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

Abstract

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.

Keywords

• Fractional Schrödinger equation
• Indefinite potential
• Symmetric mountain pass theorem