Electron. J. Differential Equations, Vol. 2018 (2018), No. 182, pp. 1-14.

Nonlinear Robin problems with unilateral constraints and dependence on the gradient

Nikolaos S. Papageorgiou, Calogero Vetro, Francesca Vetro

We consider a nonlinear Robin problem driven by the p-Laplacian, with unilateral constraints and a reaction term depending also on the gradient (convection term). Using a topological approach based on fixed point theory (the Leray-Schauder alternative principle) and approximating the original problem using the Moreau-Yosida approximations of the subdifferential term, we prove the existence of a smooth solution.

Submitted December 17, 2017. Published November 13, 2018.
Math Subject Classifications: 35J20, 35J60, 35J92.
Key Words: p-Laplacian; Robin boundary condition; subdifferential term; convection term; nonlinear regularity; maximal monotone map; fixed point.

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  Nikolaos S. Papageorgiou
National Technical University
Department of Mathematics, Zografou campus
15780, Athens, Greece
email: npapg@math.ntua.gr
Calogero Vetro
University of Palermo
Department of Mathematics and Computer Science
Via Archirafi 34, 90123
Palermo, Italy
email: calogero.vetro@unipa.it
Francesca Vetro
Nonlinear Analysis Research Group
Ton Duc Thang University
Ho Chi Minh City, Vietnam
email: francescavetro@tdtu.edu.vn

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