@article{Gan2023, 
author = {Canlin Gan and Weiwei Wang},
title = {Existence result for the critical Klein-Gordon-Maxwell system involving steep potential well},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {11},
pages = {26665-26681},
keywords = {Klein-Gordon-Maxwell system, critical growth, steep potential well, ground state solution, variational methods},
url = {https://www.sciopen.com/article/10.3934/math.20231364},
doi = {10.3934/math.20231364},
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.}
}