Multiplicity solutions of a class fractional Schrodinger equations

被引：1

作者：

Jia, Li-Jiang ^{[1
]}

Ge, Bin ^{[2
]}

Cui, Ying-Xin ^{[2
]}

Sun, Liang-Liang ^{[2
]}

机构：

[1] Harbin Engn Univ, Sch Econ & Management, Harbin 150001, Heilongjiang, Peoples R China

[2] Harbin Engn Univ, Dept Appl Math, Harbin 150001, Heilongjiang, Peoples R China

来源：

OPEN MATHEMATICS | 2017年 / 15卷

基金：

高等学校博士学科点专项科研基金; 中国国家自然科学基金;

关键词：

Fractional Laplacian; Variational methods; Nontrivial solution; WEAK SOLUTIONS; EXISTENCE; STATE;

D O I：

10.1515/math-2017-0084

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the existence of nontrivial solutions to a class fractional Schr R odinger equations (-Delta)(s)u + V(x)u = lambda f(x, u) in R-N,R- where (-Delta)(s)u(x) = 2(epsilon -> 0) (lim) integral R-N\B-epsilon(X) u(x)-u(y)/vertical bar x-y vertical bar(N+2s) dy, x is an element of R-N is a fraction operetor and s is an element of (0, 1). By using variational methods, we prove this problem has at least two nontrivial solutions in a suitable weighted fractional Sobolev space.

引用

页码：1010 / 1023

页数：14

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