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.
Papageorgiou, N.S., Vetro, C., Vetro, F. (2018). NONLINEAR ROBIN PROBLEMS WITH UNILATERAL CONSTRAINTS AND DEPENDENCE ON THE GRADIENT. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2018(182), 1-14.
NONLINEAR ROBIN PROBLEMS WITH UNILATERAL CONSTRAINTS AND DEPENDENCE ON THE GRADIENT
Vetro, Calogero;Vetro, Francesca
2018-01-01
Abstract
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.
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