Existence of weak solutions for a class of fractional Schrodinger equations with periodic potential

被引：8

作者：

Pu, Yang ^{[1
,2
]}

Liu, Jiu ^{[1
]}

Tang, Chun-Lei ^{[1
]}

机构：

[1] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

[2] China West Normal Univ, Coll Math & Informat, Nanchong 637002, Sichuan, Peoples R China

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 73卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Nonlinear Schrodinger equation; Fractional Laplacian; Strongly indefinite functional;

D O I：

10.1016/j.camwa.2016.12.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a time-independent fractional Schrodinger equation -(Delta)(alpha)u + V(x)u = f (x, u) in R-N, u is an element of H-alpha (R-N), where alpha is an element of (0, 1), N > 2 alpha, V (x) is a periodic potential, f is superlinear and has a general subcritical growth. Based on a generalized linking theorem and a variant fountain theorem for strongly indefinite functional, we obtain a ground state solution and infinitely many solutions. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：465 / 482

页数：18

共 22 条

[1] On some critical problems for the fractional Laplacian operator
Barrios, B.
Colorado, E.
de Pablo, A.
Sanchez, U.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (11) : 6133 - 6162
[2] Generalized Fountain Theorem and applications to strongly indefinite semilinear problems
Batkam, Cyril Joel
Colin, Fabrice
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 405 (02) : 438 - 452
[3] On multiple solutions of a semilinear Schrodinger equation with periodic potential
Batkam, Cyril Joel
Colin, Fabrice
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 84 : 39 - 49
[4] BERESTYCKI H, 1983, ARCH RATION MECH AN, V82, P313
[5] A RELATION BETWEEN POINTWISE CONVERGENCE OF FUNCTIONS AND CONVERGENCE OF FUNCTIONALS
BREZIS, H
LIEB, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 88 (03) : 486 - 490
[6] Ground state solutions of asymptotically linear fractional Schrodinger equations
Chang, Xiaojun
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2013, 54 (06)
[7] Chen C., 2016, ELECT J DIFFERENTIAL, V88, P1
[8] Bound state for the fractional Schrodinger equation with unbounded potential
Cheng, Ming
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2012, 53 (04)
[9] Hitchhiker's guide to the fractional Sobolev spaces
Di Nezza, Eleonora
Palatucci, Giampiero
Valdinoci, Enrico
[J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2012, 136 (05): : 521 - 573
[10] EXISTENCE AND SYMMETRY RESULTS FOR A SCHRODINGER TYPE PROBLEM INVOLVING THE FRACTIONAL LAPLACIAN
Dipierro, S.
Palatucci, G.
Valdinoci, E.
[J]. MATEMATICHE, 2013, 68 (01): : 201 - 216

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