Existence of positive solutions for nonlinear Dirichlet problems with gradient dependence and arbitrary growth - Nikolaos Papageorgiou; Calogero Vetro; Francesca Vetro (Electronic Journal of Qualitative Theory of Differential Equations, 2018)
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.