%0 Journal Article
%T Existence and concentration of semiclassical states for nonlinear Schrodinger equations
%A Shaowei Chen
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X In this article, we study the semilinear Schrodinger equation $$ -epsilon^2Delta u+ u+ V(x)u=f(u),quad uin H^1(mathbb{R}^N), $$ where $Ngeq 2$ 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 $epsilon o 0$, this equation has a solution which concentrates at the critical point of V.
%K Semilinear Schrodinger equation
%K variational reduction method
%U http://ejde.math.txstate.edu/Volumes/2012/85/abstr.html