Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (2): 442-453.

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Multiplicity of Normalized Solutions for Nonlinear Schrödinger-Poisson Equation with Hardy Potential

Mengxue Du,Fanghui Li,Zhengping Wang*()   

  1. Center of Mathematics, Wuhan University of Technology, Wuhan 430070
  • Received:2021-06-23 Online:2022-04-26 Published:2022-04-18
  • Contact: Zhengping Wang E-mail:zpwang@whut.edu.cn
  • Supported by:
    the NSFC(11871386);the NSFC(11931012)

Abstract:

In this paper, we concern the multiplicity of normalized solutions for a class of nonlinear Schrödinger-Poisson equation with Hardy potential. By using some ideas of the fountain theorem, we define a sequence of minimax values and prove that these minimax values are critical values of the energy functional limited to a constraint set. Then we get the multiplicity of normalized solutions, which extends some related results in the literature.

Key words: Schrödinger-Poisson equation, Hardy potential, Normalized solution, Multiplicity

CLC Number: 

  • O175.2
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