Search results for "convection reaction term"

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

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 $f(z, \cdot,y)$. Using topological tools and the asymptotic analysis of a family of perturbed problems, we prove the existence of a positive smooth solution.