Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (3): 475-483.

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Ground-State Solutions for Schrödinger-Maxwell Equations in the Critical Growth

Liwan Fang1(),Wennian Huang2(),Minqing Wang2()   

  1. 1 School of Mathematics and Computer Science, Guangxi Science and Technology Normal University; Guangxi Laibin 546199
    2 School of Mathematics and Statistics, Guangxi Normal University, Guangxi Guilin 541004
  • Received:2017-04-28 Online:2019-06-26 Published:2019-06-27
  • Supported by:
    the Science Research Fund of Guangxi Normal University(2014ZD001);the Natural Science Foundation of Guangxi(2015GXNSFBA139018);the Postgraduate Education Innovation Plan Project of Guangxi in 2017(XYCZ2017074)


In this paper, we study the existence of the ground state solutions for the following Schrödinger-Maxwell equations

where β is a positive constant. Under some assumptions on V, K and b(x), by using the variational method and critical point theorem, we prove that such a class of equations has at least a ground state solution for α < 0 and p ∈ (3, 4).

Key words: Schrödinger-Maxwell equations, Critical point theorem, Critical growth, Ground state solution, Nehari manifold

CLC Number: 

  • O175.25