Elliptic equations involving the $p$-Laplacian and a gradient term having natural growth

Djairo G. de Figueiredo, Jean-Pierre Gossez, Humberto Ramos Quoirin +1

We investigate the problem $$ \left\{ \begin{array}{ll} -Δ_p u = g(u)|\nabla u|^p + f(x,u) \ & \mbox{in} \ \ Ω, \ \ \\ u>0 \ &\mbox{in} \ \ Ω, \ \ u = 0 \ &\mbox{on} \ \ \partialΩ,…