Infinitely many positive solutions for the nonlinear Shcrodinger equations in $R^N$

Details Infinitely many positive solutions for the nonlinear Shcrodinger equations in $R^N$ Infinitely many positive solutions for the nonlinear Shcrodinger equations in $R^N$

2008-04-25

arxiv.org/abs/0804.4031v1

Calculus of Variations and Partial Differential Equations 37(2010),423-439

Mathematics

Analysis of PDEs

17 pages

Scientific paper

We consider the following nonlinear problem in $\R^N$ $$\label{eq} - \Delta u +V(|y|)u=u^{p},\quad u>0 {in} \R^N, u \in H^1(\R^N) $$ where $V(r)$ is a positive function, $1

0$, $m>1$, $\theta>0$, and $V_0>0$, such that \[ V(r)= V_0+\frac a {r^m} +O\bigl(\frac1{r^{m+\theta}}\bigr),\quad \text{as $r\to +\infty$,} \] then \eqref{eq} has {\bf infinitely many non-radial positive} solutions, whose energy can be made arbitrarily large.

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