Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 96, Issue -, Pages 154-166Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2013.11.006
Keywords
Nonlinear elliptic problem; Gradient dependence; Leray-Lions operator; Sub-supersolution; Regularity; Maximum principle
Categories
Funding
- Fapemig CEX [APQ-02406-12]
- CEX APQ [00025/11]
- CNPq/Brazil
- UFJF-Edital [02/2013PROPG]
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The existence of positive solutions for nonlinear elliptic problems under Dirichlet boundary condition is studied as well as the compactness and directness of the solution set. The main novelties consist in the presence of a Leray-Lions operator in the differential part and in the dependence of the reaction term on the gradient of the solution. Our approach relies on the method of sub-supersolution, nonlinear regularity theory and strong maximum principle. (C) 2013 Elsevier Ltd. All rights reserved.
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