An existence result for $p$-Laplace equation with gradient nonlinearity in ${\mathbb{R}}^N$

Shilpa Gupta, Gaurav Dwivedi

We prove the existence of a weak solution to the problem \begin{equation*} \begin{split} -Δ_{p}u+V(x)|u|^{p-2}u & =f(u,|\nabla u|^{p-2}\nabla u), \ \ \ \\ u(x) & >0\ \ \forall x\in…