Ground state solution and nodal solution for fractional nonlinear Schrödinger equation with indefinite potential

Abstract

We prove that under some mild assumptions, the nonlinear fractional Schrödinger equation (−Δ)su+V(x)u=f(u) (x∈RN), where V(x) is an indefinite potential, has two nonzero solutions: one is a positive ground state solution, and the other is a sign-changing solution.