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This paper is dedicated to studying the following Schrödinger-Poisson problem where V (x) is weakly differentiable and f ∈ 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. ] and some related literature. 2010 Mathematics Subject Classification. 35J10, 35J20. Key words and phrases.doi:10.3934/dcds.2017214 fatcat:spyiu3zulngwfgnh24acflf4cu