Existence of a positive solution for quasilinear elliptic equations with nonlinearity including the gradient

We provide the existence of a positive solution for the quasilinear elliptic equation in Ω under the Dirichlet boundary condition. As a special case ( ), our equation coincides with the usual p-Laplace equation. The solution is established as the limit of a sequence of positive solutions of approximate equations. The positivity of our solution follows from the behavior of as t is small. In this paper, we do not impose the sign condition to the nonlinear term f. MSC:35J92, 35P30.