Existence and concentration of semiclassical states for nonlinear Schrodinger equations

Abstract

In this paper, we study the following semilinear Schrödinger equation $$-{\epsilon }^2△u+u+V(x)u=f(u),u\in H^1({\mathbb{R}}^N),$$ where $N\ge 2$ and $\epsilon >0$ is a small parameter. The function $V$ is bounded in ${\mathbb{R}}^N$, ${\inf }_{{\mathbb{R}}^N}(1+V(x))>0$ and it has a possibly degenerate isolated critical point. Under some conditions on $f,$ we prove that as $\epsilon \to 0,$ this equation has a solution which concentrates at the critical point of $V$.}

arXiv comment35 pages; Electron. J. Diff. Equ. 2012 No. 85

References in corpus (1)

• Multiplicity results for some nonlinear Schroedinger equations with potentials