Nonlinear Robin problems with unilateral constraints and dependence on the gradient

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.

Keywords

• p-Laplacian
• Robin boundary condition
• subdifferential term
• convection term
• nonlinear regularity
• maximal monotone map
• fixed point