A Singular nonlinear problems with natural growth in the gradient

Abstract

In this paper, we consider the equation with boundary conditions where is an open bounded subset of is a Leray-Lions operator defined on is a characteristic function, and is a Carathéodory function such thatsign Forand sufficiently small, we prove the existence of at least one solution u of this problem which is moreover such that the function belongs tofor some This solution satisfies some a priori estimates in

Keywords

• nonlinear problems
• existence
• singularity