Ground state solutions of Nehari-Pohozaev type for Schrödinger-Poisson problems with zero mass

Abstract

In this paper, we consider the following Schrödinger-Poisson problem with zero mass{−Δu+ϕu=f(u),x∈R3,−Δϕ=u2,x∈R3. By using some new tricks, we prove that the above problem has a ground state solution of Nehari-Pohozaev type under some mild assumptions on f. It is worth pointing out that our results generalize and improve the ones in Ianni and Ruiz (2012) [12] and some related literature.