Journal of Guangxi Normal University(Natural Science Edition) ›› 2018, Vol. 36 ›› Issue (4): 59-66.doi: 10.16088/j.issn.1001-6600.2018.04.008

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Ground State Solutions for the NonlinearSchrödinger-Maxwell Equations

JIANG Yingxing, HUANG Wennian*   

  1. College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China
  • Received:2017-10-19 Published:2018-10-20

Abstract: In this paper, under some assumptions of V, K and f, the following nonlinear Schrödinger-Maxwell equations are studied.
-Δu+V(x)u+K(x)φu=f(x,u), in R3,
-Δφ=K(x)u2, in R3.
First, the nontrivial solution of Schrödinger-Maxwell equations is obtained by using mountain pass theorem. Then, it is shown that the functional is achieved on Nehari manifold, and finally, ground state solutions of Schrödinger-Maxwell equations are obtained. Some conditions in previous literatures are weakened and the conclusions of high energy solutions in previous references are generalized in this paper.

Key words: Schrödinger-Maxwell equations, mountain pass theorem, ground state solution, Nehari manifold

CLC Number: 

  • O175.25
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