Existence results for nonlinear elliptic equations with Leray-Lions operator and dependence on the gradient

DOI10.1016/j.na.2013.11.006zbMath1285.35014OpenAlexW1987824611MaRDI QIDQ2436731

Mieko Tanaka, Luiz F. O. Faria, Motreanu, Dumitru, Olímpio Hiroshi Miyagaki

Publication date: 26 February 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2013.11.006

zbMATH Keywords

maximum principleregularitynonlinear elliptic problemLeray-Lions operatorsub-supersolutiongradient dependence

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Positive solutions to PDEs (35B09)

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Cites Work

• Multiple existence results of solutions for the Neumann problems via super- and sub-solutions
• Semilinear elliptic equations with dependence on the gradient via mountain-pass techniques.
• Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: an Orlicz-Sobolev space setting
• The maximum principle
• Existence results for quasilinear problems via ordered sub and supersolutions
• A priori estimates and existence of positive solutions for strongly nonlinear problems
• Existence of a positive solution for quasilinear elliptic equations with nonlinearity including the gradient
• Boundary regularity for solutions of degenerate elliptic equations
• The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
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