Existence of positive solutions for nonlinear dirichlet problems with gradient dependence and arbitrary growth
- Authors: Papageorgiou, Nikolaos; Vetro, Calogero; Vetro, Francesca
- Publication year: 2018
- Type: Articolo in rivista (Articolo in rivista)
- Key words: Convection reaction term; Hartman condition; Nonlinear maximum principle; Nonlinear regularity; Picone identity; Pseudomonotone map;
- OA Link: http://hdl.handle.net/10447/289082
Abstract
We consider a nonlinear elliptic problem driven by the Dirichlet p-Laplacian and a reaction term which depends also on the gradient (convection). No growth condition is imposed on the reaction term f (z, ·, y). Using topological tools and the asymptotic analysis of a family of perturbed problems, we prove the existence of a positive smooth solution.