Infinitely many positive solutions for nonlinear fractional Schrödinger equations

Abstract

We consider the following nonlinear fractional Schrödinger equation $$ (-Δ)^su+u=K(|x|)u^p,\ \ u>0 \ \ \hbox{in}\ \ R^N, $$ where $K(|x|)$ is a positive radial function, $N\ge 2$, $0<s<1$, $1<p<\frac{N+2s}{N-2s}$. Under some asymptotic assumptions on $K(x)$ at infinity, we show that this problem has infinitely many non-radial positive solutions, whose energy can be made arbitrarily large.

22pages. arXiv admin note: text overlap with arXiv:0804.4031, arXiv:1305.4426 by other authors