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Existence result for critical Klein-Gordon-Maxwell system involving steep potential well
  • Canlin Gan,
  • Weiwei Wang
Canlin Gan
School of Mathematics and Statistics, Xidian University

Corresponding Author:gclmath@163.com

Author Profile
Weiwei Wang
School of Mathematics and Statistics, Xidian University

Abstract

The Klein-Gordon-Maxwell system has received great attention in the community of mathematical physics. Under a special superlinear condition on the nonlinear term, the existence of solution for critical Klein-Gordon-Maxwell system with steep potential well has been solved. In this paper, under two general superlinear conditions, we obtain the existence of ground state solution for the critical Klein-Gordon-Maxwell system with steep potential well. The general superlinear conditions bring challenge in proving the boundedness of Cerami sequence, which is a key step in the proof of the existence. To solve this, we construct a Poho┼żaev identity and adopt some analytical techniques. Our results extend the previous results in the literature.