Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials

We establish the existence and multiplicity of semiclassical bound states of the following nonlinear Schrödinger equation: −ε2 u +V (x)u = g(x,u) for x ∈ RN, u(x)→0 as |x|→∞ where V changes sign and g is superlinear with critical or supercritical growth as |u|→∞. © 2007 Elsevier Inc. All rights reserved.