Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth

Nikolaos Papageorgiou, Calogero Vetro, Francesca Vetro
2018 Electronic Journal of Qualitative Theory of Differential Equations  
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.
doi:10.14232/ejqtde.2018.1.18 fatcat:jelirpgt75hozm63yi6simgxhi