Abstract

We establish the existence of a positive solution for the following non-variational equation {(- div (| x |- 2 a ∇ u) = | x |- 2 (a + 1) + c f (x, u, ∇ u),, in Ω; u = 0,, on ∂ Ω,) where the non-linearity f (x, t, ξ) belongs to a class of functions that are superlinear in the variable t and sublinear in the variable ξ. For this purpose we used an idea of a recent work by De Figueiredo et al. [D. De Figueiredo, M. Girardi, M. Matzeu, Semilinear elliptic equations with dependence on the gradient via mountain-pass techniques, Diff. Integral Equ. (in press)] and we established a new regularity result for a class of Singular Elliptic Equations. © 2005 Elsevier Ltd. All rights reserved.