Infinitely many solutions for a class of sublinear fractional Schrödinger equations with indefinite potentials
Abstract In this paper, we consider the following sublinear fractional Schrödinger equation: ( − Δ ) s u + V ( x ) u = K ( x ) | u | p − 1 u , x ∈ R N , $$ (-\Delta)^{s}u + V(x)u= K(x) \vert u \vert ^{p-1}u,\quad x\in \mathbb{R}^{N}, $$ where s , p ∈ ( 0 , 1 ) $s, p\in(0,1)$ , N > 2 s $N>2s$ ,...
Main Authors: | , , |
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Format: | Article |
Language: | English |
Published: |
SpringerOpen
2020-03-01
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Series: | Journal of Inequalities and Applications |
Subjects: | |
Online Access: | http://link.springer.com/article/10.1186/s13660-020-02326-8 |
Summary: | Abstract In this paper, we consider the following sublinear fractional Schrödinger equation: ( − Δ ) s u + V ( x ) u = K ( x ) | u | p − 1 u , x ∈ R N , $$ (-\Delta)^{s}u + V(x)u= K(x) \vert u \vert ^{p-1}u,\quad x\in \mathbb{R}^{N}, $$ where s , p ∈ ( 0 , 1 ) $s, p\in(0,1)$ , N > 2 s $N>2s$ , ( − Δ ) s $(-\Delta)^{s}$ is a fractional Laplacian operator, and K, V both change sign in R N $\mathbb{R}^{N}$ . We prove that the problem has infinitely many solutions under appropriate assumptions on K, V. The tool used in this paper is the symmetric mountain pass theorem. |
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ISSN: | 1029-242X |