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: (-) s u + V(x)u = K(x)|u| p-1 u, x ∈ R N , where s, p ∈ (0, 1), N > 2s, (-) s is a fractional Laplacian operator, and K, V both change sign in 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.