An improved result for a class of Klein–Gordon–Maxwell system with quasicritical potential vanishing at infinity

Canlin Gan, Ting Xiao and Qiongfen Zhang

Mathematische Nachrichten, 2023, vol. 296, issue 8, 3318-3327

Abstract: The following kind of Klein–Gordon–Maxwell system is investigated −Δu+V(x)u−(2ω+ϕ)ϕu=K(x)f(u),inR3,Δϕ=(ω+ϕ)u2,inR3,$$\begin{equation*} \hspace*{4pc}{\left\lbrace \begin{aligned} &{-\Delta u+ V(x) u-(2\omega +\phi ) \phi u=K(x)f(u)}, & & {\quad \text{ in } \mathbb {R}^{3}}, \\ &{\Delta \phi =(\omega +\phi ) u^{2}}, & & {\quad \text{ in } \mathbb {R}^{3}}, \end{aligned}\right.} \end{equation*}$$where ω>0$\omega >0$ is a parameter, and V is vanishing potential. By using some suitable conditions on K and f, we obtain a Palais–Smale sequence by using Pohožaev equality and prove the ground‐state solution for this system by employing variational methods. Our result improves the related one in the literature.

Date: 2023
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