Existence and multiplicity of solutions for a non-periodic Schrödinger equation

This paper is concerned with the non-periodic Schrödinger equation {−Δu+V(x)u=f(x,u),x∈RNu(x)→0as|x|→∞. Under a general spectral assumption, the existence and multiplicity of solutions are obtained for asymptotically linear nonlinearity via variational methods.