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Abstract

This paper is concerned with the following Klein–Gordon–Maxwell system ${\begin{cases} - Δ u + V (x) u - (2 ω + ϕ) ϕ u = f (u), & x \in Ω, \\ Δ ϕ = (ω + ϕ) u^{2}, & x \in Ω, \\ ϕ = u = 0, & x \in \partial Ω, \end{cases}$ where $Ω \subset R^{2}$ is a smooth bounded domain, $u, ϕ : Ω \to R$ , $V \in C (\bar{Ω}, R)$ and $f \in C (R, R)$ obeys exponential growth in the sense of the Trudinger–Moser inequality. We prove that the above system has the least energy solution and infinitely many solutions in a bounded domain of the plane, which complement and extend the results before.

Keywords

Klein–Gordon–Maxwell system exponential growth Trudinger–Moser inequality infinitely many solutions least energy solutions

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Least Energy Solutions and Infinitely Many Solutions for Klein–Gordon–Maxwell System With Exponential Growth

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