Infinitely many solutions for fractional Schr\"odinger equations in R^N

Abstract

Using variational methods we prove the existence of infinitely many solutions to the fractional Schrodinger equation $$ (-\Delta)^su+V(x)u=f(x,u), \quad x\in\mathbb{R}^N, $$ where $N\ge 2, s\in (0,1)$. $(-\Delta)^s$ stands for the fractional Laplacian. The potential function satisfies $V(x)\geq V_0>0$. The nonlinearity f(x,u) is superlinear, has subcritical growth in u, and may or may not satisfy the (AR) condition.

Keywords

• Fractional Schrodinger equation
• variational methods
• (PS) condition
• (C)c condition