Infinitely many positive solutions for nonlinear fractional Schrödinger equations

Abstract

We consider the following nonlinear fractional Schrödinger equation $$(-\Delta {)}^{s}u+u=K(|x|)u^p,u>0in{R}^N,$$ 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

References in corpus (2)

• Concentration phenomenon for fractional nonlinear Schrödinger equations
• Uniqueness of radial solutions for the fractional Laplacian