Existence of ground state solutions for Klein–Gordon–Maxwell systems with a weighted critical exponent

The Klein–Gordon–Maxwell systems with Sobolev critical exponent have been investigated widely in the existing works. In this paper, we prove the existence of ground state solutions for the Klein–Gordon–Maxwell systems with a weighted Hénon–Sobolev or Hardy–Sobolev-type critical exponent, which have not been studied so far. The proof requires establishing the boundedness of Palais–Smale sequence of the associated system. However, the presence of the nonlocal term brings difficulties. We construct a Pohožaev identity and adopt some analytical techniques to overcome these difficulties. Our results are novel in the literature.