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Comparison and Positive Solutions for Problems with the (p, q)-Laplacian and a Convection Term

Published online by Cambridge University Press:  16 April 2014

Luiz F. O. Faria ,
Olímpio H. Miyagaki  and
Dumitru Motreanu
Luiz F. O. Faria
Affiliation:
Departamento de Matemática – ICE, Universidade Federal de Juiz de Fora, Juiz de Fora, CEP 36036-330, Minas Gerais, Brazil
Olímpio H. Miyagaki
Affiliation:
Departamento de Matemática – ICE, Universidade Federal de Juiz de Fora, Juiz de Fora, CEP 36036-330, Minas Gerais, Brazil
Dumitru Motreanu
Affiliation:
Département de Mathématiques, Université de Perpignan, 66860 Perpignan, France, (xlink:href="[email protected]">[email protected])
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Abstract

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The aim of this paper is to prove the existence of a positive solution for a quasi-linear elliptic problem involving the (p, q)-Laplacian and a convection term, which means an expression that is not in the principal part and depends on the solution and its gradient. The solution is constructed through an approximating process based on gradient bounds and regularity up to the boundary. The positivity of the solution is shown by applying a new comparison principle, which is established here.

Keywords

quasi-linear elliptic equation(p, q)-Laplacianconvection termpositive solutionapproximationcomparisonPrimary 35J60Secondary 35J92
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 3 , October 2014 , pp. 687 - 698
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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