Infinitely many solutions for a class of sublinear fractional Schrödinger equations with indefinite potentials

[摘要] In this paper, we consider the following sublinear fractional Schrödinger equation: $$ (-\Delta)^{s}u + V(x)u= K(x) \vert u \vert ^{p-1}u,\quad x\in \mathbb{R}^{N}, $$ where $s, p\in(0,1)$, $N>2s$, $(-\Delta)^{s}$ is a fractional Laplacian operator, and K, V both change sign in $\mathbb{R}^{N}$. 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.

[学科分类] 电力

[关键词] Fractional Schrödinger equation;Indefinite potential;Symmetric mountain pass theorem