Solution manifolds for some semilinear Schrodinger equations

Details Solution manifolds for some semilinear Schrodinger equations Solution manifolds for some semilinear Schrodinger equations

2012-04-04

arxiv.org/abs/1204.0935v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper, we study the following semilinear Schr\"odinger system $$
-\triangle u+u=(1+K_\alpha(\epsilon x))|u|^{p-2}u\ in \mathbb{R}^N, u\in
H^1(\mathbb{R}^N) $$ where $3\leq p<2^*$ 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.

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