Infinitely many positive solutions for nonlinear fractional Schrödinger equations
Abstract
We consider the following nonlinear fractional Schrödinger equation $$ (\Delta)^su+u=K(x)u^p,\ \ u>0 \ \ \hbox{in}\ \ R^N, $$ where $K(x)$ is a positive radial function, $N\ge 2$, $0<s<1$, $1<p<\frac{N+2s}{N2s}$. Under some asymptotic assumptions on $K(x)$ at infinity, we show that this problem has infinitely many nonradial positive solutions, whose energy can be made arbitrarily large.
 Publication:

arXiv eprints
 Pub Date:
 February 2014
 arXiv:
 arXiv:1402.1902
 Bibcode:
 2014arXiv1402.1902L
 Keywords:

 Mathematics  Analysis of PDEs;
 35J20;
 35J60
 EPrint:
 22pages. arXiv admin note: text overlap with arXiv:0804.4031, arXiv:1305.4426 by other authors