Infinitely many positive solutions for nonlinear fractional Schrödinger equations

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.

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