Electron. J. Diff. Equ., Vol. 2016 (2016), No. 88, pp. 1-15.

Infinitely many solutions for fractional Schrodinger equations in $\mathbb{R}^N$

Caisheng Chen

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.

Submitted January 31, 2016. Published March 30, 2016.
Math Subject Classifications: 35R11, 35A15, 35J60, 47G20.
Key Words: Fractional Schrodinger equation; variational methods; (PS) condition; (C)c condition

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Caisheng Chen
College of Science, Hohai University
Nanjing 210098, China
email: cshengchen@hhu.edu.cn

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