Multiple solutions for perturbed semilinear Schrödinger equations

Abstract

In this paper, we study multiple solutions for a class of perturbed semilinear Schrödinger equations −△u+V(x)u=f(x,u)+λg(x,u), u∈H1(RN), where f(x,u) is odd in u, and λg(x,u) is regarded as a perturbation term with parameter λ, which is not necessarily odd in u. Under some mild conditions on f and g, we prove that they admit arbitrarily many solutions provided that the perturbation parameter |λ| is small enough.