Harnack’s Inequality for Quasilinear Elliptic Equations with Singular Absorption Term

In this article we study nonnegative solutions of quasilinear equation model of which is −△pu+V(x)f(u)=h(x)|∇u|p−1+g(x),p>1.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\triangle_{p} u+V(x) f(u)= h(x)|\nabla u|^{p-1}+g(x), \,\,\,\, p>1.$$\end{document} Under the natural assumptions on the functions f, V, h and g we prove the Harnack inequality with constant independent of the solution. In the case g(x) ≡ V (x) we obtain an analogue of the well known Kilpeläinen-Malý sub-bound.