Standing waves for nonlinear Schrodinger equations with singular potentials

Abstract

We study semiclassical states of nonlinear Schrodinger equations with anisotropic type potentials which may exhibit a combination of vanishing and singularity while allowing decays and unboundedness at infinity. We give existence of spike type standing waves concentrating at the singularities of the potentials. (C) 2008 Elsevier Masson SAS. All rights reserved.