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

Canlin Gan; Weiwei Wang; Canlin Gan; Weiwei Wang

doi:10.3934/math.20231364

AIMS Mathematics

2023, Volume 8, Issue 11: 26665-26681. doi: 10.3934/math.20231364

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Research article

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

Canlin Gan ,
Weiwei Wang ^,

School of Mathematics and Statistics, Xidian University, Xi'an 710126, China

Received: 02 August 2023 Revised: 18 August 2023 Accepted: 21 August 2023 Published: 19 September 2023
MSC : 35J20, 35J62

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.
- Klein-Gordon-Maxwell system,
- critical growth,
- steep potential well,
- ground state solution,
- variational methods
Citation: Canlin Gan, Weiwei Wang. Existence result for the critical Klein-Gordon-Maxwell system involving steep potential well[J]. AIMS Mathematics, 2023, 8(11): 26665-26681. doi: 10.3934/math.20231364

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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 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.

References

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