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Existence of solution for elliptic equations with supercritical Trudinger–Moser growth

Part of: Elliptic equations and systems Partial differential equations Infinite-dimensional dissipative dynamical systems

Published online by Cambridge University Press:  16 February 2021

Luiz F. O. Faria  and
Marcelo Montenegro
Luiz F. O. Faria
Affiliation:
Departamento de Matemática, Universidade Federal de Juiz de Fora, ICE, Campus Universitário, Rua José Lourenço Kelmer, s/n, Juiz de Fora, MG, CEP 36036-900, Brazil ([email protected])
Marcelo Montenegro
Affiliation:
Departamento de Matemática, Universidade Estadual de Campinas, IMECC, Rua Sérgio Buarque de Holanda, 651, Campinas, SP, CEP 13083-859, Brazil ([email protected])
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Abstract

This paper is concerned with the existence of solutions for a class of elliptic equations on the unit ball with zero Dirichlet boundary condition. The nonlinearity is supercritical in the sense of Trudinger–Moser. Using a suitable approximating scheme we obtain the existence of at least one positive solution.

Keywords

Elliptic equationpositive solutionsupercritical exponential growth

MSC classification

Primary: 35J25: Boundary value problems for second-order elliptic equations 35B33: Critical exponents
Secondary: 37L65: Special approximation methods (nonlinear Galerkin, etc.) 35B09: Positive solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 2 , April 2022 , pp. 291 - 310
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Copyright
Copyright © The Author(s) 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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