(u	∪u∈abd(u	X
ejde-350	257	28	)	)	PUNCT
ejde-350	257	29	.	.	PUNCT
ejde-350	258	1	lemma	lemma	PROPN
ejde-350	258	2	4.3	4.3	NUM
ejde-350	258	3	.	.	PUNCT
ejde-350	259	1	set	set	VERB
ejde-350	259	2	d1	d1	PROPN
ejde-350	259	3	=	=	SYM
ejde-350	260	1	√	√	PROPN
ejde-350	260	2	2	2	NUM
ejde-350	260	3	·	·	SYM
ejde-350	260	4	2∗s	2∗s	NUM
ejde-350	260	5	·	·	PUNCT
ejde-350	260	6	c0/(2∗s	c0/(2∗s	ADJ
ejde-350	260	7	−	−	NOUN
ejde-350	260	8	2	2	NUM
ejde-350	260	9	)	)	PUNCT
ejde-350	260	10	.	.	PUNCT
ejde-350	261	1	let	let	VERB
ejde-350	261	2	d	d	X
ejde-350	261	3	∈	∈	PROPN
ejde-350	261	4	(	(	PUNCT
ejde-350	261	5	0	0	NUM
ejde-350	261	6	,	,	PUNCT
ejde-350	261	7	d1	d1	PROPN
ejde-350	261	8	)	)	PUNCT
ejde-350	261	9	.	.	PUNCT
ejde-350	262	1	for	for	ADP
ejde-350	262	2	any	any	DET
ejde-350	262	3	u	u	PROPN
ejde-350	262	4	⊂	⊂	PROPN
ejde-350	262	5	sd	sd	PROPN
ejde-350	262	6	,	,	PUNCT
ejde-350	262	7	we	we	PRON
ejde-350	262	8	have	have	VERB
ejde-350	262	9	u	u	NOUN
ejde-350	262	10	6≡	6≡	NUM
ejde-350	262	11	0	0	NUM
ejde-350	262	12	.	.	PUNCT
ejde-350	263	1	proof	proof	NOUN
ejde-350	263	2	.	.	PUNCT
ejde-350	264	1	for	for	ADP
ejde-350	264	2	any	any	PRON
ejde-350	264	3	v	v	ADP
ejde-350	264	4	⊂	⊂	PROPN
ejde-350	264	5	sd	sd	NOUN
ejde-350	264	6	,	,	PUNCT
ejde-350	264	7	we	we	PRON
ejde-350	264	8	have	have	VERB
ejde-350	264	9	‖v‖2s	‖v‖2s	PROPN
ejde-350	264	10	>	>	PUNCT
ejde-350	264	11	‖v‖2φ	‖v‖2φ	PUNCT
ejde-350	264	12	=	=	SYM
ejde-350	264	13	2	2	NUM
ejde-350	264	14	·	·	SYM
ejde-350	264	15	2∗s	2∗s	NUM
ejde-350	264	16	2∗s	2∗s	NUM
ejde-350	264	17	−	−	NOUN
ejde-350	264	18	2	2	NUM
ejde-350	264	19	(	(	PUNCT
ejde-350	264	20	j0(v)−	j0(v)−	DET
ejde-350	264	21	1	1	NUM
ejde-350	264	22	2∗s	2∗s	NUM
ejde-350	264	23	〈	〈	PROPN
ejde-350	264	24	j	j	PROPN
ejde-350	264	25	′0(v	′0(v	PROPN
ejde-350	264	26	)	)	PUNCT
ejde-350	264	27	,	,	PUNCT
ejde-350	264	28	v	v	NOUN
ejde-350	264	29	〉	〉	NOUN
ejde-350	264	30	)	)	PUNCT
ejde-350	264	31	=	=	SYM
ejde-350	265	1	2	2	NUM
ejde-350	265	2	·	·	SYM
ejde-350	265	3	2∗s	2∗s	NUM
ejde-350	265	4	·	·	PUNCT
ejde-350	265	5	c0	c0	NOUN
ejde-350	265	6	2∗s	2∗s	NUM
ejde-350	265	7	−	−	NUM
ejde-350	265	8	2	2	NUM
ejde-350	265	9	,	,	PUNCT
ejde-350	265	10	which	which	PRON
ejde-350	265	11	gives	give	VERB
ejde-350	265	12	‖v‖s	‖v‖s	PROPN
ejde-350	265	13	>	>	X
ejde-350	265	14	d1	d1	PROPN
ejde-350	265	15	.	.	PUNCT
ejde-350	266	1	(	(	PUNCT
ejde-350	266	2	4.1	4.1	NUM
ejde-350	266	3	)	)	PUNCT
ejde-350	266	4	by	by	ADP
ejde-350	266	5	the	the	DET
ejde-350	266	6	definition	definition	NOUN
ejde-350	266	7	of	of	ADP
ejde-350	266	8	sd	sd	NOUN
ejde-350	266	9	and	and	CCONJ
ejde-350	266	10	u	u	NOUN
ejde-350	266	11	⊂	⊂	PROPN
ejde-350	266	12	sd	sd	PROPN
ejde-350	266	13	,	,	PUNCT
ejde-350	266	14	there	there	PRON
ejde-350	266	15	exists	exist	VERB
ejde-350	266	16	some	some	PRON
ejde-350	266	17	v	v	ADP
ejde-350	266	18	⊂	⊂	PROPN
ejde-350	266	19	sd	sd	ADP
ejde-350	266	20	such	such	ADJ
ejde-350	266	21	that	that	SCONJ
ejde-350	266	22	‖u−	‖u−	PROPN
ejde-350	266	23	v‖s	v‖s	NOUN
ejde-350	266	24	6	6	NUM
ejde-350	266	25	d	d	NOUN
ejde-350	266	26	<	<	X
ejde-350	266	27	d1	d1	PROPN
ejde-350	266	28	.	.	PUNCT
ejde-350	267	1	(	(	PUNCT
ejde-350	267	2	4.2	4.2	NUM
ejde-350	267	3	)	)	PUNCT
ejde-350	267	4	applying	apply	VERB
ejde-350	267	5	the	the	DET
ejde-350	267	6	triangle	triangle	NOUN
ejde-350	267	7	inequality	inequality	NOUN
ejde-350	267	8	,	,	PUNCT
ejde-350	267	9	we	we	PRON
ejde-350	267	10	have	have	VERB
ejde-350	267	11	‖v‖s	‖v‖s	NOUN
ejde-350	267	12	=	=	SYM
ejde-350	268	1	‖v	‖v	PROPN
ejde-350	268	2	−	−	PROPN
ejde-350	268	3	u+	u+	NOUN
ejde-350	268	4	u‖s	u‖s	PROPN
ejde-350	268	5	6	6	NUM
ejde-350	268	6	‖v	‖v	NOUN
ejde-350	268	7	−	−	NOUN
ejde-350	268	8	u‖s	u‖s	ADJ
ejde-350	268	9	+	+	NUM
ejde-350	268	10	‖u‖s	‖u‖s	NOUN
ejde-350	268	11	.	.	PUNCT
ejde-350	269	1	which	which	PRON
ejde-350	269	2	gives	give	VERB
ejde-350	269	3	‖v‖s	‖v‖s	NOUN
ejde-350	269	4	−	−	PROPN
ejde-350	269	5	‖v	‖v	PROPN
ejde-350	270	1	−	−	PROPN
ejde-350	270	2	u‖s	u‖s	ADJ
ejde-350	270	3	6	6	NUM
ejde-350	270	4	‖u‖s	‖u‖s	NOUN
ejde-350	270	5	.	.	PUNCT
ejde-350	271	1	(	(	PUNCT
ejde-350	271	2	4.3	4.3	NUM
ejde-350	271	3	)	)	PUNCT
ejde-350	271	4	putting	put	VERB
ejde-350	271	5	(	(	PUNCT
ejde-350	271	6	4.1	4.1	NUM
ejde-350	271	7	)	)	PUNCT
ejde-350	271	8	and	and	CCONJ
ejde-350	271	9	(	(	PUNCT
ejde-350	271	10	4.2	4.2	NUM
ejde-350	271	11	)	)	PUNCT
ejde-350	271	12	into	into	ADP
ejde-350	271	13	(	(	PUNCT
ejde-350	271	14	4.3	4.3	NUM
ejde-350	271	15	)	)	PUNCT
ejde-350	271	16	,	,	PUNCT
ejde-350	271	17	we	we	PRON
ejde-350	271	18	obtain	obtain	VERB
ejde-350	271	19	‖u‖s	‖u‖s	NOUN
ejde-350	271	20	>	>	X
ejde-350	271	21	d1	d1	PROPN
ejde-350	271	22	−	−	PROPN
ejde-350	271	23	‖v	‖v	NOUN
ejde-350	271	24	−	−	PROPN
ejde-350	271	25	u‖s	u‖s	NOUN
ejde-350	271	26	>	>	X
ejde-350	271	27	0	0	X
ejde-350	271	28	.	.	PUNCT
ejde-350	272	1	the	the	DET
ejde-350	272	2	proof	proof	NOUN
ejde-350	272	3	is	be	AUX
ejde-350	272	4	complete	complete	ADJ
ejde-350	272	5	.	.	PUNCT
ejde-350	273	1	�	�	PROPN
ejde-350	273	2	lemma	lemma	PROPN
ejde-350	273	3	4.4	4.4	NUM
ejde-350	273	4	.	.	PUNCT
ejde-350	274	1	let	let	VERB
ejde-350	274	2	d	d	PRON
ejde-350	274	3	>	>	X
ejde-350	274	4	0	0	PUNCT
ejde-350	274	5	be	be	AUX
ejde-350	274	6	a	a	DET
ejde-350	274	7	fixed	fix	VERB
ejde-350	274	8	number	number	NOUN
ejde-350	274	9	and	and	CCONJ
ejde-350	274	10	let	let	VERB
ejde-350	274	11	{	{	PUNCT
ejde-350	274	12	uj	uj	PROPN
ejde-350	274	13	}	}	PUNCT
ejde-350	274	14	⊂	⊂	PROPN
ejde-350	274	15	sd	sd	PROPN
ejde-350	274	16	.	.	PUNCT
ejde-350	275	1	then	then	ADV
ejde-350	275	2	there	there	PRON
ejde-350	275	3	exists	exist	VERB
ejde-350	275	4	{	{	PUNCT
ejde-350	275	5	σj	σj	NOUN
ejde-350	275	6	}	}	PUNCT
ejde-350	275	7	,	,	PUNCT
ejde-350	275	8	such	such	ADJ
ejde-350	275	9	that	that	SCONJ
ejde-350	275	10	‖ūj‖s	‖ūj‖s	ADV
ejde-350	275	11	=	=	X
ejde-350	276	1	‖uj‖s	‖uj‖	NOUN
ejde-350	276	2	,	,	PUNCT
ejde-350	276	3	where	where	SCONJ
ejde-350	276	4	ūj(x	ūj(x	ADJ
ejde-350	276	5	)	)	PUNCT
ejde-350	276	6	=	=	SYM
ejde-350	277	1	σ	σ	NOUN
ejde-350	277	2	3−2s	3−2s	NUM
ejde-350	277	3	2	2	NUM
ejde-350	277	4	j	j	NOUN
ejde-350	277	5	uj(σjx	uj(σjx	PROPN
ejde-350	277	6	)	)	PUNCT
ejde-350	277	7	.	.	PUNCT
ejde-350	278	1	and	and	CCONJ
ejde-350	278	2	,	,	PUNCT
ejde-350	278	3	up	up	ADP
ejde-350	278	4	to	to	ADP
ejde-350	278	5	a	a	DET
ejde-350	278	6	subsequence	subsequence	NOUN
ejde-350	278	7	,	,	PUNCT
ejde-350	278	8	ūj	ūj	PROPN
ejde-350	278	9	⇀	⇀	PROPN
ejde-350	278	10	ū	ū	NOUN
ejde-350	278	11	∈	∈	PROPN
ejde-350	278	12	s2d	s2d	PROPN
ejde-350	278	13	.	.	PUNCT
ejde-350	278	14	ejde-2020/01	ejde-2020/01	PROPN
ejde-350	278	15	fractional	fractional	ADJ
ejde-350	278	16	schrödinger	schrödinger	NOUN
ejde-350	278	17	-	-	PUNCT
ejde-350	278	18	poisson	poisson	NOUN
ejde-350	278	19	system	system	NOUN
ejde-350	278	20	13	13	NUM
ejde-350	278	21	proof	proof	NOUN
ejde-350	278	22	.	.	PUNCT
ejde-350	279	1	let	let	VERB
ejde-350	279	2	{	{	PUNCT
ejde-350	279	3	uj	uj	PROPN
ejde-350	279	4	}	}	PUNCT
ejde-350	279	5	⊂	⊂	PROPN
ejde-350	279	6	sd	sd	PROPN
ejde-350	279	7	.	.	PUNCT
ejde-350	280	1	by	by	ADP
ejde-350	280	2	the	the	DET
ejde-350	280	3	definition	definition	NOUN
ejde-350	280	4	of	of	ADP
ejde-350	280	5	sd	sd	NOUN
ejde-350	280	6	and	and	CCONJ
ejde-350	280	7	lemma	lemma	PROPN
ejde-350	280	8	4.1(5	4.1(5	PROPN
ejde-350	280	9	)	)	PUNCT
ejde-350	280	10	,	,	PUNCT
ejde-350	280	11	there	there	PRON
ejde-350	280	12	exists	exist	VERB
ejde-350	280	13	wj	wj	PROPN
ejde-350	280	14	∈	∈	PROPN
ejde-350	280	15	s	s	VERB
ejde-350	280	16	such	such	ADJ
ejde-350	280	17	that	that	SCONJ
ejde-350	280	18	‖uj	‖uj	NUM
ejde-350	280	19	−	−	PROPN
ejde-350	280	20	wj‖s	wj‖s	PROPN
ejde-350	280	21	6	6	NUM
ejde-350	280	22	d.	d.	NOUN
ejde-350	280	23	by	by	ADP
ejde-350	280	24	property	property	NOUN
ejde-350	280	25	(	(	PUNCT
ejde-350	280	26	5	5	NUM
ejde-350	280	27	)	)	PUNCT
ejde-350	280	28	again	again	ADV
ejde-350	280	29	,	,	PUNCT
ejde-350	280	30	there	there	PRON
ejde-350	280	31	exists	exist	VERB
ejde-350	280	32	{	{	PUNCT
ejde-350	280	33	σj	σj	NOUN
ejde-350	280	34	}	}	PUNCT
ejde-350	280	35	,	,	PUNCT
ejde-350	280	36	such	such	ADJ
ejde-350	280	37	that	that	SCONJ
ejde-350	280	38	w̄j	w̄j	PROPN
ejde-350	280	39	∈	∈	PROPN
ejde-350	280	40	s	s	PART
ejde-350	280	41	,	,	PUNCT
ejde-350	280	42	one	one	PRON
ejde-350	280	43	can	can	AUX
ejde-350	280	44	prove	prove	VERB
ejde-350	280	45	that	that	SCONJ
ejde-350	280	46	w̄j	w̄j	PROPN
ejde-350	280	47	→	→	SYM
ejde-350	280	48	w̄	w̄	NOUN
ejde-350	280	49	∈	∈	PROPN
ejde-350	280	50	s	s	PROPN
ejde-350	280	51	,	,	PUNCT
ejde-350	280	52	where	where	SCONJ
ejde-350	280	53	w̄j(x	w̄j(x	ADP
ejde-350	280	54	)	)	PUNCT
ejde-350	280	55	=	=	SYM
ejde-350	281	1	σ	σ	NOUN
ejde-350	281	2	3−2s	3−2s	NUM
ejde-350	281	3	2	2	NUM
ejde-350	281	4	j	j	PROPN
ejde-350	281	5	wj(σjx	wj(σjx	PROPN
ejde-350	281	6	)	)	PUNCT
ejde-350	281	7	and	and	CCONJ
ejde-350	281	8	ūj(x	ūj(x	PROPN
ejde-350	281	9	)	)	PUNCT
ejde-350	281	10	=	=	SYM
ejde-350	282	1	σ	σ	NOUN
ejde-350	282	2	3−2s	3−2s	NUM
ejde-350	282	3	2	2	NUM
ejde-350	282	4	j	j	NOUN
ejde-350	282	5	uj(σjx	uj(σjx	PROPN
ejde-350	282	6	)	)	PUNCT
ejde-350	282	7	.	.	PUNCT
ejde-350	283	1	also	also	ADV
ejde-350	283	2	‖ūj‖s	‖ūj‖s	X
ejde-350	284	1	=	=	X
ejde-350	284	2	‖uj‖s	‖uj‖s	ADJ
ejde-350	284	3	,	,	PUNCT
ejde-350	284	4	‖ūj	‖ūj	PROPN
ejde-350	284	5	−	−	NOUN
ejde-350	284	6	w̄j‖s	w̄j‖s	X
ejde-350	284	7	=	=	SYM
ejde-350	284	8	‖uj	‖uj	NUM
ejde-350	284	9	−	−	PROPN
ejde-350	284	10	wj‖s	wj‖s	PROPN
ejde-350	284	11	6	6	NUM
ejde-350	284	12	d.	d.	PROPN
ejde-350	284	13	hence	hence	ADV
ejde-350	284	14	,	,	PUNCT
ejde-350	284	15	for	for	ADP
ejde-350	284	16	j	j	PROPN
ejde-350	284	17	large	large	ADJ
ejde-350	284	18	enough	enough	ADV
ejde-350	284	19	,	,	PUNCT
ejde-350	284	20	we	we	PRON
ejde-350	284	21	obtain	obtain	VERB
ejde-350	284	22	‖ūj	‖ūj	NOUN
ejde-350	284	23	−	−	NOUN
ejde-350	284	24	w̄‖s	w̄‖s	PUNCT
ejde-350	284	25	=	=	PUNCT
ejde-350	284	26	‖ūj	‖ūj	NOUN
ejde-350	284	27	−	−	NOUN
ejde-350	285	1	w̄j	w̄j	PROPN
ejde-350	285	2	+	+	CCONJ
ejde-350	285	3	w̄j	w̄j	PROPN
ejde-350	285	4	−	−	PROPN
ejde-350	285	5	w̄‖s	w̄‖s	NUM
ejde-350	285	6	6	6	NUM
ejde-350	285	7	‖ūj	‖ūj	PROPN
ejde-350	285	8	−	−	NOUN
ejde-350	285	9	w̄j‖s	w̄j‖s	X
ejde-350	285	10	+	+	CCONJ
ejde-350	285	11	‖w̄j	‖w̄j	PROPN
ejde-350	285	12	−	−	PROPN
ejde-350	285	13	w̄‖s	w̄‖s	NUM
ejde-350	285	14	6	6	NUM
ejde-350	285	15	2d	2d	NOUN
ejde-350	285	16	.	.	PUNCT
ejde-350	286	1	thus	thus	ADV
ejde-350	286	2	,	,	PUNCT
ejde-350	286	3	{	{	PUNCT
ejde-350	286	4	ūj	ūj	NOUN
ejde-350	286	5	}	}	PUNCT
ejde-350	286	6	is	be	AUX
ejde-350	286	7	bounded	bound	VERB
ejde-350	286	8	and	and	CCONJ
ejde-350	286	9	,	,	PUNCT
ejde-350	286	10	up	up	ADP
ejde-350	286	11	to	to	ADP
ejde-350	286	12	a	a	DET
ejde-350	286	13	subsequence	subsequence	NOUN
ejde-350	286	14	,	,	PUNCT
ejde-350	286	15	ūj	ūj	PROPN
ejde-350	286	16	⇀	⇀	PROPN
ejde-350	286	17	ū	ū	NOUN
ejde-350	286	18	in	in	ADP
ejde-350	286	19	ds,2	ds,2	NOUN
ejde-350	286	20	rad(r3	rad(r3	NOUN
ejde-350	286	21	)	)	PUNCT
ejde-350	286	22	.	.	PUNCT
ejde-350	287	1	since	since	SCONJ
ejde-350	287	2	b2d(w̄	b2d(w̄	NOUN
ejde-350	287	3	)	)	PUNCT
ejde-350	287	4	is	be	AUX
ejde-350	287	5	weakly	weakly	ADV
ejde-350	287	6	closed	closed	ADJ
ejde-350	287	7	in	in	ADP
ejde-350	287	8	ds,2	ds,2	NOUN
ejde-350	287	9	rad(r3	rad(r3	NOUN
ejde-350	287	10	)	)	PUNCT
ejde-350	287	11	,	,	PUNCT
ejde-350	287	12	we	we	PRON
ejde-350	287	13	obtain	obtain	VERB
ejde-350	287	14	ū	ū	NOUN
ejde-350	287	15	∈	∈	PROPN
ejde-350	287	16	b2d(w̄	b2d(w̄	NOUN
ejde-350	287	17	)	)	PUNCT
ejde-350	288	1	⊂	⊂	PROPN
ejde-350	288	2	s2d	s2d	PROPN
ejde-350	288	3	.	.	PUNCT
ejde-350	289	1	the	the	DET
ejde-350	289	2	proof	proof	NOUN
ejde-350	289	3	is	be	AUX
ejde-350	289	4	complete	complete	ADJ
ejde-350	289	5	.	.	PUNCT
ejde-350	290	1	�	�	PROPN
ejde-350	290	2	lemma	lemma	PROPN
ejde-350	290	3	4.5	4.5	NUM
ejde-350	290	4	.	.	PUNCT
ejde-350	291	1	set	set	VERB
ejde-350	291	2	d	d	PROPN
ejde-350	291	3	∈	∈	PROPN
ejde-350	291	4	(	(	PUNCT
ejde-350	291	5	0	0	NUM
ejde-350	291	6	,	,	PUNCT
ejde-350	291	7	d1	d1	PROPN
ejde-350	291	8	)	)	PUNCT
ejde-350	291	9	.	.	PUNCT
ejde-350	292	1	suppose	suppose	VERB
ejde-350	292	2	that	that	SCONJ
ejde-350	292	3	there	there	PRON
ejde-350	292	4	exist	exist	VERB
ejde-350	292	5	sequences	sequence	NOUN
ejde-350	292	6	λj	λj	PROPN
ejde-350	292	7	>	>	X
ejde-350	292	8	0	0	PROPN
ejde-350	292	9	,	,	PUNCT
ejde-350	292	10	λj	λj	PROPN
ejde-350	292	11	→	→	SYM
ejde-350	292	12	0	0	NUM
ejde-350	292	13	,	,	PUNCT
ejde-350	292	14	and	and	CCONJ
ejde-350	292	15	{	{	PUNCT
ejde-350	292	16	uj	uj	PROPN
ejde-350	292	17	}	}	PUNCT
ejde-350	292	18	⊂	⊂	PROPN
ejde-350	292	19	sd	sd	ADP
ejde-350	292	20	satisfying	satisfy	VERB
ejde-350	292	21	lim	lim	PROPN
ejde-350	292	22	j→∞	j→∞	PROPN
ejde-350	292	23	jλj	jλj	PROPN
ejde-350	292	24	(	(	PUNCT
ejde-350	292	25	uj	uj	PROPN
ejde-350	292	26	)	)	PUNCT
ejde-350	292	27	6	6	NUM
ejde-350	292	28	c0	c0	NOUN
ejde-350	292	29	and	and	CCONJ
ejde-350	292	30	lim	lim	PROPN
ejde-350	292	31	j→∞	j→∞	PROPN
ejde-350	292	32	j	j	PROPN
ejde-350	292	33	′λj	′λj	ADV
ejde-350	292	34	(	(	PUNCT
ejde-350	292	35	uj	uj	PROPN
ejde-350	292	36	)	)	PUNCT
ejde-350	292	37	=	=	SYM
ejde-350	293	1	0	0	X
ejde-350	293	2	.	.	PUNCT
ejde-350	294	1	then	then	ADV
ejde-350	294	2	there	there	PRON
ejde-350	294	3	is	be	VERB
ejde-350	294	4	sequence	sequence	NOUN
ejde-350	294	5	{	{	PUNCT
ejde-350	294	6	σj	σj	NOUN
ejde-350	294	7	}	}	PUNCT
ejde-350	294	8	such	such	ADJ
ejde-350	294	9	that	that	SCONJ
ejde-350	294	10	‖ūj‖s	‖ūj‖s	ADV
ejde-350	295	1	=	=	X
ejde-350	295	2	‖uj‖s	‖uj‖	NOUN
ejde-350	295	3	,	,	PUNCT
ejde-350	295	4	where	where	SCONJ
ejde-350	295	5	ūj(x	ūj(x	ADJ
ejde-350	295	6	)	)	PUNCT
ejde-350	295	7	=	=	SYM
ejde-350	295	8	σ	σ	NOUN
ejde-350	295	9	3−2s	3−2s	NUM
ejde-350	295	10	2	2	NUM
ejde-350	295	11	j	j	NOUN
ejde-350	295	12	uj(σjx	uj(σjx	PROPN
ejde-350	295	13	)	)	PUNCT
ejde-350	295	14	.	.	PUNCT
ejde-350	296	1	and	and	CCONJ
ejde-350	296	2	,	,	PUNCT
ejde-350	296	3	up	up	ADP
ejde-350	296	4	to	to	ADP
ejde-350	296	5	a	a	DET
ejde-350	296	6	subsequence	subsequence	NOUN
ejde-350	296	7	,	,	PUNCT
ejde-350	296	8	{	{	PUNCT
ejde-350	296	9	ūj	ūj	NOUN
ejde-350	296	10	}	}	PUNCT
ejde-350	296	11	converges	converge	NOUN
ejde-350	296	12	to	to	ADP
ejde-350	296	13	some	some	DET
ejde-350	296	14	ū	ū	NOUN
ejde-350	296	15	∈	∈	PROPN
ejde-350	296	16	s.	s.	PROPN
ejde-350	296	17	proof	proof	PROPN
ejde-350	296	18	.	.	PUNCT
ejde-350	297	1	considering	consider	VERB
ejde-350	297	2	that	that	SCONJ
ejde-350	297	3	limj→∞	limj→∞	PROPN
ejde-350	297	4	j	j	PROPN
ejde-350	297	5	′λj	′λj	ADV
ejde-350	297	6	(	(	PUNCT
ejde-350	297	7	uj	uj	PROPN
ejde-350	297	8	)	)	PUNCT
ejde-350	297	9	=	=	SYM
ejde-350	297	10	0	0	PUNCT
ejde-350	297	11	and	and	CCONJ
ejde-350	297	12	that	that	SCONJ
ejde-350	297	13	{	{	PUNCT
ejde-350	297	14	uj	uj	PROPN
ejde-350	297	15	}	}	PUNCT
ejde-350	297	16	is	be	AUX
ejde-350	297	17	bounded	bound	VERB
ejde-350	297	18	.	.	PUNCT
ejde-350	298	1	by	by	ADP
ejde-350	298	2	lemma	lemma	PROPN
ejde-350	298	3	4.4	4.4	NUM
ejde-350	298	4	,	,	PUNCT
ejde-350	298	5	up	up	ADP
ejde-350	298	6	to	to	ADP
ejde-350	298	7	a	a	DET
ejde-350	298	8	subsequence	subsequence	NOUN
ejde-350	298	9	,	,	PUNCT
ejde-350	298	10	ūj	ūj	PROPN
ejde-350	298	11	⇀	⇀	PROPN
ejde-350	298	12	ū	ū	NOUN
ejde-350	298	13	∈	∈	PROPN
ejde-350	298	14	s2d	s2d	PROPN
ejde-350	298	15	,	,	PUNCT
ejde-350	298	16	and	and	CCONJ
ejde-350	298	17	by	by	ADP
ejde-350	298	18	the	the	DET
ejde-350	298	19	choice	choice	NOUN
ejde-350	298	20	of	of	ADP
ejde-350	298	21	d1	d1	NOUN
ejde-350	298	22	,	,	PUNCT
ejde-350	298	23	ū	ū	NOUN
ejde-350	298	24	6=	6=	ADP
ejde-350	298	25	0	0	X
ejde-350	298	26	.	.	PUNCT
ejde-350	299	1	we	we	PRON
ejde-350	299	2	may	may	AUX
ejde-350	299	3	readily	readily	ADV
ejde-350	299	4	verify	verify	VERB
ejde-350	299	5	that	that	SCONJ
ejde-350	299	6	lim	lim	PROPN
ejde-350	299	7	j→∞	j→∞	PROPN
ejde-350	299	8	jλj	jλj	PROPN
ejde-350	299	9	(	(	PUNCT
ejde-350	299	10	ūj	ūj	NOUN
ejde-350	299	11	)	)	PUNCT
ejde-350	299	12	=	=	PROPN
ejde-350	300	1	lim	lim	PROPN
ejde-350	300	2	j→∞	j→∞	PROPN
ejde-350	300	3	jλj	jλj	PROPN
ejde-350	300	4	(	(	PUNCT
ejde-350	300	5	uj	uj	PROPN
ejde-350	300	6	)	)	PUNCT
ejde-350	300	7	6	6	NUM
ejde-350	300	8	c0	c0	NOUN
ejde-350	300	9	and	and	CCONJ
ejde-350	300	10	lim	lim	PROPN
ejde-350	301	1	j→∞	j→∞	PROPN
ejde-350	301	2	j	j	PROPN
ejde-350	301	3	′λj	′λj	ADV
ejde-350	301	4	(	(	PUNCT
ejde-350	301	5	ūj	ūj	NOUN
ejde-350	301	6	)	)	PUNCT
ejde-350	301	7	=	=	NOUN
ejde-350	301	8	0	0	X
ejde-350	301	9	.	.	PUNCT
ejde-350	302	1	for	for	ADP
ejde-350	302	2	all	all	DET
ejde-350	302	3	ϕ	ϕ	PROPN
ejde-350	302	4	∈	∈	PROPN
ejde-350	302	5	ds,2	ds,2	NOUN
ejde-350	302	6	rad(r3	rad(r3	NOUN
ejde-350	302	7	)	)	PUNCT
ejde-350	302	8	,	,	PUNCT
ejde-350	302	9	we	we	PRON
ejde-350	302	10	obtain	obtain	VERB
ejde-350	302	11	|〈j	|〈j	ADJ
ejde-350	302	12	′λj	′λj	NOUN
ejde-350	302	13	(	(	PUNCT
ejde-350	302	14	ūj	ūj	NOUN
ejde-350	302	15	)	)	PUNCT
ejde-350	302	16	,	,	PUNCT
ejde-350	302	17	ϕ〉|	ϕ〉|	PUNCT
ejde-350	303	1	=	=	NOUN
ejde-350	303	2	|〈j	|〈j	ADJ
ejde-350	303	3	′	′	NUM
ejde-350	303	4	λj	λj	PROPN
ejde-350	303	5	(	(	PUNCT
ejde-350	303	6	uj	uj	PROPN
ejde-350	303	7	)	)	PUNCT
ejde-350	303	8	,	,	PUNCT
ejde-350	303	9	ϕ̄〉|	ϕ̄〉|	NOUN
ejde-350	303	10	6	6	NUM
ejde-350	303	11	‖j	‖j	ADV
ejde-350	303	12	′	′	NUM
ejde-350	304	1	λj	λj	INTJ
ejde-350	304	2	(	(	PUNCT
ejde-350	304	3	uj)‖s−1‖ϕ̄‖s	uj)‖s−1‖ϕ̄‖s	NOUN
ejde-350	304	4	=	=	SYM
ejde-350	304	5	o(1)‖ϕ̄‖s	o(1)‖ϕ̄‖s	NOUN
ejde-350	304	6	,	,	PUNCT
ejde-350	304	7	where	where	SCONJ
ejde-350	304	8	ϕ̄	ϕ̄	PROPN
ejde-350	304	9	=	=	PROPN
ejde-350	304	10	σ	σ	PROPN
ejde-350	305	1	−	−	PROPN
ejde-350	305	2	3−2s	3−2s	NUM
ejde-350	305	3	2	2	NUM
ejde-350	305	4	j	j	PROPN
ejde-350	305	5	ϕ	ϕ	X
ejde-350	305	6	(	(	PUNCT
ejde-350	305	7	xσj	xσj	PROPN
ejde-350	305	8	)	)	PUNCT
ejde-350	305	9	.	.	PUNCT
ejde-350	306	1	since	since	SCONJ
ejde-350	306	2	‖ϕ̄‖s	‖ϕ̄‖s	NOUN
ejde-350	306	3	=	=	PUNCT
ejde-350	306	4	‖ϕ‖s	‖ϕ‖s	ADV
ejde-350	306	5	,	,	PUNCT
ejde-350	306	6	we	we	PRON
ejde-350	306	7	obtain	obtain	VERB
ejde-350	306	8	j	j	PROPN
ejde-350	306	9	′λj	′λj	NOUN
ejde-350	306	10	(	(	PUNCT
ejde-350	306	11	ūj)→	ūj)→	PROPN
ejde-350	306	12	0	0	PROPN
ejde-350	306	13	as	as	ADP
ejde-350	306	14	j	j	PROPN
ejde-350	306	15	→∞.	→∞.	PROPN
ejde-350	307	1	now	now	ADV
ejde-350	307	2	,	,	PUNCT
ejde-350	307	3	we	we	PRON
ejde-350	307	4	have	have	VERB
ejde-350	307	5	〈	〈	PROPN
ejde-350	307	6	j	j	PROPN
ejde-350	307	7	′0(ū	′0(ū	PROPN
ejde-350	307	8	)	)	PUNCT
ejde-350	307	9	,	,	PUNCT
ejde-350	307	10	ϕ	ϕ	NOUN
ejde-350	308	1	〉	〉	PROPN
ejde-350	308	2	=	=	SYM
ejde-350	308	3	lim	lim	PROPN
ejde-350	308	4	j→∞	j→∞	NOUN
ejde-350	309	1	〈	〈	PROPN
ejde-350	309	2	j	j	PROPN
ejde-350	309	3	′λj	′λj	X
ejde-350	309	4	(	(	PUNCT
ejde-350	309	5	ūj	ūj	NOUN
ejde-350	309	6	)	)	PUNCT
ejde-350	309	7	,	,	PUNCT
ejde-350	309	8	ϕ	ϕ	NOUN
ejde-350	309	9	〉	〉	NOUN
ejde-350	309	10	−	−	NOUN
ejde-350	309	11	λj	λj	PROPN
ejde-350	309	12	∫	∫	PROPN
ejde-350	309	13	r3	r3	PROPN
ejde-350	309	14	∫	∫	PROPN
ejde-350	309	15	r3	r3	PROPN
ejde-350	309	16	|ūj(y)|2ūj(x)ϕ(x	|ūj(y)|2ūj(x)ϕ(x	PROPN
ejde-350	309	17	)	)	PUNCT
ejde-350	309	18	|x−	|x−	PART
ejde-350	309	19	y|3−2	y|3−2	PROPN
ejde-350	309	20	t	t	PROPN
ejde-350	309	21	dxdy	dxdy	NOUN
ejde-350	309	22	=	=	PUNCT
ejde-350	309	23	0	0	X
ejde-350	309	24	.	.	PUNCT
ejde-350	310	1	hence	hence	ADV
ejde-350	310	2	,	,	PUNCT
ejde-350	310	3	j	j	PROPN
ejde-350	310	4	′0(ū	′0(ū	PROPN
ejde-350	310	5	)	)	PUNCT
ejde-350	310	6	=	=	SYM
ejde-350	311	1	0	0	X
ejde-350	311	2	.	.	PUNCT
ejde-350	312	1	furthermore	furthermore	ADV
ejde-350	312	2	,	,	PUNCT
ejde-350	312	3	applying	apply	VERB
ejde-350	312	4	lemma	lemma	PROPN
ejde-350	312	5	2.2	2.2	NUM
ejde-350	312	6	and	and	CCONJ
ejde-350	312	7	ūj	ūj	PROPN
ejde-350	312	8	∈	∈	PROPN
ejde-350	312	9	s2d	s2d	PROPN
ejde-350	312	10	for	for	ADP
ejde-350	312	11	all	all	DET
ejde-350	312	12	j	j	NOUN
ejde-350	312	13	,	,	PUNCT
ejde-350	312	14	we	we	PRON
ejde-350	312	15	obtain	obtain	VERB
ejde-350	312	16	lim	lim	PROPN
ejde-350	312	17	j→∞	j→∞	NOUN
ejde-350	312	18	〈	〈	PROPN
ejde-350	312	19	j	j	PROPN
ejde-350	312	20	′0(ūj	′0(ūj	PROPN
ejde-350	312	21	)	)	PUNCT
ejde-350	312	22	,	,	PUNCT
ejde-350	312	23	ϕ	ϕ	NOUN
ejde-350	313	1	〉	〉	PROPN
ejde-350	313	2	=	=	SYM
ejde-350	313	3	lim	lim	PROPN
ejde-350	313	4	j→∞	j→∞	NOUN
ejde-350	314	1	〈	〈	PROPN
ejde-350	314	2	j	j	PROPN
ejde-350	314	3	′λj	′λj	X
ejde-350	314	4	(	(	PUNCT
ejde-350	314	5	ūj	ūj	NOUN
ejde-350	314	6	)	)	PUNCT
ejde-350	314	7	,	,	PUNCT
ejde-350	314	8	ϕ	ϕ	NOUN
ejde-350	314	9	〉	〉	NOUN
ejde-350	314	10	−	−	NOUN
ejde-350	314	11	λj	λj	PROPN
ejde-350	314	12	∫	∫	PROPN
ejde-350	314	13	r3	r3	PROPN
ejde-350	314	14	∫	∫	PROPN
ejde-350	314	15	r3	r3	PROPN
ejde-350	314	16	|ūj(y)|2ūj(x)ϕ(x	|ūj(y)|2ūj(x)ϕ(x	PROPN
ejde-350	314	17	)	)	PUNCT
ejde-350	314	18	|x−	|x−	PART
ejde-350	314	19	y|3−2	y|3−2	PROPN
ejde-350	314	20	t	t	PROPN
ejde-350	314	21	dxdy	dxdy	NOUN
ejde-350	314	22	=	=	PUNCT
ejde-350	314	23	o(1)‖ϕ‖s	o(1)‖ϕ‖s	ADV
ejde-350	314	24	.	.	PUNCT
ejde-350	315	1	on	on	ADP
ejde-350	315	2	the	the	DET
ejde-350	315	3	other	other	ADJ
ejde-350	315	4	hand	hand	NOUN
ejde-350	315	5	,	,	PUNCT
ejde-350	315	6	c0	c0	PROPN
ejde-350	315	7	>	>	X
ejde-350	315	8	lim	lim	PROPN
ejde-350	315	9	j→∞	j→∞	PROPN
ejde-350	315	10	jλj	jλj	PROPN
ejde-350	315	11	(	(	PUNCT
ejde-350	315	12	ūj	ūj	NOUN
ejde-350	315	13	)	)	PUNCT
ejde-350	315	14	=	=	PROPN
ejde-350	315	15	lim	lim	PROPN
ejde-350	315	16	j→∞	j→∞	NUM
ejde-350	315	17	j0(ūj	j0(ūj	PROPN
ejde-350	315	18	)	)	PUNCT
ejde-350	316	1	+	+	CCONJ
ejde-350	316	2	λj	λj	PROPN
ejde-350	316	3	4	4	NUM
ejde-350	316	4	∫	∫	NOUN
ejde-350	316	5	r3	r3	PROPN
ejde-350	316	6	∫	∫	PROPN
ejde-350	316	7	r3	r3	PROPN
ejde-350	316	8	|ūj(y)|2|ūj(x)|2	|ūj(y)|2|ūj(x)|2	PROPN
ejde-350	316	9	|x−	|x−	PROPN
ejde-350	316	10	y|3−2	y|3−2	PROPN
ejde-350	316	11	t	t	PROPN
ejde-350	316	12	dxdy	dxdy	PROPN
ejde-350	316	13	=	=	PROPN
ejde-350	316	14	lim	lim	PROPN
ejde-350	316	15	j→∞	j→∞	NUM
ejde-350	316	16	j0(ūj	j0(ūj	PROPN
ejde-350	316	17	)	)	PUNCT
ejde-350	316	18	.	.	PUNCT
ejde-350	317	1	(	(	PUNCT
ejde-350	317	2	4.4	4.4	NUM
ejde-350	317	3	)	)	PUNCT
ejde-350	317	4	14	14	NUM
ejde-350	317	5	y.	y.	PROPN
ejde-350	317	6	su	su	PROPN
ejde-350	317	7	,	,	PUNCT
ejde-350	317	8	h.	h.	PROPN
ejde-350	317	9	chen	chen	PROPN
ejde-350	317	10	,	,	PUNCT
ejde-350	317	11	s.	s.	PROPN
ejde-350	317	12	liu	liu	PROPN
ejde-350	317	13	,	,	PUNCT
ejde-350	317	14	x.	x.	NOUN
ejde-350	317	15	fang	fang	PROPN
ejde-350	317	16	ejde-2020/01	ejde-2020/01	PROPN
ejde-350	317	17	so	so	CCONJ
ejde-350	317	18	{	{	PUNCT
ejde-350	317	19	ūj	ūj	NOUN
ejde-350	317	20	}	}	PUNCT
ejde-350	317	21	is	be	AUX
ejde-350	317	22	a	a	DET
ejde-350	317	23	(	(	PUNCT
ejde-350	317	24	ps)m	ps)m	PROPN
ejde-350	317	25	sequence	sequence	NOUN
ejde-350	317	26	for	for	ADP
ejde-350	317	27	j0	j0	PROPN
ejde-350	317	28	with	with	ADP
ejde-350	317	29	m	m	PRON
ejde-350	317	30	:	:	PUNCT
ejde-350	317	31	=	=	PROPN
ejde-350	317	32	limj→∞	limj→∞	PROPN
ejde-350	317	33	j0(ūj	j0(ūj	NOUN
ejde-350	317	34	)	)	PUNCT
ejde-350	317	35	.	.	PUNCT
ejde-350	318	1	thus	thus	ADV
ejde-350	318	2	,	,	PUNCT
ejde-350	318	3	up	up	ADP
ejde-350	318	4	to	to	ADP
ejde-350	318	5	a	a	DET
ejde-350	318	6	subsequence	subsequence	NOUN
ejde-350	318	7	,	,	PUNCT
ejde-350	318	8	ūj	ūj	NOUN
ejde-350	318	9	⇀	⇀	X
ejde-350	318	10	ū	ū	NOUN
ejde-350	318	11	and	and	CCONJ
ejde-350	318	12	j0(ū	j0(ū	PRON
ejde-350	318	13	)	)	PUNCT
ejde-350	318	14	=	=	SYM
ejde-350	319	1	1	1	NUM
ejde-350	319	2	2	2	NUM
ejde-350	319	3	‖ū‖2φ	‖ū‖2φ	PROPN
ejde-350	319	4	−	−	PROPN
ejde-350	319	5	1	1	NUM
ejde-350	319	6	2∗s	2∗s	NUM
ejde-350	319	7	∫	∫	NOUN
ejde-350	319	8	r3	r3	PROPN
ejde-350	319	9	|ū|2	|ū|2	PROPN
ejde-350	319	10	∗	∗	NOUN
ejde-350	319	11	sdx	sdx	NOUN
ejde-350	319	12	=	=	SYM
ejde-350	319	13	(	(	PUNCT
ejde-350	319	14	1	1	NUM
ejde-350	319	15	2	2	NUM
ejde-350	319	16	−	−	NUM
ejde-350	319	17	1	1	NUM
ejde-350	319	18	2∗s	2∗s	NUM
ejde-350	319	19	)	)	PUNCT
ejde-350	319	20	‖ū‖2φ	‖ū‖2φ	PROPN
ejde-350	319	21	6	6	NUM
ejde-350	319	22	(	(	PUNCT
ejde-350	319	23	1	1	NUM
ejde-350	319	24	2	2	NUM
ejde-350	319	25	−	−	NUM
ejde-350	319	26	1	1	NUM
ejde-350	319	27	2∗s	2∗s	NUM
ejde-350	319	28	)	)	PUNCT
ejde-350	319	29	lim	lim	PROPN
ejde-350	319	30	inf	inf	PROPN
ejde-350	319	31	j→∞	j→∞	NUM
ejde-350	319	32	‖ūj‖2φ	‖ūj‖2φ	PROPN
ejde-350	319	33	=	=	SYM
ejde-350	319	34	lim	lim	PROPN
ejde-350	319	35	inf	inf	PROPN
ejde-350	320	1	j→∞	j→∞	NOUN
ejde-350	320	2	(	(	PUNCT
ejde-350	320	3	j0(ūj)−	j0(ūj)−	NOUN
ejde-350	320	4	1	1	NUM
ejde-350	320	5	2∗s	2∗s	NUM
ejde-350	320	6	〈	〈	PROPN
ejde-350	320	7	j	j	PROPN
ejde-350	320	8	′0(ūj	′0(ūj	NOUN
ejde-350	320	9	)	)	PUNCT
ejde-350	320	10	,	,	PUNCT
ejde-350	320	11	ūj	ūj	PROPN
ejde-350	320	12	〉	〉	NOUN
ejde-350	320	13	)	)	PUNCT
ejde-350	321	1	=	=	PUNCT
ejde-350	321	2	m.	m.	NOUN
ejde-350	321	3	then	then	ADV
ejde-350	321	4	,	,	PUNCT
ejde-350	321	5	property	property	NOUN
ejde-350	321	6	(	(	PUNCT
ejde-350	321	7	3	3	NUM
ejde-350	321	8	)	)	PUNCT
ejde-350	321	9	implies	imply	VERB
ejde-350	321	10	m	m	VERB
ejde-350	321	11	>	>	X
ejde-350	321	12	j0(ū	j0(ū	PROPN
ejde-350	321	13	)	)	PUNCT
ejde-350	321	14	>	>	X
ejde-350	322	1	c0	c0	PROPN
ejde-350	322	2	,	,	PUNCT
ejde-350	322	3	which	which	PRON
ejde-350	322	4	,	,	PUNCT
ejde-350	322	5	combined	combine	VERB
ejde-350	322	6	with	with	ADP
ejde-350	322	7	(	(	PUNCT
ejde-350	322	8	4.4	4.4	NUM
ejde-350	322	9	)	)	PUNCT
ejde-350	322	10	,	,	PUNCT
ejde-350	322	11	yields	yield	VERB
ejde-350	322	12	m	m	NOUN
ejde-350	322	13	=	=	PUNCT
ejde-350	322	14	j0(ū	j0(ū	PROPN
ejde-350	322	15	)	)	PUNCT
ejde-350	322	16	=	=	SYM
ejde-350	322	17	c0	c0	NOUN
ejde-350	322	18	,	,	PUNCT
ejde-350	322	19	which	which	PRON
ejde-350	322	20	implies	imply	VERB
ejde-350	322	21	ū	ū	NOUN
ejde-350	322	22	∈	∈	PROPN
ejde-350	322	23	s.	s.	PROPN
ejde-350	322	24	�	�	PROPN
ejde-350	322	25	now	now	ADV
ejde-350	322	26	,	,	PUNCT
ejde-350	322	27	we	we	PRON
ejde-350	322	28	set	set	VERB
ejde-350	322	29	mλ	mλ	NOUN
ejde-350	322	30	:	:	PUNCT
ejde-350	322	31	=	=	SYM
ejde-350	322	32	max	max	PROPN
ejde-350	322	33	t∈[0,1	t∈[0,1	PROPN
ejde-350	322	34	]	]	X
ejde-350	322	35	jλ(υ0(t	jλ(υ0(t	PROPN
ejde-350	322	36	)	)	PUNCT
ejde-350	322	37	)	)	PUNCT
ejde-350	322	38	.	.	PUNCT
ejde-350	323	1	then	then	ADV
ejde-350	323	2	cλ	cλ	VERB
ejde-350	323	3	6	6	NUM
ejde-350	323	4	mλ	mλ	NOUN
ejde-350	323	5	.	.	PUNCT
ejde-350	324	1	it	it	PRON
ejde-350	324	2	is	be	AUX
ejde-350	324	3	easy	easy	ADJ
ejde-350	324	4	to	to	PART
ejde-350	324	5	see	see	VERB
ejde-350	324	6	that	that	DET
ejde-350	324	7	limλ→0mλ	limλ→0mλ	ADJ
ejde-350	324	8	6	6	NUM
ejde-350	324	9	c0	c0	NOUN
ejde-350	324	10	,	,	PUNCT
ejde-350	324	11	this	this	DET
ejde-350	324	12	inequality	inequality	NOUN
ejde-350	324	13	together	together	ADV
ejde-350	324	14	with	with	ADP
ejde-350	324	15	lemma	lemma	PROPN
ejde-350	324	16	4.2	4.2	NUM
ejde-350	324	17	,	,	PUNCT
ejde-350	324	18	provides	provide	VERB
ejde-350	324	19	limλ→0	limλ→0	PROPN
ejde-350	324	20	cλ	cλ	ADP
ejde-350	324	21	=	=	PUNCT
ejde-350	324	22	limλ→0mλ	limλ→0mλ	PROPN
ejde-350	324	23	=	=	SYM
ejde-350	324	24	c0	c0	NOUN
ejde-350	324	25	.	.	PUNCT
ejde-350	325	1	we	we	PRON
ejde-350	325	2	also	also	ADV
ejde-350	325	3	define	define	VERB
ejde-350	325	4	jmλλ	jmλλ	NOUN
ejde-350	325	5	=	=	SYM
ejde-350	325	6	{	{	PUNCT
ejde-350	325	7	u	u	NOUN
ejde-350	325	8	∈	∈	PROPN
ejde-350	325	9	ds,2	ds,2	NOUN
ejde-350	325	10	rad(r3)|jλ(u	rad(r3)|jλ(u	NOUN
ejde-350	325	11	)	)	PUNCT
ejde-350	325	12	6	6	NUM
ejde-350	325	13	mλ	mλ	NOUN
ejde-350	325	14	}	}	PUNCT
ejde-350	325	15	.	.	PUNCT
ejde-350	326	1	lemma	lemma	PROPN
ejde-350	326	2	4.6	4.6	NUM
ejde-350	326	3	.	.	PUNCT
ejde-350	327	1	for	for	ADP
ejde-350	327	2	any	any	DET
ejde-350	327	3	d2	d2	NOUN
ejde-350	327	4	,	,	PUNCT
ejde-350	327	5	d3	d3	PROPN
ejde-350	327	6	>	>	X
ejde-350	327	7	0	0	PUNCT
ejde-350	328	1	satisfying	satisfy	VERB
ejde-350	328	2	d3	d3	PROPN
ejde-350	328	3	<	<	X
ejde-350	328	4	d2	d2	PROPN
ejde-350	328	5	<	<	X
ejde-350	328	6	d1	d1	PROPN
ejde-350	328	7	,	,	PUNCT
ejde-350	328	8	there	there	PRON
ejde-350	328	9	are	be	VERB
ejde-350	328	10	constants	constant	NOUN
ejde-350	328	11	ι	ι	INTJ
ejde-350	328	12	>	>	X
ejde-350	328	13	0	0	PUNCT
ejde-350	328	14	and	and	CCONJ
ejde-350	328	15	λ̃	λ̃	PROPN
ejde-350	328	16	>	>	X
ejde-350	328	17	0	0	PUNCT
ejde-350	329	1	depending	depend	VERB
ejde-350	329	2	on	on	ADP
ejde-350	329	3	d2	d2	PROPN
ejde-350	329	4	,	,	PUNCT
ejde-350	329	5	d3	d3	VERB
ejde-350	329	6	such	such	ADJ
ejde-350	329	7	that	that	PRON
ejde-350	329	8	for	for	ADP
ejde-350	329	9	λ	λ	PROPN
ejde-350	329	10	∈	∈	PROPN
ejde-350	329	11	(	(	PUNCT
ejde-350	329	12	0	0	NUM
ejde-350	329	13	,	,	PUNCT
ejde-350	329	14	λ̃	λ̃	PROPN
ejde-350	329	15	)	)	PUNCT
ejde-350	329	16	,	,	PUNCT
ejde-350	329	17	we	we	PRON
ejde-350	329	18	have	have	VERB
ejde-350	329	19	‖j	‖j	ADV
ejde-350	329	20	′λ(u)‖s−1	′λ(u)‖s−1	NUM
ejde-350	329	21	>	>	PUNCT
ejde-350	329	22	ι	ι	PROPN
ejde-350	329	23	,	,	PUNCT
ejde-350	329	24	for	for	ADP
ejde-350	329	25	all	all	PRON
ejde-350	330	1	u	u	PRON
ejde-350	330	2	∈	∈	PROPN
ejde-350	330	3	jmλλ	jmλλ	NOUN
ejde-350	330	4	∩	∩	NOUN
ejde-350	330	5	(	(	PUNCT
ejde-350	330	6	sd2\sd3	sd2\sd3	ADJ
ejde-350	330	7	)	)	PUNCT
ejde-350	330	8	.	.	PUNCT
ejde-350	331	1	proof	proof	NOUN
ejde-350	331	2	.	.	PUNCT
ejde-350	332	1	to	to	ADP
ejde-350	332	2	the	the	DET
ejde-350	332	3	contrary	contrary	NOUN
ejde-350	332	4	,	,	PUNCT
ejde-350	332	5	suppose	suppose	VERB
ejde-350	332	6	that	that	SCONJ
ejde-350	332	7	for	for	ADP
ejde-350	332	8	some	some	DET
ejde-350	332	9	d2	d2	NOUN
ejde-350	332	10	,	,	PUNCT
ejde-350	332	11	d3	d3	PROPN
ejde-350	332	12	>	>	X
ejde-350	332	13	0	0	PUNCT
ejde-350	332	14	satisfying	satisfy	VERB
ejde-350	332	15	d3	d3	PROPN
ejde-350	332	16	<	<	X
ejde-350	332	17	d2	d2	PROPN
ejde-350	332	18	<	<	X
ejde-350	332	19	d1	d1	PROPN
ejde-350	332	20	,	,	PUNCT
ejde-350	332	21	there	there	PRON
ejde-350	332	22	exist	exist	VERB
ejde-350	332	23	sequences	sequence	NOUN
ejde-350	332	24	{	{	PUNCT
ejde-350	332	25	λj	λj	PROPN
ejde-350	332	26	}	}	PUNCT
ejde-350	332	27	with	with	ADP
ejde-350	332	28	limj→∞	limj→∞	PROPN
ejde-350	332	29	λj	λj	PROPN
ejde-350	332	30	=	=	SYM
ejde-350	332	31	0	0	PROPN
ejde-350	332	32	and	and	CCONJ
ejde-350	332	33	{	{	PUNCT
ejde-350	332	34	uj	uj	PROPN
ejde-350	332	35	}	}	PUNCT
ejde-350	332	36	∈	∈	PROPN
ejde-350	332	37	j	j	PROPN
ejde-350	332	38	mλj	mλj	PROPN
ejde-350	332	39	λj	λj	PROPN
ejde-350	332	40	∩	∩	PROPN
ejde-350	332	41	(	(	PUNCT
ejde-350	332	42	sd2	sd2	PROPN
ejde-350	332	43	\sd3	\sd3	PROPN
ejde-350	332	44	)	)	PUNCT
ejde-350	332	45	,	,	PUNCT
ejde-350	332	46	such	such	ADJ
ejde-350	332	47	that	that	SCONJ
ejde-350	332	48	lim	lim	PROPN
ejde-350	332	49	j→∞	j→∞	PROPN
ejde-350	332	50	jλj	jλj	PROPN
ejde-350	332	51	(	(	PUNCT
ejde-350	332	52	uj	uj	PROPN
ejde-350	332	53	)	)	PUNCT
ejde-350	332	54	6	6	NUM
ejde-350	332	55	c0	c0	NOUN
ejde-350	332	56	and	and	CCONJ
ejde-350	332	57	lim	lim	PROPN
ejde-350	332	58	j→∞	j→∞	PROPN
ejde-350	332	59	j	j	PROPN
ejde-350	332	60	′λj	′λj	ADV
ejde-350	332	61	(	(	PUNCT
ejde-350	332	62	uj	uj	PROPN
ejde-350	332	63	)	)	PUNCT
ejde-350	332	64	=	=	NOUN
ejde-350	333	1	0	0	X
ejde-350	333	2	.	.	PUNCT
ejde-350	333	3	by	by	ADP
ejde-350	333	4	using	use	VERB
ejde-350	333	5	property	property	NOUN
ejde-350	333	6	(	(	PUNCT
ejde-350	333	7	5	5	NUM
ejde-350	333	8	)	)	PUNCT
ejde-350	333	9	,	,	PUNCT
ejde-350	333	10	there	there	PRON
ejde-350	333	11	exists	exist	VERB
ejde-350	333	12	a	a	DET
ejde-350	333	13	sequence	sequence	NOUN
ejde-350	333	14	{	{	PUNCT
ejde-350	333	15	σj	σj	NOUN
ejde-350	333	16	}	}	PUNCT
ejde-350	333	17	such	such	ADJ
ejde-350	333	18	that	that	SCONJ
ejde-350	333	19	{	{	PUNCT
ejde-350	333	20	ūj	ūj	NOUN
ejde-350	333	21	}	}	PUNCT
ejde-350	333	22	∈	∈	PROPN
ejde-350	333	23	j	j	PROPN
ejde-350	333	24	mλj	mλj	PROPN
ejde-350	333	25	λj	λj	PROPN
ejde-350	333	26	∩	∩	PROPN
ejde-350	333	27	(	(	PUNCT
ejde-350	333	28	sd2	sd2	PROPN
ejde-350	333	29	\	\	PROPN
ejde-350	333	30	sd3	sd3	PROPN
ejde-350	333	31	)	)	PUNCT
ejde-350	333	32	,	,	PUNCT
ejde-350	333	33	lim	lim	PROPN
ejde-350	333	34	j→∞	j→∞	PROPN
ejde-350	333	35	jλj	jλj	PROPN
ejde-350	333	36	(	(	PUNCT
ejde-350	333	37	ūj	ūj	NOUN
ejde-350	333	38	)	)	PUNCT
ejde-350	333	39	6	6	NUM
ejde-350	333	40	c0	c0	NOUN
ejde-350	333	41	,	,	PUNCT
ejde-350	333	42	lim	lim	PROPN
ejde-350	333	43	j→∞	j→∞	PROPN
ejde-350	333	44	j	j	PROPN
ejde-350	333	45	′λj	′λj	ADV
ejde-350	333	46	(	(	PUNCT
ejde-350	333	47	ūj	ūj	NOUN
ejde-350	333	48	)	)	PUNCT
ejde-350	333	49	=	=	SYM
ejde-350	333	50	0	0	NUM
ejde-350	333	51	,	,	PUNCT
ejde-350	333	52	where	where	SCONJ
ejde-350	333	53	ūj(x	ūj(x	ADJ
ejde-350	333	54	)	)	PUNCT
ejde-350	333	55	=	=	SYM
ejde-350	334	1	σ	σ	NOUN
ejde-350	334	2	3−2s	3−2s	NUM
ejde-350	334	3	2	2	NUM
ejde-350	334	4	j	j	NOUN
ejde-350	334	5	uj(σjx	uj(σjx	PROPN
ejde-350	334	6	)	)	PUNCT
ejde-350	334	7	.	.	PUNCT
ejde-350	335	1	hence	hence	ADV
ejde-350	335	2	,	,	PUNCT
ejde-350	335	3	we	we	PRON
ejde-350	335	4	can	can	AUX
ejde-350	335	5	apply	apply	VERB
ejde-350	335	6	lemma	lemma	PROPN
ejde-350	335	7	4.4	4.4	NUM
ejde-350	335	8	and	and	CCONJ
ejde-350	335	9	assert	assert	VERB
ejde-350	335	10	the	the	DET
ejde-350	335	11	existence	existence	NOUN
ejde-350	335	12	of	of	ADP
ejde-350	335	13	some	some	DET
ejde-350	335	14	ū	ū	NOUN
ejde-350	335	15	∈	∈	NOUN
ejde-350	335	16	s	s	VERB
ejde-350	335	17	such	such	ADJ
ejde-350	335	18	that	that	DET
ejde-350	335	19	ūj	ūj	PROPN
ejde-350	335	20	→	→	SYM
ejde-350	335	21	ū	ū	NOUN
ejde-350	335	22	in	in	ADP
ejde-350	335	23	ds,2	ds,2	NOUN
ejde-350	335	24	rad(r3	rad(r3	NOUN
ejde-350	335	25	)	)	PUNCT
ejde-350	335	26	.	.	PUNCT
ejde-350	336	1	as	as	ADP
ejde-350	336	2	a	a	DET
ejde-350	336	3	consequence	consequence	NOUN
ejde-350	336	4	,	,	PUNCT
ejde-350	336	5	dist(ūj	dist(ūj	NOUN
ejde-350	336	6	,	,	PUNCT
ejde-350	336	7	s)→	s)→	NOUN
ejde-350	336	8	0	0	PUNCT
ejde-350	336	9	as	as	ADP
ejde-350	336	10	j	j	PROPN
ejde-350	336	11	→∞	→∞	PROPN
ejde-350	336	12	,	,	PUNCT
ejde-350	336	13	contradicting	contradict	VERB
ejde-350	336	14	the	the	DET
ejde-350	336	15	relation	relation	NOUN
ejde-350	336	16	ūj	ūj	PROPN
ejde-350	336	17	6∈	6∈	PROPN
ejde-350	336	18	sd3	sd3	PROPN
ejde-350	336	19	.	.	PUNCT
ejde-350	337	1	�	�	PROPN
ejde-350	337	2	lemma	lemma	PROPN
ejde-350	337	3	4.7	4.7	NUM
ejde-350	337	4	.	.	PUNCT
ejde-350	338	1	for	for	ADP
ejde-350	338	2	d	d	PROPN
ejde-350	338	3	>	>	X
ejde-350	338	4	0	0	PROPN
ejde-350	338	5	,	,	PUNCT
ejde-350	338	6	there	there	PRON
ejde-350	338	7	exists	exist	VERB
ejde-350	338	8	δ	δ	PROPN
ejde-350	338	9	>	>	X
ejde-350	338	10	0	0	PROPN
ejde-350	338	11	,	,	PUNCT
ejde-350	338	12	such	such	ADJ
ejde-350	338	13	that	that	SCONJ
ejde-350	338	14	if	if	SCONJ
ejde-350	338	15	λ	λ	PROPN
ejde-350	338	16	>	>	X
ejde-350	338	17	0	0	PUNCT
ejde-350	339	1	with	with	ADP
ejde-350	339	2	λ	λ	X
ejde-350	339	3	small	small	ADJ
ejde-350	339	4	enough	enough	ADV
ejde-350	339	5	,	,	PUNCT
ejde-350	339	6	t	t	PROPN
ejde-350	339	7	∈	∈	PROPN
ejde-350	340	1	[	[	X
ejde-350	340	2	0	0	NUM
ejde-350	340	3	,	,	PUNCT
ejde-350	340	4	1	1	NUM
ejde-350	340	5	]	]	PUNCT
ejde-350	340	6	,	,	PUNCT
ejde-350	340	7	jλ(υ0(t	jλ(υ0(t	PROPN
ejde-350	340	8	)	)	PUNCT
ejde-350	340	9	)	)	PUNCT
ejde-350	341	1	>	>	X
ejde-350	342	1	cλ	cλ	INTJ
ejde-350	342	2	−	−	PROPN
ejde-350	342	3	δ	δ	PROPN
ejde-350	342	4	implies	imply	VERB
ejde-350	342	5	υ0(t	υ0(t	NOUN
ejde-350	342	6	)	)	PUNCT
ejde-350	342	7	∈	∈	PROPN
ejde-350	342	8	sd	sd	NOUN
ejde-350	342	9	.	.	PUNCT
ejde-350	343	1	since	since	SCONJ
ejde-350	343	2	the	the	DET
ejde-350	343	3	proof	proof	NOUN
ejde-350	343	4	of	of	ADP
ejde-350	343	5	the	the	DET
ejde-350	343	6	above	above	ADJ
ejde-350	343	7	lemma	lemma	PROPN
ejde-350	343	8	is	be	AUX
ejde-350	343	9	quite	quite	ADV
ejde-350	343	10	similar	similar	ADJ
ejde-350	343	11	to	to	ADP
ejde-350	343	12	that	that	PRON
ejde-350	343	13	of	of	ADP
ejde-350	343	14	[	[	X
ejde-350	343	15	25	25	NUM
ejde-350	343	16	,	,	PUNCT
ejde-350	343	17	propositions	proposition	NOUN
ejde-350	343	18	4	4	NUM
ejde-350	343	19	]	]	PUNCT
ejde-350	343	20	,	,	PUNCT
ejde-350	343	21	we	we	PRON
ejde-350	343	22	omit	omit	VERB
ejde-350	343	23	it	it	PRON
ejde-350	343	24	here	here	ADV
ejde-350	343	25	.	.	PUNCT
ejde-350	344	1	lemma	lemma	PROPN
ejde-350	344	2	4.8	4.8	NUM
ejde-350	344	3	.	.	PUNCT
ejde-350	345	1	to	to	ADP
ejde-350	345	2	each	each	DET
ejde-350	345	3	0	0	NUM
ejde-350	345	4	<	<	X
ejde-350	345	5	d	d	X
ejde-350	345	6	<	<	X
ejde-350	345	7	d1	d1	PROPN
ejde-350	345	8	corresponds	correspond	VERB
ejde-350	345	9	a	a	DET
ejde-350	345	10	number	number	NOUN
ejde-350	345	11	λ0	λ0	NOUN
ejde-350	345	12	>	>	X
ejde-350	345	13	0	0	NUM
ejde-350	346	1	such	such	ADJ
ejde-350	346	2	that	that	PRON
ejde-350	346	3	for	for	ADP
ejde-350	346	4	all	all	DET
ejde-350	346	5	λ	λ	X
ejde-350	346	6	∈	∈	PROPN
ejde-350	346	7	(	(	PUNCT
ejde-350	346	8	0	0	NUM
ejde-350	346	9	,	,	PUNCT
ejde-350	346	10	λ0	λ0	NOUN
ejde-350	346	11	)	)	PUNCT
ejde-350	346	12	,	,	PUNCT
ejde-350	346	13	there	there	PRON
ejde-350	346	14	exists	exist	VERB
ejde-350	346	15	a	a	DET
ejde-350	346	16	sequence	sequence	NOUN
ejde-350	346	17	{	{	PUNCT
ejde-350	346	18	uj	uj	PROPN
ejde-350	346	19	}	}	PUNCT
ejde-350	346	20	∈	∈	PROPN
ejde-350	346	21	jmλλ	jmλλ	NOUN
ejde-350	346	22	∩	∩	PROPN
ejde-350	346	23	sd	sd	ADP
ejde-350	346	24	such	such	ADJ
ejde-350	346	25	that	that	DET
ejde-350	346	26	j	j	PROPN
ejde-350	346	27	′λ(uj	′λ(uj	NOUN
ejde-350	346	28	)	)	PUNCT
ejde-350	346	29	→	→	SYM
ejde-350	346	30	0	0	PUNCT
ejde-350	346	31	as	as	ADP
ejde-350	346	32	j	j	PROPN
ejde-350	346	33	→∞.	→∞.	PROPN
ejde-350	346	34	since	since	SCONJ
ejde-350	346	35	the	the	DET
ejde-350	346	36	proof	proof	NOUN
ejde-350	346	37	of	of	ADP
ejde-350	346	38	the	the	DET
ejde-350	346	39	above	above	ADJ
ejde-350	346	40	lemma	lemma	PROPN
ejde-350	346	41	is	be	AUX
ejde-350	346	42	quite	quite	ADV
ejde-350	346	43	similar	similar	ADJ
ejde-350	346	44	to	to	ADP
ejde-350	346	45	that	that	PRON
ejde-350	346	46	of	of	ADP
ejde-350	346	47	[	[	X
ejde-350	346	48	12	12	NUM
ejde-350	346	49	,	,	PUNCT
ejde-350	346	50	propositions	proposition	VERB
ejde-350	346	51	5.3	5.3	NUM
ejde-350	346	52	]	]	PUNCT
ejde-350	346	53	,	,	PUNCT
ejde-350	346	54	we	we	PRON
ejde-350	346	55	omit	omit	VERB
ejde-350	346	56	it	it	PRON
ejde-350	346	57	here	here	ADV
ejde-350	346	58	.	.	PUNCT
ejde-350	347	1	ejde-2020/01	ejde-2020/01	NOUN
ejde-350	347	2	fractional	fractional	ADJ
ejde-350	347	3	schrödinger	schrödinger	NOUN
ejde-350	347	4	-	-	PUNCT
ejde-350	347	5	poisson	poisson	NOUN
ejde-350	347	6	system	system	NOUN
ejde-350	347	7	15	15	NUM
ejde-350	347	8	proof	proof	NOUN
ejde-350	347	9	of	of	ADP
ejde-350	347	10	theorem	theorem	ADJ
ejde-350	347	11	1.2	1.2	NUM
ejde-350	347	12	.	.	PUNCT
ejde-350	348	1	taking	take	VERB
ejde-350	348	2	d	d	X
ejde-350	348	3	∈	∈	PROPN
ejde-350	348	4	(	(	PUNCT
ejde-350	348	5	0	0	NUM
ejde-350	348	6	,	,	PUNCT
ejde-350	348	7	d1	d1	PROPN
ejde-350	348	8	)	)	PUNCT
ejde-350	348	9	,	,	PUNCT
ejde-350	348	10	by	by	ADP
ejde-350	348	11	lemma	lemma	PROPN
ejde-350	348	12	4.8	4.8	NUM
ejde-350	348	13	,	,	PUNCT
ejde-350	348	14	there	there	PRON
ejde-350	348	15	exists	exist	VERB
ejde-350	348	16	λ0	λ0	NOUN
ejde-350	348	17	>	>	X
ejde-350	348	18	0	0	NUM
ejde-350	349	1	such	such	ADJ
ejde-350	349	2	that	that	PRON
ejde-350	349	3	for	for	ADP
ejde-350	349	4	all	all	DET
ejde-350	349	5	λ	λ	X
ejde-350	349	6	∈	∈	PROPN
ejde-350	349	7	(	(	PUNCT
ejde-350	349	8	0	0	NUM
ejde-350	349	9	,	,	PUNCT
ejde-350	349	10	λ0	λ0	NOUN
ejde-350	349	11	)	)	PUNCT
ejde-350	349	12	,	,	PUNCT
ejde-350	349	13	there	there	PRON
ejde-350	349	14	exists	exist	VERB
ejde-350	349	15	a	a	DET
ejde-350	349	16	palais	palais	PROPN
ejde-350	349	17	smale	smale	NOUN
ejde-350	349	18	sequence	sequence	NOUN
ejde-350	349	19	{	{	PUNCT
ejde-350	349	20	uλj	uλj	NOUN
ejde-350	349	21	}	}	PUNCT
ejde-350	349	22	⊂	⊂	PROPN
ejde-350	349	23	s	s	PART
ejde-350	349	24	d	d	X
ejde-350	349	25	2	2	NUM
ejde-350	349	26	.	.	PUNCT
ejde-350	350	1	by	by	ADP
ejde-350	350	2	using	use	VERB
ejde-350	350	3	property	property	NOUN
ejde-350	350	4	(	(	PUNCT
ejde-350	350	5	5	5	NUM
ejde-350	350	6	)	)	PUNCT
ejde-350	350	7	,	,	PUNCT
ejde-350	350	8	there	there	PRON
ejde-350	350	9	exists	exist	VERB
ejde-350	350	10	sequence	sequence	NOUN
ejde-350	350	11	{	{	PUNCT
ejde-350	350	12	σj	σj	NOUN
ejde-350	350	13	}	}	PUNCT
ejde-350	350	14	such	such	ADJ
ejde-350	350	15	that	that	SCONJ
ejde-350	350	16	{	{	PUNCT
ejde-350	350	17	ūλj	ūλj	PROPN
ejde-350	350	18	}	}	PUNCT
ejde-350	350	19	⊂	⊂	PROPN
ejde-350	350	20	s	s	PART
ejde-350	351	1	d	d	X
ejde-350	351	2	2	2	NUM
ejde-350	351	3	where	where	SCONJ
ejde-350	351	4	ūλj	ūλj	PROPN
ejde-350	351	5	(	(	PUNCT
ejde-350	351	6	x	x	NOUN
ejde-350	351	7	)	)	PUNCT
ejde-350	351	8	=	=	SYM
ejde-350	351	9	σ	σ	NOUN
ejde-350	351	10	3−2s	3−2s	NUM
ejde-350	351	11	2	2	NUM
ejde-350	351	12	j	j	NOUN
ejde-350	351	13	uλj	uλj	NOUN
ejde-350	351	14	(	(	PUNCT
ejde-350	351	15	σjx	σjx	PROPN
ejde-350	351	16	)	)	PUNCT
ejde-350	351	17	.	.	PUNCT
ejde-350	352	1	it	it	PRON
ejde-350	352	2	is	be	AUX
ejde-350	352	3	easy	easy	ADJ
ejde-350	352	4	to	to	PART
ejde-350	352	5	see	see	VERB
ejde-350	352	6	that	that	SCONJ
ejde-350	352	7	{	{	PUNCT
ejde-350	352	8	ūλj	ūλj	PROPN
ejde-350	352	9	}	}	PUNCT
ejde-350	352	10	is	be	AUX
ejde-350	352	11	bounded	bound	VERB
ejde-350	352	12	in	in	ADP
ejde-350	352	13	ds,2	ds,2	NOUN
ejde-350	352	14	rad(r3	rad(r3	NOUN
ejde-350	352	15	)	)	PUNCT
ejde-350	352	16	.	.	PUNCT
ejde-350	353	1	then	then	ADV
ejde-350	353	2	by	by	ADP
ejde-350	353	3	lemma	lemma	PROPN
ejde-350	353	4	4.4	4.4	NUM
ejde-350	353	5	,	,	PUNCT
ejde-350	353	6	up	up	ADP
ejde-350	353	7	to	to	ADP
ejde-350	353	8	a	a	DET
ejde-350	353	9	subsequence	subsequence	NOUN
ejde-350	353	10	,	,	PUNCT
ejde-350	353	11	there	there	PRON
ejde-350	353	12	exists	exist	VERB
ejde-350	353	13	some	some	DET
ejde-350	353	14	ūλ	ūλ	PROPN
ejde-350	353	15	∈	∈	PROPN
ejde-350	353	16	s	s	PART
ejde-350	353	17	d2	d2	PROPN
ejde-350	353	18	·	·	SYM
ejde-350	353	19	2	2	NUM
ejde-350	353	20	=	=	SYM
ejde-350	353	21	sd	sd	ADP
ejde-350	353	22	such	such	ADJ
ejde-350	353	23	that	that	DET
ejde-350	353	24	ūλj	ūλj	PROPN
ejde-350	353	25	⇀	⇀	PUNCT
ejde-350	354	1	ūλ	ūλ	PROPN
ejde-350	354	2	.	.	PUNCT
ejde-350	355	1	then	then	ADV
ejde-350	355	2	we	we	PRON
ejde-350	355	3	obtain	obtain	VERB
ejde-350	355	4	j	j	NOUN
ejde-350	355	5	′λ(ūλ	′λ(ūλ	NUM
ejde-350	355	6	)	)	PUNCT
ejde-350	355	7	=	=	SYM
ejde-350	355	8	0	0	NUM
ejde-350	355	9	,	,	PUNCT
ejde-350	355	10	and	and	CCONJ
ejde-350	355	11	by	by	ADP
ejde-350	355	12	the	the	DET
ejde-350	355	13	choice	choice	NOUN
ejde-350	355	14	of	of	ADP
ejde-350	355	15	d	d	PROPN
ejde-350	355	16	,	,	PUNCT
ejde-350	355	17	ūλ	ūλ	PROPN
ejde-350	355	18	6≡	6≡	NUM
ejde-350	355	19	0	0	NUM
ejde-350	355	20	.	.	PUNCT
ejde-350	356	1	hence	hence	ADV
ejde-350	356	2	ūλ	ūλ	PROPN
ejde-350	356	3	is	be	AUX
ejde-350	356	4	a	a	DET
ejde-350	356	5	nontrivial	nontrivial	ADJ
ejde-350	356	6	critical	critical	ADJ
ejde-350	356	7	point	point	NOUN
ejde-350	356	8	of	of	ADP
ejde-350	356	9	jλ	jλ	PROPN
ejde-350	356	10	.	.	PUNCT
ejde-350	356	11	the	the	DET
ejde-350	356	12	principle	principle	NOUN
ejde-350	356	13	of	of	ADP
ejde-350	356	14	symmetric	symmetric	ADJ
ejde-350	356	15	criticality	criticality	NOUN
ejde-350	356	16	implies	imply	VERB
ejde-350	356	17	that	that	SCONJ
ejde-350	356	18	the	the	DET
ejde-350	356	19	critical	critical	ADJ
ejde-350	356	20	points	point	NOUN
ejde-350	356	21	of	of	ADP
ejde-350	356	22	jλ	jλ	NOUN
ejde-350	356	23	are	be	AUX
ejde-350	356	24	also	also	ADV
ejde-350	356	25	critical	critical	ADJ
ejde-350	356	26	points	point	NOUN
ejde-350	356	27	for	for	ADP
ejde-350	356	28	iλ	iλ	PROPN
ejde-350	356	29	.	.	PUNCT
ejde-350	356	30	�	�	PROPN
ejde-350	356	31	5	5	NUM
ejde-350	356	32	.	.	PUNCT
ejde-350	356	33	open	open	ADJ
ejde-350	356	34	problem	problem	NOUN
ejde-350	356	35	in	in	ADP
ejde-350	356	36	theorem	theorem	NOUN
ejde-350	356	37	1.1	1.1	NUM
ejde-350	356	38	,	,	PUNCT
ejde-350	356	39	we	we	PRON
ejde-350	356	40	obtain	obtain	VERB
ejde-350	356	41	a	a	DET
ejde-350	356	42	ground	ground	NOUN
ejde-350	356	43	state	state	NOUN
ejde-350	356	44	solution	solution	NOUN
ejde-350	356	45	v	v	ADP
ejde-350	356	46	∈	∈	PROPN
ejde-350	356	47	ds,2	ds,2	NOUN
ejde-350	356	48	rad(r3	rad(r3	NOUN
ejde-350	356	49	)	)	PUNCT
ejde-350	356	50	to	to	ADP
ejde-350	356	51	equation	equation	NOUN
ejde-350	356	52	(	(	PUNCT
ejde-350	356	53	1.8	1.8	NUM
ejde-350	356	54	)	)	PUNCT
ejde-350	356	55	.	.	PUNCT
ejde-350	357	1	since	since	SCONJ
ejde-350	357	2	ds,2	ds,2	NOUN
ejde-350	357	3	rad(r3	rad(r3	NOUN
ejde-350	357	4	)	)	PUNCT
ejde-350	357	5	⊂	⊂	X
ejde-350	358	1	ds,2(r3	ds,2(r3	PROPN
ejde-350	358	2	)	)	PUNCT
ejde-350	358	3	,	,	PUNCT
ejde-350	358	4	so	so	ADV
ejde-350	358	5	v	v	INTJ
ejde-350	358	6	just	just	ADV
ejde-350	358	7	is	be	AUX
ejde-350	358	8	a	a	DET
ejde-350	358	9	ground	ground	NOUN
ejde-350	358	10	state	state	NOUN
ejde-350	358	11	solution	solution	NOUN
ejde-350	358	12	in	in	ADP
ejde-350	358	13	ds,2	ds,2	NOUN
ejde-350	358	14	rad(r3	rad(r3	NOUN
ejde-350	358	15	)	)	PUNCT
ejde-350	358	16	,	,	PUNCT
ejde-350	358	17	not	not	PART
ejde-350	358	18	a	a	DET
ejde-350	358	19	ground	ground	NOUN
ejde-350	358	20	state	state	NOUN
ejde-350	358	21	solution	solution	NOUN
ejde-350	358	22	in	in	ADP
ejde-350	358	23	ds,2(r3	ds,2(r3	PROPN
ejde-350	358	24	)	)	PUNCT
ejde-350	358	25	.	.	PUNCT
ejde-350	359	1	it	it	PRON
ejde-350	359	2	is	be	AUX
ejde-350	359	3	natural	natural	ADJ
ejde-350	359	4	to	to	PART
ejde-350	359	5	ask	ask	VERB
ejde-350	359	6	:	:	PUNCT
ejde-350	359	7	does	do	AUX
ejde-350	359	8	there	there	PRON
ejde-350	359	9	exist	exist	VERB
ejde-350	359	10	a	a	DET
ejde-350	359	11	ground	ground	NOUN
ejde-350	359	12	state	state	NOUN
ejde-350	359	13	solution	solution	NOUN
ejde-350	359	14	to	to	ADP
ejde-350	359	15	equation	equation	NOUN
ejde-350	359	16	(	(	PUNCT
ejde-350	359	17	1.8	1.8	NUM
ejde-350	359	18	)	)	PUNCT
ejde-350	359	19	in	in	ADP
ejde-350	359	20	ds,2(r3	ds,2(r3	PROPN
ejde-350	359	21	)	)	PUNCT
ejde-350	359	22	?	?	PUNCT
ejde-350	360	1	acknowledgements	acknowledgement	NOUN
ejde-350	360	2	.	.	PUNCT
ejde-350	361	1	this	this	DET
ejde-350	361	2	research	research	NOUN
ejde-350	361	3	was	be	AUX
ejde-350	361	4	supported	support	VERB
ejde-350	361	5	by	by	ADP
ejde-350	361	6	the	the	DET
ejde-350	361	7	national	national	ADJ
ejde-350	361	8	natural	natural	PROPN
ejde-350	361	9	science	science	PROPN
ejde-350	361	10	foundation	foundation	NOUN
ejde-350	361	11	of	of	ADP
ejde-350	361	12	china	china	PROPN
ejde-350	361	13	11671403	11671403	NUM
ejde-350	361	14	,	,	PUNCT
ejde-350	361	15	and	and	CCONJ
ejde-350	361	16	by	by	ADP
ejde-350	361	17	the	the	DET
ejde-350	361	18	university	university	NOUN
ejde-350	361	19	-	-	PUNCT
ejde-350	361	20	level	level	NOUN
ejde-350	361	21	key	key	ADJ
ejde-350	361	22	projects	project	NOUN
ejde-350	361	23	of	of	ADP
ejde-350	361	24	anhui	anhui	PROPN
ejde-350	361	25	university	university	PROPN
ejde-350	361	26	of	of	ADP
ejde-350	361	27	science	science	NOUN
ejde-350	361	28	and	and	CCONJ
ejde-350	361	29	technology	technology	NOUN
ejde-350	361	30	qn2019101	qn2019101	PROPN
ejde-350	361	31	.	.	PUNCT
ejde-350	362	1	references	reference	NOUN
ejde-350	362	2	[	[	X
ejde-350	362	3	1	1	NUM
ejde-350	362	4	]	]	X
ejde-350	362	5	l.	l.	PROPN
ejde-350	362	6	abatangelo	abatangelo	PROPN
ejde-350	362	7	,	,	PUNCT
ejde-350	362	8	s.	s.	PROPN
ejde-350	362	9	terracini	terracini	PROPN
ejde-350	362	10	;	;	PUNCT
ejde-350	362	11	solutions	solution	NOUN
ejde-350	362	12	to	to	ADP
ejde-350	362	13	nonlinear	nonlinear	NOUN
ejde-350	362	14	schrödinger	schrödinger	NOUN
ejde-350	362	15	equations	equation	NOUN
ejde-350	362	16	with	with	ADP
ejde-350	362	17	singular	singular	ADJ
ejde-350	362	18	electromagnetic	electromagnetic	ADJ
ejde-350	362	19	potential	potential	ADJ
ejde-350	362	20	and	and	CCONJ
ejde-350	362	21	critical	critical	ADJ
ejde-350	362	22	exponent	exponent	NOUN
ejde-350	362	23	,	,	PUNCT
ejde-350	362	24	j.	j.	PROPN
ejde-350	362	25	fixed	fix	VERB
ejde-350	362	26	point	point	PROPN
ejde-350	362	27	theory	theory	NOUN
ejde-350	362	28	appl	appl	PROPN
ejde-350	362	29	.	.	PROPN
ejde-350	362	30	,	,	PUNCT
ejde-350	362	31	10	10	NUM
ejde-350	362	32	(	(	PUNCT
ejde-350	362	33	2011	2011	NUM
ejde-350	362	34	)	)	PUNCT
ejde-350	362	35	,	,	PUNCT
ejde-350	362	36	no	no	INTJ
ejde-350	362	37	.	.	NOUN
ejde-350	362	38	1	1	NUM
ejde-350	362	39	,	,	PUNCT
ejde-350	362	40	147–180	147–180	NUM
ejde-350	362	41	.	.	PUNCT
ejde-350	363	1	[	[	X
ejde-350	363	2	2	2	X
ejde-350	363	3	]	]	PUNCT
ejde-350	363	4	v.	v.	PROPN
ejde-350	363	5	ambrosio	ambrosio	PROPN
ejde-350	363	6	;	;	PUNCT
ejde-350	363	7	ground	ground	NOUN
ejde-350	363	8	states	state	NOUN
ejde-350	363	9	solutions	solution	NOUN
ejde-350	363	10	for	for	ADP
ejde-350	363	11	a	a	DET
ejde-350	363	12	non	non	ADJ
ejde-350	363	13	-	-	ADJ
ejde-350	363	14	linear	linear	ADJ
ejde-350	363	15	equation	equation	NOUN
ejde-350	363	16	involving	involve	VERB
ejde-350	363	17	a	a	DET
ejde-350	363	18	pseudo	pseudo	NOUN
ejde-350	363	19	-	-	ADJ
ejde-350	363	20	relativistic	relativistic	ADJ
ejde-350	363	21	schrödinger	schrödinger	NOUN
ejde-350	363	22	operator	operator	NOUN
ejde-350	363	23	,	,	PUNCT
ejde-350	363	24	j.	j.	PROPN
ejde-350	363	25	math	math	PROPN
ejde-350	363	26	.	.	PUNCT
ejde-350	364	1	phys	phy	NOUN
ejde-350	364	2	.	.	PUNCT
ejde-350	364	3	,	,	PUNCT
ejde-350	364	4	57	57	NUM
ejde-350	364	5	(	(	PUNCT
ejde-350	364	6	2016	2016	NUM
ejde-350	364	7	)	)	PUNCT
ejde-350	364	8	,	,	PUNCT
ejde-350	364	9	no	no	INTJ
ejde-350	364	10	.	.	NOUN
ejde-350	364	11	5	5	NUM
ejde-350	364	12	,	,	PUNCT
ejde-350	364	13	051502	051502	NUM
ejde-350	364	14	,	,	PUNCT
ejde-350	364	15	18	18	NUM
ejde-350	364	16	pp	pp	NOUN
ejde-350	364	17	.	.	PUNCT
ejde-350	365	1	[	[	X
ejde-350	365	2	3	3	X
ejde-350	365	3	]	]	PUNCT
ejde-350	365	4	v.	v.	X
ejde-350	365	5	ambrosio	ambrosio	PROPN
ejde-350	365	6	;	;	PUNCT
ejde-350	365	7	periodic	periodic	ADJ
ejde-350	365	8	solutions	solution	NOUN
ejde-350	365	9	for	for	ADP
ejde-350	365	10	the	the	DET
ejde-350	365	11	non	non	ADJ
ejde-350	365	12	-	-	ADJ
ejde-350	365	13	local	local	ADJ
ejde-350	365	14	operator	operator	NOUN
ejde-350	365	15	(	(	PUNCT
ejde-350	365	16	−∆	−∆	X
ejde-350	365	17	+	+	NUM
ejde-350	365	18	m2)s	m2)s	NOUN
ejde-350	365	19	−m2s	−m2s	PROPN
ejde-350	365	20	with	with	ADP
ejde-350	365	21	m	m	PROPN
ejde-350	365	22	≥	≥	NUM
ejde-350	365	23	0	0	NUM
ejde-350	365	24	,	,	PUNCT
ejde-350	365	25	topol	topol	NOUN
ejde-350	365	26	.	.	PUNCT
ejde-350	366	1	methods	method	NOUN
ejde-350	366	2	nonlinear	nonlinear	PROPN
ejde-350	366	3	anal	anal	PROPN
ejde-350	366	4	.	.	PUNCT
ejde-350	366	5	,	,	PUNCT
ejde-350	366	6	49	49	NUM
ejde-350	366	7	(	(	PUNCT
ejde-350	366	8	2017	2017	NUM
ejde-350	366	9	)	)	PUNCT
ejde-350	366	10	,	,	PUNCT
ejde-350	366	11	75–104	75–104	NOUN
ejde-350	366	12	.	.	PUNCT
ejde-350	367	1	[	[	X
ejde-350	367	2	4	4	X
ejde-350	367	3	]	]	PUNCT
ejde-350	367	4	v.	v.	CCONJ
ejde-350	367	5	ambrosio	ambrosio	PROPN
ejde-350	367	6	;	;	PUNCT
ejde-350	367	7	an	an	DET
ejde-350	367	8	existence	existence	NOUN
ejde-350	367	9	result	result	VERB
ejde-350	367	10	for	for	ADP
ejde-350	367	11	a	a	DET
ejde-350	367	12	fractional	fractional	ADJ
ejde-350	367	13	kirchhoff	kirchhoff	NOUN
ejde-350	367	14	–	–	PUNCT
ejde-350	367	15	schrödinger	schrödinger	X
ejde-350	367	16	–	–	PUNCT
ejde-350	367	17	poisson	poisson	NOUN
ejde-350	367	18	system	system	NOUN
ejde-350	367	19	,	,	PUNCT
ejde-350	367	20	z.	z.	PROPN
ejde-350	367	21	angew	angew	PROPN
ejde-350	367	22	.	.	PUNCT
ejde-350	368	1	math	math	NOUN
ejde-350	368	2	.	.	PUNCT
ejde-350	369	1	phys	phy	NOUN
ejde-350	369	2	.	.	PUNCT
ejde-350	369	3	,	,	PUNCT
ejde-350	369	4	69	69	NUM
ejde-350	369	5	(	(	PUNCT
ejde-350	369	6	2018	2018	NUM
ejde-350	369	7	)	)	PUNCT
ejde-350	369	8	,	,	PUNCT
ejde-350	369	9	no	no	INTJ
ejde-350	369	10	.	.	NOUN
ejde-350	369	11	2	2	NUM
ejde-350	369	12	,	,	PUNCT
ejde-350	369	13	art	art	NOUN
ejde-350	369	14	.	.	PUNCT
ejde-350	370	1	30	30	NUM
ejde-350	370	2	,	,	PUNCT
ejde-350	370	3	13	13	NUM
ejde-350	370	4	pp	pp	NOUN
ejde-350	370	5	.	.	PUNCT
ejde-350	371	1	[	[	X
ejde-350	371	2	5	5	X
ejde-350	371	3	]	]	PUNCT
ejde-350	371	4	v.	v.	PROPN
ejde-350	371	5	ambrosio	ambrosio	PROPN
ejde-350	371	6	;	;	PUNCT
ejde-350	371	7	multiplicity	multiplicity	NOUN
ejde-350	371	8	and	and	CCONJ
ejde-350	371	9	concentration	concentration	NOUN
ejde-350	371	10	results	result	NOUN
ejde-350	371	11	for	for	ADP
ejde-350	371	12	a	a	DET
ejde-350	371	13	class	class	NOUN
ejde-350	371	14	of	of	ADP
ejde-350	371	15	critical	critical	ADJ
ejde-350	371	16	fractional	fractional	ADJ
ejde-350	371	17	schrödinger	schrödinger	NOUN
ejde-350	371	18	-	-	PUNCT
ejde-350	371	19	poisson	poisson	NOUN
ejde-350	371	20	systems	system	NOUN
ejde-350	371	21	via	via	ADP
ejde-350	371	22	penalization	penalization	NOUN
ejde-350	371	23	method	method	NOUN
ejde-350	371	24	,	,	PUNCT
ejde-350	371	25	commun	commun	PROPN
ejde-350	371	26	.	.	PUNCT
ejde-350	372	1	contemp	contemp	PROPN
ejde-350	372	2	.	.	PUNCT
ejde-350	373	1	math	math	NOUN
ejde-350	373	2	.	.	PUNCT
ejde-350	373	3	,	,	PUNCT
ejde-350	373	4	doi	doi	PROPN
ejde-350	373	5	:	:	PUNCT
ejde-350	373	6	10.1142	10.1142	NUM
ejde-350	373	7	/	/	SYM
ejde-350	373	8	s0219199718500785	s0219199718500785	VERB
ejde-350	373	9	.	.	PUNCT
ejde-350	374	1	[	[	X
ejde-350	374	2	6	6	NUM
ejde-350	374	3	]	]	PUNCT
ejde-350	374	4	a.	a.	NOUN
ejde-350	374	5	azzollini	azzollini	PROPN
ejde-350	374	6	,	,	PUNCT
ejde-350	374	7	a.	a.	NOUN
ejde-350	374	8	pomponio	pomponio	NOUN
ejde-350	374	9	;	;	PUNCT
ejde-350	374	10	ground	ground	NOUN
ejde-350	374	11	state	state	NOUN
ejde-350	374	12	solutions	solution	NOUN
ejde-350	374	13	for	for	ADP
ejde-350	374	14	the	the	DET
ejde-350	374	15	nonlinear	nonlinear	ADJ
ejde-350	374	16	schrödinger	schrödinger	NOUN
ejde-350	374	17	–	–	PUNCT
ejde-350	374	18	maxwell	maxwell	PROPN
ejde-350	374	19	equations	equation	NOUN
ejde-350	374	20	,	,	PUNCT
ejde-350	374	21	j.	j.	PROPN
ejde-350	374	22	math	math	PROPN
ejde-350	374	23	.	.	PUNCT
ejde-350	375	1	anal	anal	PROPN
ejde-350	375	2	.	.	PUNCT
ejde-350	375	3	appl	appl	PROPN
ejde-350	375	4	.	.	PROPN
ejde-350	375	5	,	,	PUNCT
ejde-350	375	6	345	345	NUM
ejde-350	375	7	(	(	PUNCT
ejde-350	375	8	2008	2008	NUM
ejde-350	375	9	)	)	PUNCT
ejde-350	375	10	,	,	PUNCT
ejde-350	375	11	no	no	INTJ
ejde-350	375	12	.	.	NOUN
ejde-350	375	13	1	1	NUM
ejde-350	375	14	,	,	PUNCT
ejde-350	375	15	90–108	90–108	NUM
ejde-350	375	16	.	.	PUNCT
ejde-350	376	1	[	[	X
ejde-350	376	2	7	7	X
ejde-350	376	3	]	]	X
ejde-350	376	4	j.	j.	PROPN
ejde-350	376	5	bellazzini	bellazzini	PROPN
ejde-350	376	6	,	,	PUNCT
ejde-350	376	7	m.	m.	PROPN
ejde-350	376	8	ghimenti	ghimenti	PROPN
ejde-350	376	9	,	,	PUNCT
ejde-350	376	10	c.	c.	PROPN
ejde-350	376	11	mercuri	mercuri	PROPN
ejde-350	376	12	,	,	PUNCT
ejde-350	376	13	v.	v.	PROPN
ejde-350	376	14	moroz	moroz	PROPN
ejde-350	376	15	,	,	PUNCT
ejde-350	376	16	j.	j.	PROPN
ejde-350	376	17	van	van	PROPN
ejde-350	376	18	schaftingen	schaftingen	PROPN
ejde-350	376	19	;	;	PUNCT
ejde-350	376	20	sharp	sharp	ADJ
ejde-350	376	21	gagliardo	gagliardo	NOUN
ejde-350	376	22	–	–	PUNCT
ejde-350	376	23	nirenberg	nirenberg	PROPN
ejde-350	376	24	inequalities	inequality	NOUN
ejde-350	376	25	in	in	ADP
ejde-350	376	26	fractional	fractional	ADJ
ejde-350	376	27	coulomb	coulomb	NOUN
ejde-350	376	28	–	–	PUNCT
ejde-350	376	29	sobolev	sobolev	NOUN
ejde-350	376	30	spaces	space	NOUN
ejde-350	376	31	,	,	PUNCT
ejde-350	376	32	trans	trans	PROPN
ejde-350	376	33	.	.	PROPN
ejde-350	377	1	amer	amer	PROPN
ejde-350	377	2	.	.	PUNCT
ejde-350	377	3	math	math	PROPN
ejde-350	377	4	.	.	PUNCT
ejde-350	378	1	soc	soc	PROPN
ejde-350	378	2	.	.	PUNCT
ejde-350	378	3	,	,	PUNCT
ejde-350	378	4	(	(	PUNCT
ejde-350	378	5	2017	2017	NUM
ejde-350	378	6	)	)	PUNCT
ejde-350	378	7	,	,	PUNCT
ejde-350	378	8	doi.org/10.1090/tran/7426	doi.org/10.1090/tran/7426	PROPN
ejde-350	378	9	.	.	PUNCT
ejde-350	379	1	[	[	X
ejde-350	379	2	8	8	NUM
ejde-350	379	3	]	]	PUNCT
ejde-350	379	4	v.	v.	PROPN
ejde-350	379	5	benci	benci	PROPN
ejde-350	379	6	,	,	PUNCT
ejde-350	379	7	d.	d.	PROPN
ejde-350	379	8	fortunato	fortunato	PROPN
ejde-350	379	9	;	;	PUNCT
ejde-350	379	10	an	an	DET
ejde-350	379	11	eigenvalue	eigenvalue	NOUN
ejde-350	379	12	problem	problem	NOUN
ejde-350	379	13	for	for	ADP
ejde-350	379	14	the	the	DET
ejde-350	379	15	schrödinger	schrödinger	NOUN
ejde-350	379	16	–	–	PUNCT
ejde-350	379	17	maxwell	maxwell	PROPN
ejde-350	379	18	equations	equation	NOUN
ejde-350	379	19	,	,	PUNCT
ejde-350	379	20	topol	topol	NOUN
ejde-350	379	21	.	.	PUNCT
ejde-350	380	1	methods	method	NOUN
ejde-350	380	2	nonlinear	nonlinear	PROPN
ejde-350	380	3	anal	anal	PROPN
ejde-350	380	4	.	.	PUNCT
ejde-350	380	5	,	,	PUNCT
ejde-350	380	6	11	11	NUM
ejde-350	380	7	(	(	PUNCT
ejde-350	380	8	1998	1998	NUM
ejde-350	380	9	)	)	PUNCT
ejde-350	380	10	,	,	PUNCT
ejde-350	380	11	no	no	INTJ
ejde-350	380	12	.	.	NOUN
ejde-350	380	13	2	2	NUM
ejde-350	380	14	,	,	PUNCT
ejde-350	380	15	283–293	283–293	NUM
ejde-350	380	16	.	.	PUNCT
ejde-350	381	1	[	[	X
ejde-350	381	2	9	9	NUM
ejde-350	381	3	]	]	X
ejde-350	381	4	h.	h.	NOUN
ejde-350	381	5	berestycki	berestycki	PROPN
ejde-350	381	6	,	,	PUNCT
ejde-350	381	7	p.	p.	NOUN
ejde-350	381	8	l.	l.	PROPN
ejde-350	381	9	lions	lion	NOUN
ejde-350	381	10	;	;	PUNCT
ejde-350	381	11	nonlinear	nonlinear	ADJ
ejde-350	381	12	scalar	scalar	ADJ
ejde-350	381	13	field	field	NOUN
ejde-350	381	14	equations	equation	NOUN
ejde-350	381	15	.	.	PUNCT
ejde-350	382	1	i.	i.	PROPN
ejde-350	382	2	existence	existence	NOUN
ejde-350	382	3	of	of	ADP
ejde-350	382	4	a	a	DET
ejde-350	382	5	ground	ground	NOUN
ejde-350	382	6	state	state	NOUN
ejde-350	382	7	,	,	PUNCT
ejde-350	382	8	arch	arch	NOUN
ejde-350	382	9	.	.	PUNCT
ejde-350	383	1	rational	rational	ADJ
ejde-350	383	2	mech	mech	NOUN
ejde-350	383	3	.	.	PUNCT
ejde-350	384	1	anal	anal	PROPN
ejde-350	384	2	.	.	PROPN
ejde-350	384	3	,	,	PUNCT
ejde-350	384	4	82	82	NUM
ejde-350	384	5	(	(	PUNCT
ejde-350	384	6	1983	1983	NUM
ejde-350	384	7	)	)	PUNCT
ejde-350	384	8	,	,	PUNCT
ejde-350	385	1	no	no	INTJ
ejde-350	385	2	.	.	NOUN
ejde-350	385	3	4	4	NUM
ejde-350	385	4	,	,	PUNCT
ejde-350	385	5	313–345	313–345	NUM
ejde-350	385	6	.	.	PUNCT
ejde-350	386	1	[	[	X
ejde-350	386	2	10	10	NUM
ejde-350	386	3	]	]	X
ejde-350	386	4	h.	h.	PROPN
ejde-350	386	5	brézis	brézis	PROPN
ejde-350	386	6	,	,	PUNCT
ejde-350	386	7	e.	e.	PROPN
ejde-350	386	8	h.	h.	PROPN
ejde-350	386	9	lieb	lieb	PROPN
ejde-350	386	10	;	;	PUNCT
ejde-350	386	11	a	a	DET
ejde-350	386	12	relation	relation	NOUN
ejde-350	386	13	between	between	ADP
ejde-350	386	14	pointwise	pointwise	ADJ
ejde-350	386	15	convergence	convergence	NOUN
ejde-350	386	16	of	of	ADP
ejde-350	386	17	functions	function	NOUN
ejde-350	386	18	and	and	CCONJ
ejde-350	386	19	convergence	convergence	NOUN
ejde-350	386	20	of	of	ADP
ejde-350	386	21	functionals	functional	NOUN
ejde-350	386	22	,	,	PUNCT
ejde-350	386	23	proc	proc	NOUN
ejde-350	386	24	.	.	PUNCT
ejde-350	387	1	amer	amer	PROPN
ejde-350	387	2	.	.	PUNCT
ejde-350	387	3	math	math	PROPN
ejde-350	387	4	.	.	PUNCT
ejde-350	388	1	soc	soc	PROPN
ejde-350	388	2	.	.	PUNCT
ejde-350	388	3	,	,	PUNCT
ejde-350	388	4	88	88	NUM
ejde-350	388	5	(	(	PUNCT
ejde-350	388	6	1983	1983	NUM
ejde-350	388	7	)	)	PUNCT
ejde-350	388	8	,	,	PUNCT
ejde-350	388	9	no	no	INTJ
ejde-350	388	10	.	.	NOUN
ejde-350	388	11	3	3	NUM
ejde-350	388	12	,	,	PUNCT
ejde-350	388	13	486–490	486–490	NUM
ejde-350	388	14	.	.	PUNCT
ejde-350	389	1	[	[	X
ejde-350	389	2	11	11	NUM
ejde-350	389	3	]	]	X
ejde-350	389	4	g.	g.	PROPN
ejde-350	389	5	cerami	cerami	PROPN
ejde-350	389	6	,	,	PUNCT
ejde-350	389	7	g.	g.	PROPN
ejde-350	389	8	vaira	vaira	PROPN
ejde-350	389	9	;	;	PUNCT
ejde-350	389	10	positive	positive	ADJ
ejde-350	389	11	solutions	solution	NOUN
ejde-350	389	12	for	for	ADP
ejde-350	389	13	some	some	DET
ejde-350	389	14	non	non	ADJ
ejde-350	389	15	–	–	PROPN
ejde-350	389	16	autonomous	autonomous	ADJ
ejde-350	389	17	schrödinger	schrödinger	NOUN
ejde-350	389	18	-	-	PUNCT
ejde-350	389	19	poisson	poisson	NOUN
ejde-350	389	20	systems	system	NOUN
ejde-350	389	21	,	,	PUNCT
ejde-350	389	22	j.	j.	PROPN
ejde-350	389	23	differential	differential	PROPN
ejde-350	389	24	equations	equations	PROPN
ejde-350	389	25	,	,	PUNCT
ejde-350	389	26	248	248	NUM
ejde-350	389	27	(	(	PUNCT
ejde-350	389	28	2010	2010	NUM
ejde-350	389	29	)	)	PUNCT
ejde-350	389	30	,	,	PUNCT
ejde-350	389	31	no	no	INTJ
ejde-350	389	32	.	.	NOUN
ejde-350	389	33	3	3	NUM
ejde-350	389	34	,	,	PUNCT
ejde-350	389	35	521–543	521–543	NUM
ejde-350	389	36	.	.	PUNCT
ejde-350	390	1	[	[	X
ejde-350	390	2	12	12	NUM
ejde-350	390	3	]	]	X
ejde-350	390	4	g.	g.	PROPN
ejde-350	390	5	cerami	cerami	PROPN
ejde-350	390	6	,	,	PUNCT
ejde-350	390	7	x.	x.	PROPN
ejde-350	390	8	zhong	zhong	PROPN
ejde-350	390	9	,	,	PUNCT
ejde-350	390	10	w.	w.	PROPN
ejde-350	390	11	zou	zou	PROPN
ejde-350	390	12	;	;	PUNCT
ejde-350	390	13	on	on	ADP
ejde-350	390	14	some	some	DET
ejde-350	390	15	nonlinear	nonlinear	ADJ
ejde-350	390	16	elliptic	elliptic	ADJ
ejde-350	390	17	pdes	pde	NOUN
ejde-350	390	18	with	with	ADP
ejde-350	390	19	sobolev	sobolev	NOUN
ejde-350	390	20	–	–	PUNCT
ejde-350	390	21	hardy	hardy	ADJ
ejde-350	390	22	critical	critical	ADJ
ejde-350	390	23	exponents	exponent	NOUN
ejde-350	390	24	and	and	CCONJ
ejde-350	390	25	a	a	DET
ejde-350	390	26	li	li	PROPN
ejde-350	390	27	-	-	PROPN
ejde-350	390	28	lin	lin	PROPN
ejde-350	390	29	open	open	ADJ
ejde-350	390	30	problem	problem	NOUN
ejde-350	390	31	,	,	PUNCT
ejde-350	390	32	calc	calc	NOUN
ejde-350	390	33	.	.	PUNCT
ejde-350	391	1	var	var	PROPN
ejde-350	391	2	.	.	PUNCT
ejde-350	392	1	partial	partial	ADJ
ejde-350	392	2	differential	differential	NOUN
ejde-350	392	3	equations	equation	NOUN
ejde-350	392	4	,	,	PUNCT
ejde-350	392	5	54	54	NUM
ejde-350	392	6	(	(	PUNCT
ejde-350	392	7	2015	2015	NUM
ejde-350	392	8	)	)	PUNCT
ejde-350	392	9	,	,	PUNCT
ejde-350	392	10	no	no	INTJ
ejde-350	392	11	.	.	NOUN
ejde-350	392	12	2	2	NUM
ejde-350	392	13	,	,	PUNCT
ejde-350	392	14	1793–1829	1793–1829	NUM
ejde-350	392	15	.	.	PUNCT
ejde-350	393	1	[	[	X
ejde-350	393	2	13	13	NUM
ejde-350	393	3	]	]	X
ejde-350	393	4	g.	g.	PROPN
ejde-350	393	5	che	che	PROPN
ejde-350	393	6	,	,	PUNCT
ejde-350	393	7	h.	h.	PROPN
ejde-350	393	8	shi	shi	PROPN
ejde-350	393	9	,	,	PUNCT
ejde-350	393	10	z.	z.	PROPN
ejde-350	393	11	wang	wang	PROPN
ejde-350	393	12	;	;	PUNCT
ejde-350	393	13	existence	existence	NOUN
ejde-350	393	14	and	and	CCONJ
ejde-350	393	15	concentration	concentration	NOUN
ejde-350	393	16	of	of	ADP
ejde-350	393	17	positive	positive	ADJ
ejde-350	393	18	ground	ground	NOUN
ejde-350	393	19	states	state	NOUN
ejde-350	393	20	for	for	ADP
ejde-350	393	21	a	a	DET
ejde-350	393	22	1laplacian	1laplacian	NUM
ejde-350	393	23	problem	problem	NOUN
ejde-350	393	24	in	in	ADP
ejde-350	393	25	rn	rn	PROPN
ejde-350	393	26	,	,	PUNCT
ejde-350	393	27	appl	appl	PROPN
ejde-350	393	28	.	.	PROPN
ejde-350	393	29	math	math	PROPN
ejde-350	393	30	.	.	PUNCT
ejde-350	394	1	lett	lett	PROPN
ejde-350	394	2	.	.	PROPN
ejde-350	394	3	,	,	PUNCT
ejde-350	394	4	100	100	NUM
ejde-350	394	5	(	(	PUNCT
ejde-350	394	6	2020	2020	NUM
ejde-350	394	7	)	)	PUNCT
ejde-350	394	8	,	,	PUNCT
ejde-350	394	9	106045	106045	NUM
ejde-350	394	10	.	.	PUNCT
ejde-350	395	1	[	[	X
ejde-350	395	2	14	14	NUM
ejde-350	395	3	]	]	X
ejde-350	395	4	g.	g.	PROPN
ejde-350	395	5	che	che	PROPN
ejde-350	395	6	,	,	PUNCT
ejde-350	395	7	h.	h.	PROPN
ejde-350	395	8	chen	chen	PROPN
ejde-350	395	9	,	,	PUNCT
ejde-350	395	10	t.	t.	PROPN
ejde-350	395	11	wu	wu	PROPN
ejde-350	395	12	;	;	PUNCT
ejde-350	395	13	existence	existence	NOUN
ejde-350	395	14	and	and	CCONJ
ejde-350	395	15	multiplicity	multiplicity	NOUN
ejde-350	395	16	of	of	ADP
ejde-350	395	17	positive	positive	ADJ
ejde-350	395	18	solutions	solution	NOUN
ejde-350	395	19	for	for	ADP
ejde-350	395	20	fractional	fractional	ADJ
ejde-350	395	21	laplacian	laplacian	ADJ
ejde-350	395	22	systems	system	NOUN
ejde-350	395	23	with	with	ADP
ejde-350	395	24	nonlinear	nonlinear	ADJ
ejde-350	395	25	coupling	coupling	NOUN
ejde-350	395	26	,	,	PUNCT
ejde-350	395	27	j.	j.	PROPN
ejde-350	395	28	math	math	PROPN
ejde-350	395	29	.	.	PUNCT
ejde-350	396	1	phys	phy	NOUN
ejde-350	396	2	.	.	PUNCT
ejde-350	396	3	,	,	PUNCT
ejde-350	396	4	60	60	NUM
ejde-350	396	5	(	(	PUNCT
ejde-350	396	6	2019	2019	NUM
ejde-350	396	7	)	)	PUNCT
ejde-350	396	8	,	,	PUNCT
ejde-350	396	9	081511	081511	NUM
ejde-350	396	10	.	.	PUNCT
ejde-350	397	1	16	16	NUM
ejde-350	397	2	y.	y.	PROPN
ejde-350	397	3	su	su	PROPN
ejde-350	397	4	,	,	PUNCT
ejde-350	397	5	h.	h.	PROPN
ejde-350	397	6	chen	chen	PROPN
ejde-350	397	7	,	,	PUNCT
ejde-350	397	8	s.	s.	PROPN
ejde-350	397	9	liu	liu	PROPN
ejde-350	397	10	,	,	PUNCT
ejde-350	397	11	x.	x.	NOUN
ejde-350	397	12	fang	fang	PROPN
ejde-350	397	13	ejde-2020/01	ejde-2020/01	X
ejde-350	398	1	[	[	X
ejde-350	398	2	15	15	NUM
ejde-350	398	3	]	]	X
ejde-350	398	4	s.	s.	PROPN
ejde-350	398	5	dipierro	dipierro	PROPN
ejde-350	398	6	,	,	PUNCT
ejde-350	398	7	l.	l.	PROPN
ejde-350	398	8	montoro	montoro	PROPN
ejde-350	398	9	,	,	PUNCT
ejde-350	398	10	i.	i.	NOUN
ejde-350	398	11	peral	peral	PROPN
ejde-350	398	12	,	,	PUNCT
ejde-350	398	13	b.	b.	PROPN
ejde-350	398	14	sciunzi	sciunzi	PROPN
ejde-350	398	15	;	;	PUNCT
ejde-350	398	16	qualitative	qualitative	ADJ
ejde-350	398	17	properties	property	NOUN
ejde-350	398	18	of	of	ADP
ejde-350	398	19	positive	positive	ADJ
ejde-350	398	20	solutions	solution	NOUN
ejde-350	398	21	to	to	ADP
ejde-350	398	22	nonlocal	nonlocal	ADJ
ejde-350	398	23	critical	critical	ADJ
ejde-350	398	24	problems	problem	NOUN
ejde-350	398	25	involving	involve	VERB
ejde-350	398	26	the	the	DET
ejde-350	398	27	hardy	hardy	ADJ
ejde-350	398	28	-	-	PUNCT
ejde-350	398	29	leray	leray	ADJ
ejde-350	398	30	potential	potential	NOUN
ejde-350	398	31	,	,	PUNCT
ejde-350	398	32	calc	calc	NOUN
ejde-350	398	33	.	.	PUNCT
ejde-350	399	1	var	var	PROPN
ejde-350	399	2	.	.	PUNCT
ejde-350	400	1	partial	partial	ADJ
ejde-350	400	2	differential	differential	NOUN
ejde-350	400	3	equations	equation	NOUN
ejde-350	400	4	,	,	PUNCT
ejde-350	400	5	55	55	NUM
ejde-350	400	6	(	(	PUNCT
ejde-350	400	7	2016	2016	NUM
ejde-350	400	8	)	)	PUNCT
ejde-350	400	9	,	,	PUNCT
ejde-350	400	10	no	no	INTJ
ejde-350	400	11	.	.	NOUN
ejde-350	400	12	4	4	NUM
ejde-350	400	13	,	,	PUNCT
ejde-350	400	14	art	art	NOUN
ejde-350	400	15	.	.	PUNCT
ejde-350	401	1	99	99	NUM
ejde-350	401	2	,	,	PUNCT
ejde-350	401	3	29	29	NUM
ejde-350	401	4	.	.	PUNCT
ejde-350	402	1	[	[	X
ejde-350	402	2	16	16	NUM
ejde-350	402	3	]	]	PUNCT
ejde-350	402	4	m.	m.	NOUN
ejde-350	402	5	m.	m.	NOUN
ejde-350	402	6	fall	fall	NOUN
ejde-350	402	7	,	,	PUNCT
ejde-350	402	8	v.	v.	X
ejde-350	402	9	felli	felli	NOUN
ejde-350	402	10	;	;	PUNCT
ejde-350	402	11	sharp	sharp	ADJ
ejde-350	402	12	essential	essential	ADJ
ejde-350	402	13	self	self	NOUN
ejde-350	402	14	-	-	PUNCT
ejde-350	402	15	adjointness	adjointness	NOUN
ejde-350	402	16	of	of	ADP
ejde-350	402	17	relativistic	relativistic	ADJ
ejde-350	402	18	schrödinger	schrödinger	NOUN
ejde-350	402	19	operators	operator	NOUN
ejde-350	402	20	with	with	ADP
ejde-350	402	21	a	a	DET
ejde-350	402	22	singular	singular	ADJ
ejde-350	402	23	potential	potential	NOUN
ejde-350	402	24	,	,	PUNCT
ejde-350	402	25	j.	j.	PROPN
ejde-350	402	26	funct	funct	PROPN
ejde-350	402	27	.	.	PUNCT
ejde-350	403	1	anal	anal	PROPN
ejde-350	403	2	.	.	PUNCT
ejde-350	404	1	267	267	NUM
ejde-350	404	2	(	(	PUNCT
ejde-350	404	3	2014	2014	NUM
ejde-350	404	4	)	)	PUNCT
ejde-350	404	5	,	,	PUNCT
ejde-350	404	6	no	no	INTJ
ejde-350	404	7	.	.	NOUN
ejde-350	404	8	6	6	NUM
ejde-350	404	9	,	,	PUNCT
ejde-350	404	10	1851–1877	1851–1877	NUM
ejde-350	404	11	.	.	PUNCT
ejde-350	405	1	[	[	X
ejde-350	405	2	17	17	NUM
ejde-350	405	3	]	]	PUNCT
ejde-350	405	4	m.	m.	NOUN
ejde-350	405	5	m.	m.	NOUN
ejde-350	405	6	fall	fall	NOUN
ejde-350	405	7	,	,	PUNCT
ejde-350	405	8	v.	v.	X
ejde-350	405	9	felli	felli	NOUN
ejde-350	405	10	;	;	PUNCT
ejde-350	405	11	unique	unique	ADJ
ejde-350	405	12	continuation	continuation	NOUN
ejde-350	405	13	properties	property	NOUN
ejde-350	405	14	for	for	ADP
ejde-350	405	15	relativistic	relativistic	ADJ
ejde-350	405	16	schrödinger	schrödinger	NOUN
ejde-350	405	17	operators	operator	NOUN
ejde-350	405	18	with	with	ADP
ejde-350	405	19	a	a	DET
ejde-350	405	20	singular	singular	ADJ
ejde-350	405	21	potential	potential	NOUN
ejde-350	405	22	,	,	PUNCT
ejde-350	405	23	discrete	discrete	ADJ
ejde-350	405	24	contin	contin	NOUN
ejde-350	405	25	.	.	PUNCT
ejde-350	406	1	dyn	dyn	NOUN
ejde-350	406	2	.	.	PUNCT
ejde-350	407	1	syst	syst	PROPN
ejde-350	407	2	.	.	PROPN
ejde-350	407	3	,	,	PUNCT
ejde-350	407	4	35	35	NUM
ejde-350	407	5	(	(	PUNCT
ejde-350	407	6	2015	2015	NUM
ejde-350	407	7	)	)	PUNCT
ejde-350	407	8	,	,	PUNCT
ejde-350	408	1	no	no	INTJ
ejde-350	408	2	.	.	NOUN
ejde-350	408	3	12	12	NUM
ejde-350	408	4	,	,	PUNCT
ejde-350	408	5	5827–5867	5827–5867	NUM
ejde-350	408	6	.	.	PUNCT
ejde-350	409	1	[	[	X
ejde-350	409	2	18	18	NUM
ejde-350	409	3	]	]	X
ejde-350	409	4	v.	v.	X
ejde-350	409	5	felli	felli	PROPN
ejde-350	409	6	,	,	PUNCT
ejde-350	409	7	a.	a.	PROPN
ejde-350	409	8	ferrero	ferrero	PROPN
ejde-350	409	9	,	,	PUNCT
ejde-350	409	10	s.	s.	PROPN
ejde-350	409	11	terracini	terracini	PROPN
ejde-350	409	12	;	;	PUNCT
ejde-350	409	13	asymptotic	asymptotic	ADJ
ejde-350	409	14	behavior	behavior	NOUN
ejde-350	409	15	of	of	ADP
ejde-350	409	16	solutions	solution	NOUN
ejde-350	409	17	to	to	ADP
ejde-350	409	18	schrödinger	schrödinger	NOUN
ejde-350	409	19	equations	equation	NOUN
ejde-350	409	20	near	near	ADP
ejde-350	409	21	an	an	DET
ejde-350	409	22	isolated	isolated	ADJ
ejde-350	409	23	singularity	singularity	NOUN
ejde-350	409	24	of	of	ADP
ejde-350	409	25	the	the	DET
ejde-350	409	26	electromagnetic	electromagnetic	ADJ
ejde-350	409	27	potential	potential	NOUN
ejde-350	409	28	,	,	PUNCT
ejde-350	409	29	j.	j.	PROPN
ejde-350	409	30	eur	eur	PROPN
ejde-350	409	31	.	.	PUNCT
ejde-350	409	32	math	math	PROPN
ejde-350	409	33	.	.	PUNCT
ejde-350	410	1	soc	soc	PROPN
ejde-350	410	2	.	.	PUNCT
ejde-350	411	1	(	(	PUNCT
ejde-350	411	2	jems	jem	NOUN
ejde-350	411	3	)	)	PUNCT
ejde-350	411	4	13	13	NUM
ejde-350	411	5	(	(	PUNCT
ejde-350	411	6	2011	2011	NUM
ejde-350	411	7	)	)	PUNCT
ejde-350	411	8	,	,	PUNCT
ejde-350	411	9	no	no	INTJ
ejde-350	411	10	.	.	NOUN
ejde-350	411	11	1	1	NUM
ejde-350	411	12	,	,	PUNCT
ejde-350	411	13	119–174	119–174	NUM
ejde-350	411	14	.	.	PUNCT
ejde-350	412	1	[	[	X
ejde-350	412	2	19	19	NUM
ejde-350	412	3	]	]	X
ejde-350	412	4	v.	v.	X
ejde-350	412	5	felli	felli	PROPN
ejde-350	412	6	,	,	PUNCT
ejde-350	412	7	a.	a.	PROPN
ejde-350	412	8	ferrero	ferrero	PROPN
ejde-350	412	9	,	,	PUNCT
ejde-350	412	10	s.	s.	PROPN
ejde-350	412	11	terracini	terracini	PROPN
ejde-350	412	12	;	;	PUNCT
ejde-350	412	13	on	on	ADP
ejde-350	412	14	the	the	DET
ejde-350	412	15	behavior	behavior	NOUN
ejde-350	412	16	at	at	ADP
ejde-350	412	17	collisions	collision	NOUN
ejde-350	412	18	of	of	ADP
ejde-350	412	19	solutions	solution	NOUN
ejde-350	412	20	to	to	ADP
ejde-350	412	21	schrödinger	schrödinger	NOUN
ejde-350	412	22	equations	equation	NOUN
ejde-350	412	23	with	with	ADP
ejde-350	412	24	many	many	ADJ
ejde-350	412	25	-	-	PUNCT
ejde-350	412	26	particle	particle	NOUN
ejde-350	412	27	and	and	CCONJ
ejde-350	412	28	cylindrical	cylindrical	ADJ
ejde-350	412	29	potentials	potential	NOUN
ejde-350	412	30	,	,	PUNCT
ejde-350	412	31	discrete	discrete	ADJ
ejde-350	412	32	contin	contin	NOUN
ejde-350	412	33	.	.	PUNCT
ejde-350	413	1	dyn	dyn	NOUN
ejde-350	413	2	.	.	PUNCT
ejde-350	414	1	syst	syst	PROPN
ejde-350	414	2	.	.	PROPN
ejde-350	414	3	,	,	PUNCT
ejde-350	414	4	32	32	NUM
ejde-350	414	5	(	(	PUNCT
ejde-350	414	6	2012	2012	NUM
ejde-350	414	7	)	)	PUNCT
ejde-350	414	8	,	,	PUNCT
ejde-350	414	9	no	no	INTJ
ejde-350	414	10	.	.	NOUN
ejde-350	414	11	11	11	NUM
ejde-350	414	12	,	,	PUNCT
ejde-350	414	13	3895–3956	3895–3956	NUM
ejde-350	414	14	.	.	PUNCT
ejde-350	415	1	[	[	X
ejde-350	415	2	20	20	NUM
ejde-350	415	3	]	]	PUNCT
ejde-350	415	4	v.	v.	X
ejde-350	415	5	felli	felli	PROPN
ejde-350	415	6	,	,	PUNCT
ejde-350	415	7	e.	e.	PROPN
ejde-350	415	8	m.	m.	PROPN
ejde-350	415	9	marchini	marchini	PROPN
ejde-350	415	10	,	,	PUNCT
ejde-350	415	11	s.	s.	PROPN
ejde-350	415	12	terracini	terracini	PROPN
ejde-350	415	13	;	;	PUNCT
ejde-350	415	14	on	on	ADP
ejde-350	415	15	the	the	DET
ejde-350	415	16	behavior	behavior	NOUN
ejde-350	415	17	of	of	ADP
ejde-350	415	18	solutions	solution	NOUN
ejde-350	415	19	to	to	ADP
ejde-350	415	20	schrödinger	schrödinger	NOUN
ejde-350	415	21	equations	equation	NOUN
ejde-350	415	22	with	with	ADP
ejde-350	415	23	dipole	dipole	NOUN
ejde-350	415	24	type	type	NOUN
ejde-350	415	25	potentials	potential	NOUN
ejde-350	415	26	near	near	ADP
ejde-350	415	27	the	the	DET
ejde-350	415	28	singularity	singularity	NOUN
ejde-350	415	29	,	,	PUNCT
ejde-350	415	30	discrete	discrete	ADJ
ejde-350	415	31	contin	contin	NOUN
ejde-350	415	32	.	.	PUNCT
ejde-350	416	1	dyn	dyn	NOUN
ejde-350	416	2	.	.	PUNCT
ejde-350	417	1	syst	syst	PROPN
ejde-350	417	2	.	.	PROPN
ejde-350	417	3	,	,	PUNCT
ejde-350	417	4	21	21	NUM
ejde-350	417	5	(	(	PUNCT
ejde-350	417	6	2008	2008	NUM
ejde-350	417	7	)	)	PUNCT
ejde-350	417	8	,	,	PUNCT
ejde-350	417	9	no	no	INTJ
ejde-350	417	10	.	.	NOUN
ejde-350	417	11	1	1	NUM
ejde-350	417	12	,	,	PUNCT
ejde-350	417	13	91–119	91–119	NUM
ejde-350	417	14	.	.	PUNCT
ejde-350	418	1	[	[	X
ejde-350	418	2	21	21	NUM
ejde-350	418	3	]	]	X
ejde-350	418	4	v.	v.	X
ejde-350	418	5	felli	felli	PROPN
ejde-350	418	6	,	,	PUNCT
ejde-350	418	7	e.	e.	PROPN
ejde-350	418	8	m.	m.	PROPN
ejde-350	418	9	marchini	marchini	PROPN
ejde-350	418	10	,	,	PUNCT
ejde-350	418	11	s.	s.	PROPN
ejde-350	418	12	terracini	terracini	PROPN
ejde-350	418	13	;	;	PUNCT
ejde-350	418	14	on	on	ADP
ejde-350	418	15	schrödinger	schrödinger	NOUN
ejde-350	418	16	operators	operator	NOUN
ejde-350	418	17	with	with	ADP
ejde-350	418	18	multisingular	multisingular	ADJ
ejde-350	418	19	inversesquare	inversesquare	NOUN
ejde-350	418	20	anisotropic	anisotropic	NOUN
ejde-350	418	21	potentials	potential	NOUN
ejde-350	418	22	,	,	PUNCT
ejde-350	418	23	indiana	indiana	PROPN
ejde-350	418	24	univ	univ	PROPN
ejde-350	418	25	.	.	PUNCT
ejde-350	418	26	math	math	PROPN
ejde-350	418	27	.	.	PUNCT
ejde-350	419	1	j.	j.	PROPN
ejde-350	419	2	,	,	PUNCT
ejde-350	419	3	58	58	NUM
ejde-350	419	4	(	(	PUNCT
ejde-350	419	5	2009	2009	NUM
ejde-350	419	6	)	)	PUNCT
ejde-350	419	7	,	,	PUNCT
ejde-350	419	8	no	no	INTJ
ejde-350	419	9	.	.	NOUN
ejde-350	419	10	2	2	NUM
ejde-350	419	11	,	,	PUNCT
ejde-350	419	12	617–676	617–676	NUM
ejde-350	419	13	.	.	PUNCT
ejde-350	420	1	[	[	X
ejde-350	420	2	22	22	NUM
ejde-350	420	3	]	]	PUNCT
ejde-350	420	4	r.	r.	PROPN
ejde-350	420	5	l.	l.	PROPN
ejde-350	420	6	frank	frank	PROPN
ejde-350	420	7	,	,	PUNCT
ejde-350	420	8	r.	r.	PROPN
ejde-350	420	9	seiringer	seiringer	PROPN
ejde-350	420	10	;	;	PUNCT
ejde-350	420	11	non	non	ADJ
ejde-350	420	12	–	–	NOUN
ejde-350	420	13	linear	linear	ADJ
ejde-350	420	14	ground	ground	NOUN
ejde-350	420	15	state	state	NOUN
ejde-350	420	16	representations	representation	NOUN
ejde-350	420	17	and	and	CCONJ
ejde-350	420	18	sharp	sharp	ADJ
ejde-350	420	19	hardy	hardy	ADJ
ejde-350	420	20	inequalities	inequality	NOUN
ejde-350	420	21	,	,	PUNCT
ejde-350	420	22	j.	j.	PROPN
ejde-350	420	23	funct	funct	PROPN
ejde-350	420	24	.	.	PUNCT
ejde-350	421	1	anal	anal	PROPN
ejde-350	421	2	.	.	PUNCT
ejde-350	422	1	255	255	NUM
ejde-350	422	2	(	(	PUNCT
ejde-350	422	3	2008	2008	NUM
ejde-350	422	4	)	)	PUNCT
ejde-350	422	5	,	,	PUNCT
ejde-350	423	1	no	no	INTJ
ejde-350	423	2	.	.	NOUN
ejde-350	423	3	12	12	NUM
ejde-350	423	4	,	,	PUNCT
ejde-350	423	5	3407–3430	3407–3430	NUM
ejde-350	423	6	.	.	PUNCT
ejde-350	424	1	[	[	X
ejde-350	424	2	23	23	NUM
ejde-350	424	3	]	]	X
ejde-350	424	4	i.	i.	PROPN
ejde-350	424	5	w.	w.	PROPN
ejde-350	424	6	herbst	herbst	PROPN
ejde-350	424	7	;	;	PUNCT
ejde-350	424	8	spectral	spectral	ADJ
ejde-350	424	9	theory	theory	NOUN
ejde-350	424	10	of	of	ADP
ejde-350	424	11	the	the	DET
ejde-350	424	12	operator	operator	NOUN
ejde-350	424	13	(	(	PUNCT
ejde-350	424	14	p2	p2	PROPN
ejde-350	424	15	+	+	CCONJ
ejde-350	424	16	m2)1/2	m2)1/2	PROPN
ejde-350	424	17	−	−	PROPN
ejde-350	425	1	ze2	ze2	NOUN
ejde-350	425	2	r	r	NOUN
ejde-350	425	3	,	,	PUNCT
ejde-350	425	4	comm	comm	NOUN
ejde-350	425	5	.	.	PUNCT
ejde-350	425	6	math	math	NOUN
ejde-350	425	7	.	.	PUNCT
ejde-350	426	1	phys	phy	NOUN
ejde-350	426	2	.	.	PUNCT
ejde-350	426	3	,	,	PUNCT
ejde-350	426	4	53	53	NUM
ejde-350	426	5	(	(	PUNCT
ejde-350	426	6	1977	1977	NUM
ejde-350	426	7	)	)	PUNCT
ejde-350	426	8	,	,	PUNCT
ejde-350	426	9	no	no	INTJ
ejde-350	426	10	.	.	NOUN
ejde-350	426	11	3	3	NUM
ejde-350	426	12	,	,	PUNCT
ejde-350	426	13	285–294	285–294	NUM
ejde-350	426	14	.	.	PUNCT
ejde-350	427	1	[	[	X
ejde-350	427	2	24	24	NUM
ejde-350	427	3	]	]	PUNCT
ejde-350	427	4	t.	t.	PROPN
ejde-350	427	5	hoffmann	hoffmann	PROPN
ejde-350	427	6	-	-	PUNCT
ejde-350	427	7	ostenhof	ostenhof	PROPN
ejde-350	427	8	,	,	PUNCT
ejde-350	427	9	a.	a.	NOUN
ejde-350	427	10	laptev	laptev	PROPN
ejde-350	427	11	;	;	PUNCT
ejde-350	427	12	hardy	hardy	ADJ
ejde-350	427	13	inequalities	inequality	NOUN
ejde-350	427	14	with	with	ADP
ejde-350	427	15	homogeneous	homogeneous	ADJ
ejde-350	427	16	weights	weight	NOUN
ejde-350	427	17	,	,	PUNCT
ejde-350	427	18	j.	j.	PROPN
ejde-350	427	19	funct	funct	PROPN
ejde-350	427	20	.	.	PUNCT
ejde-350	428	1	anal	anal	PROPN
ejde-350	428	2	.	.	PROPN
ejde-350	428	3	,	,	PUNCT
ejde-350	428	4	268	268	NUM
ejde-350	428	5	(	(	PUNCT
ejde-350	428	6	2015	2015	NUM
ejde-350	428	7	)	)	PUNCT
ejde-350	428	8	,	,	PUNCT
ejde-350	429	1	no	no	INTJ
ejde-350	429	2	.	.	NOUN
ejde-350	429	3	11	11	NUM
ejde-350	429	4	,	,	PUNCT
ejde-350	429	5	3278–3289	3278–3289	NUM
ejde-350	429	6	.	.	PUNCT
ejde-350	430	1	[	[	X
ejde-350	430	2	25	25	NUM
ejde-350	430	3	]	]	X
ejde-350	430	4	w.	w.	PROPN
ejde-350	430	5	jeong	jeong	PROPN
ejde-350	430	6	,	,	PUNCT
ejde-350	430	7	j.	j.	PROPN
ejde-350	430	8	seok	seok	PROPN
ejde-350	430	9	;	;	PUNCT
ejde-350	430	10	on	on	ADP
ejde-350	430	11	perturbation	perturbation	NOUN
ejde-350	430	12	of	of	ADP
ejde-350	430	13	a	a	DET
ejde-350	430	14	functional	functional	ADJ
ejde-350	430	15	with	with	ADP
ejde-350	430	16	the	the	DET
ejde-350	430	17	mountain	mountain	NOUN
ejde-350	430	18	pass	pass	NOUN
ejde-350	430	19	geometry	geometry	NOUN
ejde-350	430	20	:	:	PUNCT
ejde-350	430	21	applications	application	NOUN
ejde-350	430	22	to	to	ADP
ejde-350	430	23	the	the	DET
ejde-350	430	24	nonlinear	nonlinear	ADJ
ejde-350	430	25	schrödinger	schrödinger	NOUN
ejde-350	430	26	–	–	PUNCT
ejde-350	430	27	poisson	poisson	NOUN
ejde-350	430	28	equations	equation	NOUN
ejde-350	430	29	and	and	CCONJ
ejde-350	430	30	the	the	DET
ejde-350	430	31	nonlinear	nonlinear	PROPN
ejde-350	430	32	klein	klein	PROPN
ejde-350	430	33	–	–	PUNCT
ejde-350	430	34	gordon	gordon	PROPN
ejde-350	430	35	–	–	PUNCT
ejde-350	430	36	maxwell	maxwell	PROPN
ejde-350	430	37	equations	equation	NOUN
ejde-350	430	38	,	,	PUNCT
ejde-350	430	39	calc	calc	NOUN
ejde-350	430	40	.	.	PUNCT
ejde-350	431	1	var	var	PROPN
ejde-350	431	2	.	.	PUNCT
ejde-350	432	1	partial	partial	ADJ
ejde-350	432	2	differential	differential	NOUN
ejde-350	432	3	equations	equation	NOUN
ejde-350	432	4	,	,	PUNCT
ejde-350	432	5	49	49	NUM
ejde-350	432	6	(	(	PUNCT
ejde-350	432	7	2014	2014	NUM
ejde-350	432	8	)	)	PUNCT
ejde-350	432	9	,	,	PUNCT
ejde-350	432	10	no	no	INTJ
ejde-350	432	11	.	.	PUNCT
ejde-350	433	1	1–2	1–2	NUM
ejde-350	433	2	,	,	PUNCT
ejde-350	433	3	649–668	649–668	NUM
ejde-350	433	4	.	.	PUNCT
ejde-350	434	1	[	[	X
ejde-350	434	2	26	26	NUM
ejde-350	434	3	]	]	X
ejde-350	434	4	j.	j.	PROPN
ejde-350	434	5	m.	m.	PROPN
ejde-350	434	6	lévy	lévy	PROPN
ejde-350	434	7	-	-	PUNCT
ejde-350	434	8	leblond	leblond	NOUN
ejde-350	434	9	;	;	PUNCT
ejde-350	434	10	electron	electron	NOUN
ejde-350	434	11	capture	capture	NOUN
ejde-350	434	12	by	by	ADP
ejde-350	434	13	polar	polar	ADJ
ejde-350	434	14	molecules	molecule	NOUN
ejde-350	434	15	,	,	PUNCT
ejde-350	434	16	phys	phy	NOUN
ejde-350	434	17	.	.	PUNCT
ejde-350	435	1	rev	rev	PROPN
ejde-350	435	2	.	.	PROPN
ejde-350	435	3	153	153	NUM
ejde-350	435	4	(	(	PUNCT
ejde-350	435	5	1967	1967	NUM
ejde-350	435	6	)	)	PUNCT
ejde-350	435	7	,	,	PUNCT
ejde-350	435	8	1–4	1–4	PROPN
ejde-350	435	9	.	.	PUNCT
ejde-350	436	1	[	[	X
ejde-350	436	2	27	27	NUM
ejde-350	436	3	]	]	X
ejde-350	436	4	f.	f.	PROPN
ejde-350	436	5	li	li	PROPN
ejde-350	436	6	,	,	PUNCT
ejde-350	436	7	c.	c.	PROPN
ejde-350	436	8	gao	gao	PROPN
ejde-350	436	9	,	,	PUNCT
ejde-350	436	10	x.	x.	PROPN
ejde-350	436	11	zhu	zhu	PROPN
ejde-350	436	12	;	;	PUNCT
ejde-350	436	13	existence	existence	NOUN
ejde-350	436	14	and	and	CCONJ
ejde-350	436	15	concentration	concentration	NOUN
ejde-350	436	16	of	of	ADP
ejde-350	436	17	sign	sign	NOUN
ejde-350	436	18	–	–	PUNCT
ejde-350	436	19	changing	change	VERB
ejde-350	436	20	solutions	solution	NOUN
ejde-350	436	21	to	to	ADP
ejde-350	436	22	kirchhoff	kirchhoff	NOUN
ejde-350	436	23	–	–	PUNCT
ejde-350	436	24	type	type	NOUN
ejde-350	436	25	system	system	NOUN
ejde-350	436	26	with	with	ADP
ejde-350	436	27	hartree	hartree	ADJ
ejde-350	436	28	-	-	PUNCT
ejde-350	436	29	type	type	NOUN
ejde-350	436	30	nonlinearity	nonlinearity	NOUN
ejde-350	436	31	,	,	PUNCT
ejde-350	436	32	j.	j.	PROPN
ejde-350	436	33	math	math	PROPN
ejde-350	436	34	.	.	PUNCT
ejde-350	437	1	anal	anal	PROPN
ejde-350	437	2	.	.	PUNCT
ejde-350	437	3	appl	appl	PROPN
ejde-350	437	4	.	.	PROPN
ejde-350	438	1	,	,	PUNCT
ejde-350	438	2	448	448	NUM
ejde-350	438	3	(	(	PUNCT
ejde-350	438	4	2017	2017	NUM
ejde-350	438	5	)	)	PUNCT
ejde-350	438	6	,	,	PUNCT
ejde-350	438	7	no	no	INTJ
ejde-350	438	8	.	.	NOUN
ejde-350	438	9	1	1	NUM
ejde-350	438	10	,	,	PUNCT
ejde-350	438	11	60–80	60–80	PROPN
ejde-350	438	12	.	.	PUNCT
ejde-350	439	1	[	[	X
ejde-350	439	2	28	28	NUM
ejde-350	439	3	]	]	X
ejde-350	439	4	e.	e.	PROPN
ejde-350	439	5	h.	h.	PROPN
ejde-350	439	6	lieb	lieb	PROPN
ejde-350	439	7	;	;	PUNCT
ejde-350	439	8	the	the	DET
ejde-350	439	9	stability	stability	NOUN
ejde-350	439	10	of	of	ADP
ejde-350	439	11	matter	matter	NOUN
ejde-350	439	12	:	:	PUNCT
ejde-350	439	13	from	from	ADP
ejde-350	439	14	atoms	atom	NOUN
ejde-350	439	15	to	to	ADP
ejde-350	439	16	stars	star	NOUN
ejde-350	439	17	,	,	PUNCT
ejde-350	439	18	bull	bull	NOUN
ejde-350	439	19	.	.	PUNCT
ejde-350	440	1	amer	amer	PROPN
ejde-350	440	2	.	.	PUNCT
ejde-350	440	3	math	math	PROPN
ejde-350	440	4	.	.	PUNCT
ejde-350	441	1	soc	soc	PROPN
ejde-350	441	2	.	.	PUNCT
ejde-350	442	1	(	(	PUNCT
ejde-350	442	2	n.s	n.s	PROPN
ejde-350	442	3	.	.	PROPN
ejde-350	442	4	)	)	PUNCT
ejde-350	442	5	22	22	NUM
ejde-350	442	6	(	(	PUNCT
ejde-350	442	7	1990	1990	NUM
ejde-350	442	8	)	)	PUNCT
ejde-350	442	9	,	,	PUNCT
ejde-350	442	10	no	no	INTJ
ejde-350	442	11	.	.	NOUN
ejde-350	442	12	1	1	NUM
ejde-350	442	13	,	,	PUNCT
ejde-350	442	14	1–49	1–49	PROPN
ejde-350	442	15	.	.	PUNCT
ejde-350	443	1	[	[	X
ejde-350	443	2	29	29	NUM
ejde-350	443	3	]	]	PUNCT
ejde-350	443	4	e.	e.	PROPN
ejde-350	443	5	h.	h.	PROPN
ejde-350	443	6	lieb	lieb	PROPN
ejde-350	443	7	,	,	PUNCT
ejde-350	443	8	m.	m.	NOUN
ejde-350	443	9	loss	loss	NOUN
ejde-350	443	10	;	;	PUNCT
ejde-350	443	11	analysis	analysis	NOUN
ejde-350	443	12	,	,	PUNCT
ejde-350	443	13	graduate	graduate	NOUN
ejde-350	443	14	studies	study	NOUN
ejde-350	443	15	in	in	ADP
ejde-350	443	16	mathematics	mathematic	NOUN
ejde-350	443	17	,	,	PUNCT
ejde-350	443	18	vol	vol	NOUN
ejde-350	443	19	.	.	PROPN
ejde-350	443	20	14	14	NUM
ejde-350	443	21	,	,	PUNCT
ejde-350	443	22	american	american	PROPN
ejde-350	443	23	mathematical	mathematical	ADJ
ejde-350	443	24	society	society	NOUN
ejde-350	443	25	,	,	PUNCT
ejde-350	443	26	providence	providence	NOUN
ejde-350	443	27	,	,	PUNCT
ejde-350	443	28	2001	2001	NUM
ejde-350	443	29	.	.	PUNCT
ejde-350	444	1	[	[	X
ejde-350	444	2	30	30	NUM
ejde-350	444	3	]	]	PUNCT
ejde-350	444	4	z.	z.	PROPN
ejde-350	444	5	liu	liu	PROPN
ejde-350	444	6	,	,	PUNCT
ejde-350	444	7	j.	j.	PROPN
ejde-350	444	8	zhang	zhang	PROPN
ejde-350	444	9	;	;	PUNCT
ejde-350	444	10	multiplicity	multiplicity	NOUN
ejde-350	444	11	and	and	CCONJ
ejde-350	444	12	concentration	concentration	NOUN
ejde-350	444	13	of	of	ADP
ejde-350	444	14	positive	positive	ADJ
ejde-350	444	15	solutions	solution	NOUN
ejde-350	444	16	for	for	ADP
ejde-350	444	17	the	the	DET
ejde-350	444	18	fractional	fractional	ADJ
ejde-350	444	19	schrödinger	schrödinger	NOUN
ejde-350	444	20	–	–	PUNCT
ejde-350	444	21	poisson	poisson	NOUN
ejde-350	444	22	systems	system	NOUN
ejde-350	444	23	with	with	ADP
ejde-350	444	24	critical	critical	ADJ
ejde-350	444	25	growth	growth	NOUN
ejde-350	444	26	,	,	PUNCT
ejde-350	444	27	esaim	esaim	VERB
ejde-350	444	28	control	control	PROPN
ejde-350	444	29	optim	optim	PROPN
ejde-350	444	30	.	.	PUNCT
ejde-350	444	31	calc	calc	PROPN
ejde-350	444	32	.	.	PUNCT
ejde-350	445	1	var	var	PROPN
ejde-350	445	2	.	.	PUNCT
ejde-350	446	1	23	23	NUM
ejde-350	446	2	(	(	PUNCT
ejde-350	446	3	2017	2017	NUM
ejde-350	446	4	)	)	PUNCT
ejde-350	446	5	,	,	PUNCT
ejde-350	446	6	no	no	INTJ
ejde-350	446	7	.	.	NOUN
ejde-350	446	8	4	4	NUM
ejde-350	446	9	,	,	PUNCT
ejde-350	446	10	1515–1542	1515–1542	NUM
ejde-350	446	11	.	.	PUNCT
ejde-350	447	1	[	[	X
ejde-350	447	2	31	31	NUM
ejde-350	447	3	]	]	PUNCT
ejde-350	447	4	z.	z.	PROPN
ejde-350	447	5	liu	liu	PROPN
ejde-350	447	6	,	,	PUNCT
ejde-350	447	7	m.	m.	PROPN
ejde-350	447	8	squassina	squassina	PROPN
ejde-350	447	9	,	,	PUNCT
ejde-350	447	10	j.	j.	PROPN
ejde-350	447	11	zhang	zhang	PROPN
ejde-350	447	12	;	;	PUNCT
ejde-350	447	13	ground	ground	NOUN
ejde-350	447	14	states	state	NOUN
ejde-350	447	15	for	for	ADP
ejde-350	447	16	fractional	fractional	ADJ
ejde-350	447	17	kirchhoff	kirchhoff	NOUN
ejde-350	447	18	equations	equation	NOUN
ejde-350	447	19	with	with	ADP
ejde-350	447	20	critical	critical	ADJ
ejde-350	447	21	nonlinearity	nonlinearity	NOUN
ejde-350	447	22	in	in	ADP
ejde-350	447	23	low	low	ADJ
ejde-350	447	24	dimension	dimension	NOUN
ejde-350	447	25	,	,	PUNCT
ejde-350	447	26	nodea	nodea	ADJ
ejde-350	447	27	nonlinear	nonlinear	PROPN
ejde-350	447	28	differential	differential	PROPN
ejde-350	447	29	equations	equation	NOUN
ejde-350	447	30	appl	appl	PROPN
ejde-350	447	31	.	.	PROPN
ejde-350	447	32	,	,	PUNCT
ejde-350	447	33	24	24	NUM
ejde-350	447	34	(	(	PUNCT
ejde-350	447	35	2017	2017	NUM
ejde-350	447	36	)	)	PUNCT
ejde-350	447	37	,	,	PUNCT
ejde-350	447	38	50	50	NUM
ejde-350	447	39	.	.	PUNCT
ejde-350	448	1	[	[	X
ejde-350	448	2	32	32	NUM
ejde-350	448	3	]	]	X
ejde-350	448	4	c.	c.	PROPN
ejde-350	448	5	mercuri	mercuri	PROPN
ejde-350	448	6	,	,	PUNCT
ejde-350	448	7	v.	v.	PROPN
ejde-350	448	8	moroz	moroz	PROPN
ejde-350	448	9	,	,	PUNCT
ejde-350	448	10	j.	j.	PROPN
ejde-350	448	11	van	van	PROPN
ejde-350	448	12	schaftingen	schaftingen	PROPN
ejde-350	448	13	;	;	PUNCT
ejde-350	448	14	groundstates	groundstate	NOUN
ejde-350	448	15	and	and	CCONJ
ejde-350	448	16	radial	radial	ADJ
ejde-350	448	17	solutions	solution	NOUN
ejde-350	448	18	to	to	ADP
ejde-350	448	19	nonlinear	nonlinear	ADJ
ejde-350	448	20	schrödinger	schrödinger	NOUN
ejde-350	448	21	-	-	PUNCT
ejde-350	448	22	poisson	poisson	ADJ
ejde-350	448	23	-	-	PUNCT
ejde-350	448	24	slater	slater	NOUN
ejde-350	448	25	equations	equation	NOUN
ejde-350	448	26	at	at	ADP
ejde-350	448	27	the	the	DET
ejde-350	448	28	critical	critical	ADJ
ejde-350	448	29	frequency	frequency	NOUN
ejde-350	448	30	,	,	PUNCT
ejde-350	448	31	calc	calc	NOUN
ejde-350	448	32	.	.	PUNCT
ejde-350	449	1	var	var	PROPN
ejde-350	449	2	.	.	PUNCT
ejde-350	450	1	partial	partial	ADJ
ejde-350	450	2	differential	differential	ADJ
ejde-350	450	3	equations	equation	NOUN
ejde-350	450	4	55	55	NUM
ejde-350	450	5	(	(	PUNCT
ejde-350	450	6	2016	2016	NUM
ejde-350	450	7	)	)	PUNCT
ejde-350	450	8	,	,	PUNCT
ejde-350	450	9	no	no	INTJ
ejde-350	450	10	.	.	NOUN
ejde-350	450	11	6	6	NUM
ejde-350	450	12	,	,	PUNCT
ejde-350	450	13	146	146	NUM
ejde-350	450	14	.	.	PUNCT
ejde-350	451	1	[	[	X
ejde-350	451	2	33	33	NUM
ejde-350	451	3	]	]	PUNCT
ejde-350	451	4	t.	t.	PROPN
ejde-350	451	5	mukherjee	mukherjee	PROPN
ejde-350	451	6	,	,	PUNCT
ejde-350	451	7	k.	k.	PROPN
ejde-350	451	8	sreenadh	sreenadh	PROPN
ejde-350	451	9	;	;	PUNCT
ejde-350	451	10	fractional	fractional	ADJ
ejde-350	451	11	choquard	choquard	NOUN
ejde-350	451	12	equation	equation	NOUN
ejde-350	451	13	with	with	ADP
ejde-350	451	14	critical	critical	ADJ
ejde-350	451	15	nonlinearities	nonlinearitie	NOUN
ejde-350	451	16	,	,	PUNCT
ejde-350	451	17	nodea	nodea	ADJ
ejde-350	451	18	nonlinear	nonlinear	PROPN
ejde-350	451	19	differential	differential	PROPN
ejde-350	451	20	equations	equation	NOUN
ejde-350	451	21	appl	appl	PROPN
ejde-350	451	22	.	.	PROPN
ejde-350	451	23	,	,	PUNCT
ejde-350	451	24	24	24	NUM
ejde-350	451	25	(	(	PUNCT
ejde-350	451	26	2017	2017	NUM
ejde-350	451	27	)	)	PUNCT
ejde-350	451	28	,	,	PUNCT
ejde-350	451	29	no	no	INTJ
ejde-350	451	30	.	.	NOUN
ejde-350	451	31	6	6	NUM
ejde-350	451	32	,	,	PUNCT
ejde-350	451	33	63	63	NUM
ejde-350	451	34	.	.	PUNCT
ejde-350	452	1	[	[	X
ejde-350	452	2	34	34	NUM
ejde-350	452	3	]	]	X
ejde-350	452	4	b.	b.	PROPN
ejde-350	452	5	noris	noris	PROPN
ejde-350	452	6	,	,	PUNCT
ejde-350	452	7	m.	m.	NOUN
ejde-350	452	8	nys	nys	PROPN
ejde-350	452	9	,	,	PUNCT
ejde-350	452	10	s.	s.	PROPN
ejde-350	452	11	terracini	terracini	PROPN
ejde-350	452	12	;	;	PUNCT
ejde-350	452	13	on	on	ADP
ejde-350	452	14	the	the	DET
ejde-350	452	15	aharonov	aharonov	PROPN
ejde-350	452	16	-	-	PUNCT
ejde-350	452	17	bohm	bohm	PROPN
ejde-350	452	18	operators	operator	NOUN
ejde-350	452	19	with	with	ADP
ejde-350	452	20	varying	vary	VERB
ejde-350	452	21	poles	pole	NOUN
ejde-350	452	22	:	:	PUNCT
ejde-350	452	23	the	the	DET
ejde-350	452	24	boundary	boundary	ADJ
ejde-350	452	25	behavior	behavior	NOUN
ejde-350	452	26	of	of	ADP
ejde-350	452	27	eigenvalues	eigenvalue	NOUN
ejde-350	452	28	,	,	PUNCT
ejde-350	452	29	comm	comm	NOUN
ejde-350	452	30	.	.	PUNCT
ejde-350	452	31	math	math	NOUN
ejde-350	452	32	.	.	PUNCT
ejde-350	453	1	phys	phy	NOUN
ejde-350	453	2	.	.	PUNCT
ejde-350	453	3	,	,	PUNCT
ejde-350	453	4	339	339	NUM
ejde-350	453	5	(	(	PUNCT
ejde-350	453	6	2015	2015	NUM
ejde-350	453	7	)	)	PUNCT
ejde-350	453	8	,	,	PUNCT
ejde-350	454	1	no	no	INTJ
ejde-350	454	2	.	.	NOUN
ejde-350	454	3	3	3	NUM
ejde-350	454	4	,	,	PUNCT
ejde-350	454	5	1101–1146	1101–1146	NUM
ejde-350	454	6	.	.	PUNCT
ejde-350	455	1	[	[	X
ejde-350	455	2	35	35	NUM
ejde-350	455	3	]	]	X
ejde-350	455	4	g.	g.	NOUN
ejde-350	455	5	palatucci	palatucci	PROPN
ejde-350	455	6	,	,	PUNCT
ejde-350	455	7	a.	a.	NOUN
ejde-350	455	8	pisante	pisante	NOUN
ejde-350	455	9	;	;	PUNCT
ejde-350	455	10	improved	improve	VERB
ejde-350	455	11	sobolev	sobolev	NOUN
ejde-350	455	12	embeddings	embedding	NOUN
ejde-350	455	13	,	,	PUNCT
ejde-350	455	14	profile	profile	NOUN
ejde-350	455	15	decomposition	decomposition	NOUN
ejde-350	455	16	,	,	PUNCT
ejde-350	455	17	and	and	CCONJ
ejde-350	455	18	concentration	concentration	NOUN
ejde-350	455	19	-	-	PUNCT
ejde-350	455	20	compactness	compactness	NOUN
ejde-350	455	21	for	for	ADP
ejde-350	455	22	fractional	fractional	ADJ
ejde-350	455	23	sobolev	sobolev	NOUN
ejde-350	455	24	spaces	space	NOUN
ejde-350	455	25	,	,	PUNCT
ejde-350	455	26	calc	calc	PROPN
ejde-350	455	27	.	.	PUNCT
ejde-350	456	1	var	var	PROPN
ejde-350	456	2	.	.	PUNCT
ejde-350	457	1	partial	partial	ADJ
ejde-350	457	2	differential	differential	NOUN
ejde-350	457	3	equations	equation	NOUN
ejde-350	457	4	,	,	PUNCT
ejde-350	457	5	50	50	NUM
ejde-350	457	6	(	(	PUNCT
ejde-350	457	7	2014	2014	NUM
ejde-350	457	8	)	)	PUNCT
ejde-350	457	9	,	,	PUNCT
ejde-350	457	10	no	no	INTJ
ejde-350	457	11	.	.	NOUN
ejde-350	458	1	3	3	NUM
ejde-350	458	2	-	-	SYM
ejde-350	458	3	4	4	NUM
ejde-350	458	4	,	,	PUNCT
ejde-350	458	5	799–829	799–829	NUM
ejde-350	458	6	.	.	PUNCT
ejde-350	459	1	[	[	X
ejde-350	459	2	36	36	NUM
ejde-350	459	3	]	]	X
ejde-350	459	4	y.	y.	PROPN
ejde-350	459	5	su	su	PROPN
ejde-350	459	6	,	,	PUNCT
ejde-350	459	7	h.	h.	PROPN
ejde-350	459	8	chen	chen	PROPN
ejde-350	459	9	;	;	PUNCT
ejde-350	459	10	fractional	fractional	PROPN
ejde-350	459	11	kirchhoff	kirchhoff	NOUN
ejde-350	459	12	-	-	PUNCT
ejde-350	459	13	type	type	NOUN
ejde-350	459	14	equation	equation	NOUN
ejde-350	459	15	with	with	ADP
ejde-350	459	16	hardy	hardy	ADJ
ejde-350	459	17	-	-	PUNCT
ejde-350	459	18	littlewood	littlewood	NOUN
ejde-350	459	19	-	-	PUNCT
ejde-350	459	20	sobolev	sobolev	NOUN
ejde-350	459	21	critical	critical	ADJ
ejde-350	459	22	exponent	exponent	NOUN
ejde-350	459	23	,	,	PUNCT
ejde-350	459	24	comput	comput	NOUN
ejde-350	459	25	.	.	PUNCT
ejde-350	460	1	math	math	NOUN
ejde-350	460	2	.	.	PUNCT
ejde-350	461	1	appl	appl	PROPN
ejde-350	461	2	.	.	PROPN
ejde-350	461	3	,	,	PUNCT
ejde-350	461	4	78	78	NUM
ejde-350	461	5	(	(	PUNCT
ejde-350	461	6	2019	2019	NUM
ejde-350	461	7	)	)	PUNCT
ejde-350	461	8	,	,	PUNCT
ejde-350	462	1	no	no	INTJ
ejde-350	462	2	.	.	NOUN
ejde-350	462	3	6	6	NUM
ejde-350	462	4	,	,	PUNCT
ejde-350	462	5	2063–2082	2063–2082	NUM
ejde-350	462	6	.	.	PUNCT
ejde-350	463	1	[	[	X
ejde-350	463	2	37	37	NUM
ejde-350	463	3	]	]	X
ejde-350	463	4	y.	y.	PROPN
ejde-350	463	5	su	su	PROPN
ejde-350	463	6	,	,	PUNCT
ejde-350	463	7	l.	l.	PROPN
ejde-350	463	8	wang	wang	PROPN
ejde-350	463	9	,	,	PUNCT
ejde-350	463	10	t.	t.	PROPN
ejde-350	463	11	han	han	PROPN
ejde-350	463	12	;	;	PUNCT
ejde-350	463	13	schrödinger	schrödinger	X
ejde-350	463	14	–	–	PUNCT
ejde-350	463	15	poisson	poisson	NOUN
ejde-350	463	16	system	system	NOUN
ejde-350	463	17	with	with	ADP
ejde-350	463	18	hardy	hardy	ADJ
ejde-350	463	19	-	-	PUNCT
ejde-350	463	20	littlewood	littlewood	NOUN
ejde-350	463	21	-	-	PUNCT
ejde-350	463	22	sobolev	sobolev	NOUN
ejde-350	463	23	critical	critical	ADJ
ejde-350	463	24	exponent	exponent	NOUN
ejde-350	463	25	,	,	PUNCT
ejde-350	463	26	math	math	NOUN
ejde-350	463	27	.	.	PUNCT
ejde-350	464	1	methods	method	NOUN
ejde-350	464	2	appl	appl	PROPN
ejde-350	464	3	.	.	PUNCT
ejde-350	465	1	sci	sci	PROPN
ejde-350	465	2	.	.	PROPN
ejde-350	465	3	,	,	PUNCT
ejde-350	465	4	42	42	NUM
ejde-350	465	5	(	(	PUNCT
ejde-350	465	6	2019	2019	NUM
ejde-350	465	7	)	)	PUNCT
ejde-350	465	8	,	,	PUNCT
ejde-350	465	9	no	no	INTJ
ejde-350	465	10	.	.	NOUN
ejde-350	465	11	14	14	NUM
ejde-350	465	12	,	,	PUNCT
ejde-350	465	13	4815–4838	4815–4838	NUM
ejde-350	465	14	.	.	PUNCT
ejde-350	466	1	[	[	X
ejde-350	466	2	38	38	NUM
ejde-350	466	3	]	]	X
ejde-350	466	4	y.	y.	PROPN
ejde-350	466	5	su	su	PROPN
ejde-350	466	6	;	;	PUNCT
ejde-350	466	7	new	new	ADJ
ejde-350	466	8	result	result	NOUN
ejde-350	466	9	for	for	ADP
ejde-350	466	10	nonlinear	nonlinear	ADJ
ejde-350	466	11	choquard	choquard	NOUN
ejde-350	466	12	equations	equation	NOUN
ejde-350	466	13	:	:	PUNCT
ejde-350	466	14	doubly	doubly	ADV
ejde-350	466	15	critical	critical	ADJ
ejde-350	466	16	case	case	NOUN
ejde-350	466	17	,	,	PUNCT
ejde-350	466	18	appl	appl	PROPN
ejde-350	466	19	.	.	PROPN
ejde-350	466	20	math	math	PROPN
ejde-350	466	21	.	.	PUNCT
ejde-350	467	1	lett	lett	PROPN
ejde-350	467	2	.	.	PROPN
ejde-350	468	1	,	,	PUNCT
ejde-350	468	2	102	102	NUM
ejde-350	468	3	(	(	PUNCT
ejde-350	468	4	2020	2020	NUM
ejde-350	468	5	)	)	PUNCT
ejde-350	468	6	,	,	PUNCT
ejde-350	468	7	106092	106092	NUM
ejde-350	468	8	.	.	PUNCT
ejde-350	469	1	[	[	X
ejde-350	469	2	39	39	NUM
ejde-350	469	3	]	]	X
ejde-350	469	4	y.	y.	PROPN
ejde-350	469	5	su	su	PROPN
ejde-350	469	6	,	,	PUNCT
ejde-350	469	7	h.	h.	PROPN
ejde-350	469	8	chen	chen	PROPN
ejde-350	469	9	;	;	PUNCT
ejde-350	469	10	the	the	DET
ejde-350	469	11	minimizing	minimizing	NOUN
ejde-350	469	12	problem	problem	NOUN
ejde-350	469	13	involving	involve	VERB
ejde-350	469	14	p	p	NOUN
ejde-350	469	15	–	–	PUNCT
ejde-350	469	16	laplacian	laplacian	ADJ
ejde-350	469	17	and	and	CCONJ
ejde-350	469	18	hardy	hardy	ADJ
ejde-350	469	19	-	-	PUNCT
ejde-350	469	20	littlewoodsobolev	littlewoodsobolev	ADJ
ejde-350	469	21	upper	upper	ADJ
ejde-350	469	22	critical	critical	ADJ
ejde-350	469	23	exponent	exponent	NOUN
ejde-350	469	24	,	,	PUNCT
ejde-350	469	25	electron	electron	NOUN
ejde-350	469	26	.	.	PUNCT
ejde-350	470	1	j.	j.	PROPN
ejde-350	470	2	qual	qual	PROPN
ejde-350	470	3	.	.	PROPN
ejde-350	470	4	theory	theory	NOUN
ejde-350	470	5	differ	differ	VERB
ejde-350	470	6	.	.	PUNCT
ejde-350	471	1	equ	equ	PROPN
ejde-350	471	2	.	.	PUNCT
ejde-350	472	1	(	(	PUNCT
ejde-350	472	2	2018	2018	NUM
ejde-350	472	3	)	)	PUNCT
ejde-350	472	4	,	,	PUNCT
ejde-350	472	5	no	no	INTJ
ejde-350	472	6	.	.	NOUN
ejde-350	473	1	74	74	NUM
ejde-350	473	2	.	.	PUNCT
ejde-350	474	1	ejde-2020/01	ejde-2020/01	NOUN
ejde-350	474	2	fractional	fractional	ADJ
ejde-350	474	3	schrödinger	schrödinger	NOUN
ejde-350	474	4	-	-	PUNCT
ejde-350	474	5	poisson	poisson	NOUN
ejde-350	474	6	system	system	NOUN
ejde-350	474	7	17	17	NUM
ejde-350	475	1	[	[	X
ejde-350	475	2	40	40	NUM
ejde-350	475	3	]	]	PUNCT
ejde-350	475	4	j.	j.	PROPN
ejde-350	475	5	sun	sun	PROPN
ejde-350	475	6	;	;	PUNCT
ejde-350	475	7	infinitely	infinitely	ADV
ejde-350	475	8	many	many	ADJ
ejde-350	475	9	solutions	solution	NOUN
ejde-350	475	10	for	for	ADP
ejde-350	475	11	a	a	DET
ejde-350	475	12	class	class	NOUN
ejde-350	475	13	of	of	ADP
ejde-350	475	14	sublinear	sublinear	NOUN
ejde-350	475	15	schrödinger	schrödinger	NOUN
ejde-350	475	16	-	-	PUNCT
ejde-350	475	17	maxwell	maxwell	PROPN
ejde-350	475	18	equations	equation	NOUN
ejde-350	475	19	,	,	PUNCT
ejde-350	475	20	j.	j.	PROPN
ejde-350	475	21	math	math	PROPN
ejde-350	475	22	.	.	PUNCT
ejde-350	476	1	anal	anal	PROPN
ejde-350	476	2	.	.	PUNCT
ejde-350	477	1	appl	appl	PROPN
ejde-350	477	2	.	.	PROPN
ejde-350	477	3	,	,	PUNCT
ejde-350	477	4	390	390	NUM
ejde-350	477	5	(	(	PUNCT
ejde-350	477	6	2012	2012	NUM
ejde-350	477	7	)	)	PUNCT
ejde-350	477	8	,	,	PUNCT
ejde-350	478	1	no	no	INTJ
ejde-350	478	2	.	.	NOUN
ejde-350	478	3	2	2	NUM
ejde-350	478	4	,	,	PUNCT
ejde-350	478	5	514–522	514–522	NUM
ejde-350	478	6	.	.	PUNCT
ejde-350	479	1	[	[	X
ejde-350	479	2	41	41	NUM
ejde-350	479	3	]	]	PUNCT
ejde-350	479	4	k.	k.	PROPN
ejde-350	479	5	teng	teng	PROPN
ejde-350	479	6	;	;	PUNCT
ejde-350	479	7	existence	existence	NOUN
ejde-350	479	8	of	of	ADP
ejde-350	479	9	ground	ground	NOUN
ejde-350	479	10	state	state	NOUN
ejde-350	479	11	solutions	solution	NOUN
ejde-350	479	12	for	for	ADP
ejde-350	479	13	the	the	DET
ejde-350	479	14	nonlinear	nonlinear	ADJ
ejde-350	479	15	fractional	fractional	ADJ
ejde-350	479	16	schrödinger	schrödinger	NOUN
ejde-350	479	17	–	–	PUNCT
ejde-350	479	18	poisson	poisson	NOUN
ejde-350	479	19	system	system	NOUN
ejde-350	479	20	with	with	ADP
ejde-350	479	21	critical	critical	ADJ
ejde-350	479	22	sobolev	sobolev	NOUN
ejde-350	479	23	exponent	exponent	NOUN
ejde-350	479	24	,	,	PUNCT
ejde-350	479	25	j.	j.	PROPN
ejde-350	479	26	differential	differential	PROPN
ejde-350	479	27	equations	equations	PROPN
ejde-350	479	28	,	,	PUNCT
ejde-350	479	29	261	261	NUM
ejde-350	479	30	(	(	PUNCT
ejde-350	479	31	2016	2016	NUM
ejde-350	479	32	)	)	PUNCT
ejde-350	479	33	,	,	PUNCT
ejde-350	480	1	no	no	INTJ
ejde-350	480	2	.	.	NOUN
ejde-350	480	3	6	6	NUM
ejde-350	480	4	,	,	PUNCT
ejde-350	480	5	3061–3106	3061–3106	NUM
ejde-350	480	6	.	.	PUNCT
ejde-350	481	1	[	[	X
ejde-350	481	2	42	42	NUM
ejde-350	481	3	]	]	PUNCT
ejde-350	481	4	k.	k.	PROPN
ejde-350	481	5	teng	teng	PROPN
ejde-350	481	6	,	,	PUNCT
ejde-350	481	7	r.	r.	PROPN
ejde-350	481	8	p.	p.	PROPN
ejde-350	481	9	agarwal	agarwal	PROPN
ejde-350	481	10	;	;	PUNCT
ejde-350	481	11	existence	existence	NOUN
ejde-350	481	12	and	and	CCONJ
ejde-350	481	13	concentration	concentration	NOUN
ejde-350	481	14	of	of	ADP
ejde-350	481	15	positive	positive	ADJ
ejde-350	481	16	ground	ground	NOUN
ejde-350	481	17	state	state	NOUN
ejde-350	481	18	solutions	solution	NOUN
ejde-350	481	19	for	for	ADP
ejde-350	481	20	nonlinear	nonlinear	ADJ
ejde-350	481	21	fractional	fractional	ADJ
ejde-350	481	22	schrödinger	schrödinger	NOUN
ejde-350	481	23	–	–	PUNCT
ejde-350	481	24	poisson	poisson	NOUN
ejde-350	481	25	system	system	NOUN
ejde-350	481	26	with	with	ADP
ejde-350	481	27	critical	critical	ADJ
ejde-350	481	28	growth	growth	NOUN
ejde-350	481	29	,	,	PUNCT
ejde-350	481	30	math	math	NOUN
ejde-350	481	31	.	.	PUNCT
ejde-350	482	1	methods	method	NOUN
ejde-350	482	2	appl	appl	PROPN
ejde-350	482	3	.	.	PUNCT
ejde-350	483	1	sci	sci	PROPN
ejde-350	483	2	.	.	PROPN
ejde-350	483	3	,	,	PUNCT
ejde-350	483	4	41	41	NUM
ejde-350	483	5	(	(	PUNCT
ejde-350	483	6	2018	2018	NUM
ejde-350	483	7	)	)	PUNCT
ejde-350	483	8	,	,	PUNCT
ejde-350	483	9	no	no	INTJ
ejde-350	483	10	.	.	NOUN
ejde-350	483	11	17	17	NUM
ejde-350	483	12	,	,	PUNCT
ejde-350	483	13	8258–8293	8258–8293	NUM
ejde-350	483	14	.	.	PUNCT
ejde-350	484	1	[	[	X
ejde-350	484	2	43	43	NUM
ejde-350	484	3	]	]	PUNCT
ejde-350	484	4	z.	z.	PROPN
ejde-350	484	5	wei	wei	PROPN
ejde-350	484	6	;	;	PUNCT
ejde-350	484	7	existence	existence	NOUN
ejde-350	484	8	of	of	ADP
ejde-350	484	9	infinitely	infinitely	ADV
ejde-350	484	10	many	many	ADJ
ejde-350	484	11	solutions	solution	NOUN
ejde-350	484	12	for	for	ADP
ejde-350	484	13	the	the	DET
ejde-350	484	14	fractional	fractional	ADJ
ejde-350	484	15	schrödinger	schrödinger	NOUN
ejde-350	484	16	-	-	PUNCT
ejde-350	484	17	poisson	poisson	NOUN
ejde-350	484	18	equations	equation	NOUN
ejde-350	484	19	,	,	PUNCT
ejde-350	484	20	arxiv:1508.03088v1	arxiv:1508.03088v1	PROPN
ejde-350	484	21	.	.	PUNCT
ejde-350	485	1	[	[	X
ejde-350	485	2	44	44	NUM
ejde-350	485	3	]	]	PUNCT
ejde-350	485	4	m.	m.	NOUN
ejde-350	485	5	willem	willem	PROPN
ejde-350	485	6	;	;	PUNCT
ejde-350	485	7	minimax	minimax	NOUN
ejde-350	485	8	theorems	theorem	NOUN
ejde-350	485	9	,	,	PUNCT
ejde-350	485	10	progress	progress	NOUN
ejde-350	485	11	in	in	ADP
ejde-350	485	12	nonlinear	nonlinear	ADJ
ejde-350	485	13	differential	differential	ADJ
ejde-350	485	14	equations	equation	NOUN
ejde-350	485	15	and	and	CCONJ
ejde-350	485	16	their	their	PRON
ejde-350	485	17	applications	application	NOUN
ejde-350	485	18	,	,	PUNCT
ejde-350	485	19	vol	vol	NOUN
ejde-350	485	20	.	.	PROPN
ejde-350	485	21	24	24	NUM
ejde-350	485	22	,	,	PUNCT
ejde-350	485	23	birkhäuser	birkhäuser	X
ejde-350	485	24	boston	boston	PROPN
ejde-350	485	25	,	,	PUNCT
ejde-350	485	26	1996	1996	NUM
ejde-350	485	27	.	.	PUNCT
ejde-350	486	1	[	[	X
ejde-350	486	2	45	45	NUM
ejde-350	486	3	]	]	PUNCT
ejde-350	486	4	j.	j.	PROPN
ejde-350	486	5	yang	yang	PROPN
ejde-350	486	6	,	,	PUNCT
ejde-350	486	7	f.	f.	PROPN
ejde-350	486	8	wu	wu	PROPN
ejde-350	486	9	;	;	PUNCT
ejde-350	486	10	doubly	doubly	ADV
ejde-350	486	11	critical	critical	ADJ
ejde-350	486	12	problems	problem	NOUN
ejde-350	486	13	involving	involve	VERB
ejde-350	486	14	fractional	fractional	ADJ
ejde-350	486	15	laplacians	laplacian	NOUN
ejde-350	486	16	in	in	ADP
ejde-350	486	17	rn	rn	PROPN
ejde-350	486	18	,	,	PUNCT
ejde-350	486	19	adv	adv	PROPN
ejde-350	486	20	.	.	PUNCT
ejde-350	486	21	nonlinear	nonlinear	ADJ
ejde-350	486	22	stud	stud	NOUN
ejde-350	486	23	.	.	PUNCT
ejde-350	487	1	17	17	NUM
ejde-350	487	2	(	(	PUNCT
ejde-350	487	3	2017	2017	NUM
ejde-350	487	4	)	)	PUNCT
ejde-350	487	5	,	,	PUNCT
ejde-350	487	6	no	no	INTJ
ejde-350	487	7	.	.	NOUN
ejde-350	487	8	4	4	NUM
ejde-350	487	9	,	,	PUNCT
ejde-350	487	10	677–690	677–690	NUM
ejde-350	487	11	.	.	PUNCT
ejde-350	488	1	[	[	X
ejde-350	488	2	46	46	NUM
ejde-350	488	3	]	]	PUNCT
ejde-350	488	4	j.	j.	PROPN
ejde-350	488	5	zhang	zhang	PROPN
ejde-350	488	6	,	,	PUNCT
ejde-350	488	7	j.	j.	PROPN
ejde-350	488	8	m.	m.	PROPN
ejde-350	488	9	do	do	VERB
ejde-350	488	10	ó	ó	NOUN
ejde-350	488	11	,	,	PUNCT
ejde-350	488	12	m.	m.	NOUN
ejde-350	488	13	squassina	squassina	PROPN
ejde-350	488	14	;	;	PUNCT
ejde-350	488	15	fractional	fractional	ADJ
ejde-350	488	16	schrödinger	schrödinger	NOUN
ejde-350	488	17	–	–	PUNCT
ejde-350	488	18	poisson	poisson	NOUN
ejde-350	488	19	systems	system	NOUN
ejde-350	488	20	with	with	ADP
ejde-350	488	21	a	a	DET
ejde-350	488	22	general	general	ADJ
ejde-350	488	23	subcritical	subcritical	ADJ
ejde-350	488	24	or	or	CCONJ
ejde-350	488	25	critical	critical	ADJ
ejde-350	488	26	nonlinearity	nonlinearity	NOUN
ejde-350	488	27	,	,	PUNCT
ejde-350	488	28	adv	adv	PROPN
ejde-350	488	29	.	.	PUNCT
ejde-350	488	30	nonlinear	nonlinear	ADJ
ejde-350	488	31	stud	stud	PROPN
ejde-350	488	32	.	.	PUNCT
ejde-350	489	1	,	,	PUNCT
ejde-350	489	2	16	16	NUM
ejde-350	489	3	(	(	PUNCT
ejde-350	489	4	2016	2016	NUM
ejde-350	489	5	)	)	PUNCT
ejde-350	489	6	,	,	PUNCT
ejde-350	489	7	no	no	INTJ
ejde-350	489	8	.	.	NOUN
ejde-350	489	9	1	1	NUM
ejde-350	489	10	,	,	PUNCT
ejde-350	489	11	15–30	15–30	NUM
ejde-350	489	12	.	.	PUNCT
ejde-350	490	1	[	[	X
ejde-350	490	2	47	47	NUM
ejde-350	490	3	]	]	PUNCT
ejde-350	490	4	l.	l.	PROPN
ejde-350	490	5	zhao	zhao	PROPN
ejde-350	490	6	,	,	PUNCT
ejde-350	490	7	f.	f.	PROPN
ejde-350	490	8	zhao	zhao	PROPN
ejde-350	490	9	;	;	PUNCT
ejde-350	490	10	on	on	ADP
ejde-350	490	11	the	the	DET
ejde-350	490	12	existence	existence	NOUN
ejde-350	490	13	of	of	ADP
ejde-350	490	14	solutions	solution	NOUN
ejde-350	490	15	for	for	ADP
ejde-350	490	16	the	the	DET
ejde-350	490	17	schrödinger	schrödinger	NOUN
ejde-350	490	18	-	-	PUNCT
ejde-350	490	19	poisson	poisson	NOUN
ejde-350	490	20	equations	equation	NOUN
ejde-350	490	21	,	,	PUNCT
ejde-350	490	22	j.	j.	PROPN
ejde-350	490	23	math	math	PROPN
ejde-350	490	24	.	.	PUNCT
ejde-350	491	1	anal	anal	PROPN
ejde-350	491	2	.	.	PUNCT
ejde-350	492	1	appl	appl	PROPN
ejde-350	492	2	.	.	PROPN
ejde-350	492	3	,	,	PUNCT
ejde-350	493	1	346	346	NUM
ejde-350	493	2	(	(	PUNCT
ejde-350	493	3	2008	2008	NUM
ejde-350	493	4	)	)	PUNCT
ejde-350	493	5	,	,	PUNCT
ejde-350	493	6	no	no	INTJ
ejde-350	493	7	.	.	NOUN
ejde-350	493	8	1	1	NUM
ejde-350	493	9	,	,	PUNCT
ejde-350	493	10	155–169	155–169	NUM
ejde-350	493	11	.	.	PUNCT
ejde-350	493	12	yu	yu	PROPN
ejde-350	493	13	su	su	PROPN
ejde-350	494	1	(	(	PUNCT
ejde-350	494	2	corresponding	correspond	VERB
ejde-350	494	3	author	author	NOUN
ejde-350	494	4	)	)	PUNCT
ejde-350	494	5	school	school	NOUN
ejde-350	494	6	of	of	ADP
ejde-350	494	7	mathematics	mathematic	NOUN
ejde-350	494	8	and	and	CCONJ
ejde-350	494	9	big	big	ADJ
ejde-350	494	10	data	datum	NOUN
ejde-350	494	11	,	,	PUNCT
ejde-350	494	12	anhui	anhui	PROPN
ejde-350	494	13	university	university	PROPN
ejde-350	494	14	of	of	ADP
ejde-350	494	15	science	science	NOUN
ejde-350	494	16	and	and	CCONJ
ejde-350	494	17	technology	technology	NOUN
ejde-350	494	18	,	,	PUNCT
ejde-350	494	19	huainan	huainan	NOUN
ejde-350	494	20	,	,	PUNCT
ejde-350	494	21	232001	232001	NUM
ejde-350	494	22	anhui	anhui	PROPN
ejde-350	494	23	,	,	PUNCT
ejde-350	494	24	china	china	PROPN
ejde-350	494	25	.	.	PUNCT
ejde-350	495	1	school	school	NOUN
ejde-350	495	2	of	of	ADP
ejde-350	495	3	mathematics	mathematic	NOUN
ejde-350	495	4	and	and	CCONJ
ejde-350	495	5	statistics	statistic	NOUN
ejde-350	495	6	,	,	PUNCT
ejde-350	495	7	central	central	ADJ
ejde-350	495	8	south	south	PROPN
ejde-350	495	9	university	university	PROPN
ejde-350	495	10	,	,	PUNCT
ejde-350	495	11	changsha	changsha	PROPN
ejde-350	495	12	,	,	PUNCT
ejde-350	495	13	410083	410083	NUM
ejde-350	495	14	hunan	hunan	PROPN
ejde-350	495	15	,	,	PUNCT
ejde-350	495	16	china	china	PROPN
ejde-350	495	17	email	email	NOUN
ejde-350	495	18	address	address	NOUN
ejde-350	495	19	:	:	PUNCT
ejde-350	495	20	yusumath@qq.com	yusumath@qq.com	X
ejde-350	495	21	haibo	haibo	PROPN
ejde-350	495	22	chen	chen	PROPN
ejde-350	495	23	school	school	PROPN
ejde-350	495	24	of	of	ADP
ejde-350	495	25	mathematics	mathematic	NOUN
ejde-350	495	26	and	and	CCONJ
ejde-350	495	27	statistics	statistic	NOUN
ejde-350	495	28	,	,	PUNCT
ejde-350	495	29	central	central	ADJ
ejde-350	495	30	south	south	PROPN
ejde-350	495	31	university	university	PROPN
ejde-350	495	32	,	,	PUNCT
ejde-350	495	33	changsha	changsha	PROPN
ejde-350	495	34	,	,	PUNCT
ejde-350	495	35	410083	410083	NUM
ejde-350	495	36	hunan	hunan	PROPN
ejde-350	495	37	,	,	PUNCT
ejde-350	495	38	china	china	PROPN
ejde-350	495	39	email	email	NOUN
ejde-350	495	40	address	address	NOUN
ejde-350	495	41	:	:	PUNCT
ejde-350	495	42	math	math	NOUN
ejde-350	495	43	chb@163.com	chb@163.com	X
ejde-350	495	44	senli	senli	VERB
ejde-350	495	45	liu	liu	PROPN
ejde-350	495	46	school	school	PROPN
ejde-350	495	47	of	of	ADP
ejde-350	495	48	mathematics	mathematic	NOUN
ejde-350	495	49	and	and	CCONJ
ejde-350	495	50	statistics	statistic	NOUN
ejde-350	495	51	,	,	PUNCT
ejde-350	495	52	central	central	ADJ
ejde-350	495	53	south	south	PROPN
ejde-350	495	54	university	university	PROPN
ejde-350	495	55	,	,	PUNCT
ejde-350	495	56	changsha	changsha	PROPN
ejde-350	495	57	,	,	PUNCT
ejde-350	495	58	410083	410083	NUM
ejde-350	495	59	hunan	hunan	PROPN
ejde-350	495	60	,	,	PUNCT
ejde-350	495	61	china	china	PROPN
ejde-350	495	62	email	email	NOUN
ejde-350	495	63	address	address	NOUN
ejde-350	495	64	:	:	PUNCT
ejde-350	495	65	jasonliu0615@163.com	jasonliu0615@163.com	X
ejde-350	495	66	xianwen	xianwen	PROPN
ejde-350	495	67	fang	fang	PROPN
ejde-350	495	68	school	school	PROPN
ejde-350	495	69	of	of	ADP
ejde-350	495	70	mathematics	mathematic	NOUN
ejde-350	495	71	and	and	CCONJ
ejde-350	495	72	big	big	ADJ
ejde-350	495	73	data	datum	NOUN
ejde-350	495	74	,	,	PUNCT
ejde-350	495	75	anhui	anhui	PROPN
ejde-350	495	76	university	university	PROPN
ejde-350	495	77	of	of	ADP
ejde-350	495	78	science	science	NOUN
ejde-350	495	79	and	and	CCONJ
ejde-350	495	80	technology	technology	NOUN
ejde-350	495	81	,	,	PUNCT
ejde-350	495	82	huainan	huainan	NOUN
ejde-350	495	83	,	,	PUNCT
ejde-350	495	84	232001	232001	NUM
ejde-350	495	85	anhui	anhui	NOUN
ejde-350	495	86	,	,	PUNCT
ejde-350	495	87	china	china	PROPN
ejde-350	495	88	email	email	NOUN
ejde-350	495	89	address	address	NOUN
ejde-350	495	90	:	:	PUNCT
ejde-350	495	91	xwfang@aust.edu.cn	xwfang@aust.edu.cn	PROPN
ejde-350	495	92	1	1	NUM
ejde-350	495	93	.	.	PUNCT
ejde-350	495	94	introduction	introduction	NOUN
ejde-350	495	95	1.1	1.1	NUM
ejde-350	495	96	.	.	PUNCT
ejde-350	496	1	statement	statement	NOUN
ejde-350	496	2	of	of	ADP
ejde-350	496	3	results	result	NOUN
ejde-350	496	4	2	2	NUM
ejde-350	496	5	.	.	PUNCT
ejde-350	496	6	preliminaries	preliminary	NOUN
ejde-350	496	7	2.1	2.1	NUM
ejde-350	496	8	.	.	PUNCT
ejde-350	497	1	formulation	formulation	NOUN
ejde-350	497	2	of	of	ADP
ejde-350	497	3	system	system	NOUN
ejde-350	497	4	(	(	PUNCT
ejde-350	497	5	?	?	PUNCT
ejde-350	497	6	?	?	PUNCT
ejde-350	497	7	)	)	PUNCT
ejde-350	498	1	3	3	X
ejde-350	498	2	.	.	X
ejde-350	498	3	perturbed	perturb	VERB
ejde-350	498	4	equation	equation	NOUN
ejde-350	498	5	3.1	3.1	NUM
ejde-350	498	6	.	.	PUNCT
ejde-350	499	1	mountain	mountain	NOUN
ejde-350	499	2	pass	pass	NOUN
ejde-350	499	3	geometry	geometry	NOUN
ejde-350	499	4	and	and	CCONJ
ejde-350	499	5	nehari	nehari	NOUN
ejde-350	499	6	manifold	manifold	ADJ
ejde-350	499	7	3.2	3.2	NUM
ejde-350	499	8	.	.	PUNCT
ejde-350	500	1	ground	ground	NOUN
ejde-350	500	2	state	state	NOUN
ejde-350	500	3	solution	solution	NOUN
ejde-350	500	4	4	4	NUM
ejde-350	500	5	.	.	PUNCT
ejde-350	500	6	proof	proof	NOUN
ejde-350	500	7	of	of	ADP
ejde-350	500	8	theorem	theorem	NOUN
ejde-350	500	9	?	?	PUNCT
ejde-350	500	10	?	?	PUNCT
ejde-350	501	1	5	5	X
ejde-350	501	2	.	.	X
ejde-350	501	3	open	open	ADJ
ejde-350	501	4	problem	problem	NOUN
ejde-350	501	5	acknowledgements	acknowledgement	NOUN
ejde-350	501	6	references	reference	NOUN