Ground state solutions of Nehari-Pohozaev type for Schrödinger-poisson problems with general potentials

Abstract

This paper is dedicated to studying the following Schrödinger-Poisson problem -Δu+V (x)u + φu = f(u); x ϵ R3;-Δφ = u2; x ϵ R3; where V (x) is weakly differentiable and f 2 C(R;R). By introducing some new tricks, we prove the above problem admits a ground state solution of Nehari-Pohozaev type and a least energy solution under mild assumptions on V and f. Our results generalize and improve the ones in [D. Ruiz, J. Funct. Anal. 237 (2006) 655-674], [J.J. Sun, S.W. Ma, J. Differential Equations 260 (2016) 2119-2149] and some related literature.