Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (4): 934-944.doi: 10.1007/s10473-020-0404-2

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GROUND STATE SOLUTIONS FOR A SCHRÖDINGER-POISSON SYSTEM WITH UNCONVENTIONAL POTENTIAL

Yao DU1,2, Chunlei TANG1   

  1. 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
    2. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
  • Received:2019-06-24 Revised:2019-10-31 Online:2020-08-25 Published:2020-08-21
  • Contact: Chunlei TANG E-mail:tangcl@swu.edu.cn
  • Supported by:
    The second author was supported by National Natural Science Foundation of China (11471267) and the first author was supported by Graduate Student Scientific Research Innovation Projects of Chongqing (CYS17084).

Abstract: We consider the Schrödinger-Poisson system with nonlinear term $Q(x)|u|^{p-1}u$, where the value of $\displaystyle\lim_{|x|\rightarrow\infty} Q(x)$ may not exist and $Q$ may change sign. This means that the problem may have no limit problem. The existence of nonnegative ground state solutions is established. Our method relies upon the variational method and some analysis tricks.

Key words: Schrödinger-Poisson system, ground state solutions, no limit problem

CLC Number: 

  • 35J20
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