Sign-changing solutions for Schrödinger equations with indefinite supperlinear nonlinearities

Abstract

In this paper, we obtain existence of ground state solutions and ground state sign-changing solutions for the following Schrödinger equation {−Δu+V(x)u=K(x)|u|p−2uin RNu→0as |x|→+∞, where N≥3, 2<p<2∗:=2N/(N−2), V(x) and K(x) are sign-changing functions satisfying very mild assumptions. The proofs rely on a new perturbed method which we design in this paper.