GROUND STATE SOLUTIONS OF NEHARI-POHOZAEV TYPE FOR SCHRODINGER-POISSON PROBLEMS WITH GENERAL POTENTIALS

This paper is dedicated to studying the following Schrodinger-Poisson problem {-Delta u + V(x)u + phi u - f(u), x is an element of R-3 -Delta phi + u(2), x is an element of R-3 , where V(x) is weakly differentiable and f E is an element of 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.