Solution manifolds for some semilinear Schrodinger equations

Abstract

In this paper, we study the following semilinear Schrödinger system $$-△u+u=(1+K_{\alpha }(\epsilon x))|u{|}^{p-2}uin{\mathbb{R}}^N,u\in H^1({\mathbb{R}}^N)$$ where $3\le p<2^{\ast }$ and $\epsilon >0$, $\alpha >0$ are small parameters. Under some conditions on $K_{\alpha }$ and the parameters $\alpha$ and $\epsilon$, we show that this equation exist solution manifolds.

This paper has been withdrawn by the author due to a crucial error