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

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 throu...

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Bibliographic Details
Published in:Proceedings of the Edinburgh Mathematical Society 2014-10, Vol.57 (3), p.687-698
Main Authors: Faria, Luiz F. O., Miyagaki, Olímpio H., Motreanu, Dumitru
Format: Article
Language:English
Subjects:
Approximation
Boundaries
Construction
Convection
Mathematical analysis
Mathematics
Partial differential equations
Regularity
Theorems
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Summary: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.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091513000576