Existence and Related Properties of Solutions for Klein–Gordon–Maxwell Systems

Xiao-Qi Liu and Chun-Lei Tang ()
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Xiao-Qi Liu: School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, China
Chun-Lei Tang: School of Statistics and Mathematics, Southwest University, Chongqing 400715, China

Mathematics, 2025, vol. 13, issue 12, 1-28

Abstract: This paper aims to present the application of variational methods in studying the existence and related properties of solutions for Klein–Gordon–Maxwell systems through a literature review. First, we give an introduction and variational framework for the Klein–Gordon–Maxwell system. Second, we review the existence and nonexistence of solutions for autonomous Klein–Gordon–Maxwell systems under subcritical growth, critical growth and zero-mass conditions. Third, we introduce studies on the existence and properties of solutions for Klein–Gordon–Maxwell systems classified according to potential functions. Finally, we review the existence of solutions for Klein–Gordon–Maxwell systems in two-dimensional space.

Keywords: variational method; critical point theory; elliptic equation; standing waves (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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