AIMS Mathematics (Sep 2023)

Existence result for the critical Klein-Gordon-Maxwell system involving steep potential well

  • Canlin Gan ,
  • Weiwei Wang

DOI
https://doi.org/10.3934/math.20231364
Journal volume & issue
Vol. 8, no. 11
pp. 26665 – 26681

Abstract

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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 the critical Klein-Gordon-Maxwell system with a 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 a 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 Pohožaev identity and adopt some analytical techniques. Our results extend the previous results in the literature.

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