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

作者：Tang, Xianhua^*; Chen, Sitong

来源：Discrete and Continuous Dynamical Systems, 2017, 37(9): 4973-5002.

DOI：10.3934/dcds.2017214

• Schrodinger-Poisson problem
• ground state solution of Nehari-Pohozaev type
• the least energy solutions

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.

• 出版日期2017-9
• 单位中南大学