Journal
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY
Volume 57, Issue 3, Pages 687-698Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S0013091513000576
Keywords
quasi-linear elliptic equation; (p, q)-Laplacian; convection term; positive solution; approximation; comparison
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Funding
- INCTmat/MCT-Brazil
- Fapemig [CEX APQ 01960/10, CEX BPV 00030/11]
- CNPq/Brazil
- CEX APQ [00025/11]
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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.
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