Multiple solutions for a semiclassical Schrödinger equation

This paper is concerned with the semiclassical nonlinear Schrödinger equation {−ε2Δu+V(x)u=f(x,u),x∈RNu(x)→0as |x|→∞. where ε>0ε>0 is a small parameter. Under certain hypotheses on VV and a general spectral assumption, the existence and multiplicity of semiclassical solutions are obtained for asymptotically linear nonlinearity via variational methods.