Abstract
Let D be a bounded domain in R-n (n >= 2). We consider the following nonlinear elliptic problem: Delta u = f ((.), u) in D (in the sense of distributions), u\partial derivative D = phi, where phi is a nonnegative continuous function on partial derivative D and f is a nonnegative function satisfying some appropriate conditions related to some Kato class of functions K(D). Our aim is to prove that the above problem has a continuous positive solution bounded below by a fixed harmonic function, which is continuous on D. Next, we will be interested in the Dirichlet problem Delta u =-rho(., u) in D (in the sense of distributions), u\partial derivative D = 0, where rho is a nonnegative function satisfying some assumptions detailed below. Our approach is based on the Schauder fixed-point theorem. Copyright (c) 2006 Faten Toumi.