INFINITELY MANY SOLUTIONS OF THE NONLINEAR FRACTIONAL SCHRODINGER EQUATIONS

被引：4

作者：

Du, Miao ^{[1
]}

Tian, Lixin ^{[1
]}

机构：

[1] Nanjing Normal Univ, Sch Math Sci, Nanjing 210023, Jiangsu, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2016年 / 21卷 / 10期

关键词：

Fractional Schrodinger equations; sublinear; superlinear; concave and critical nonlinearities; variational methods; BREZIS-NIRENBERG RESULT; POSITIVE SOLUTIONS; LAPLACIAN; EXISTENCE; OPERATOR;

D O I：

10.3934/dcdsb.2016104

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the fractional Schrodinger equation (-Delta)u = V(x)u = f(x,u), x is an element of R-N, where 0 < s < 1, (-Delta)(s) denotes the fractional Laplacian of order s and the nonlinearity f is sublinear or superlinear at infinity. Under certain assumptions on V and f, we prove that this equation has infinitely many solutions via variational methods, which unifies and sharply improves the recent results of Teng (2015) [33]. Moreover, we also consider the above equation with concave and critical nonlinearities, and obtain the existence of infinitely many solutions.

引用

页码：3407 / 3428

页数：22

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