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Zeitschrift für Analysis und ihre Anwendungen


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Volume 38, Issue 2, 2019, pp. 231–247
DOI: 10.4171/ZAA/1636

Published online: 2019-04-09

A Nonlinear Klein–Gordon– Maxwell System in $\mathbb{R}^{2}$ Involving Singular and Vanishing Potentials

Lin Li[1] and Francisco S.B. Albuquerque[2]

(1) Chongqing Technology and Business University, China
(2) Universidade Estadual da Paraíba, Campina Grande, Brazil

In this paper, a nonlinear Klein–Gordon–Maxwell system in $\mathbb{R}^{2}$ and involving singular and vanishing potentials is considered. Under some mild assumptions on the potentials and nonlinearity, using variational methods and a Trudinger–Moser-type inequality, we establish sufficient conditions for the existence of solution.

Keywords: Klein–Gordon–Maxwell system, Trudinger–Moser inequality, radial potentials, exponential critical growth, Mountain–Pass Theorem

Li Lin, Albuquerque Francisco: A Nonlinear Klein–Gordon– Maxwell System in $\mathbb{R}^{2}$ Involving Singular and Vanishing Potentials. Z. Anal. Anwend. 38 (2019), 231-247. doi: 10.4171/ZAA/1636