2022 Some existence results for elliptic systems with exponential nonlinearities and convection terms in dimension two
Wei Liu
Topol. Methods Nonlinear Anal. 60(2): 673-697 (2022). DOI: 10.12775/TMNA.2022.025

Abstract

In this paper, we establish the existence of solutions to a class of elliptic systems. The nonlinearities include exponential growth terms and convection terms. The exponential growth term means it could be critical growth at $\infty$. The Trudinger-Moser inequality is used to deal with it. The convection term means it involves the gradient of unknown function. The strong convergence of sequences is employed to overcome the difficulties caused by convection terms. The variational methods are invalid and the Galerkin method and an approximation scheme are applied to obtain four different solutions. Our results supplements those from [11].

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Wei Liu. "Some existence results for elliptic systems with exponential nonlinearities and convection terms in dimension two." Topol. Methods Nonlinear Anal. 60 (2) 673 - 697, 2022. https://doi.org/10.12775/TMNA.2022.025

Information

Published: 2022
First available in Project Euclid: 10 December 2022

MathSciNet: MR4563253
zbMATH: 1512.35250
Digital Object Identifier: 10.12775/TMNA.2022.025

Keywords: convection terms , exponential growth , Galerkin method , Trudinger-Moser inequality

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.60 • No. 2 • 2022
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