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

2017
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Discrete and Continuous Dynamical Systems. Series A
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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