Sur les solutions d'un operateur differentiel singulier semi-lineaire

摘要

This paper deals with the following Dirichlet problem {Lu = 1/A (Au')'-qu = -f(centre dot, u) on]0, #omega#[, (*) u'(0) = 0, u(#omega#) = 0, where #omega# implied by]0, + infinity], q >= 0 is continuous on [0, #omega#[,,f:[0, #omega#[*]0, + infinity[ is continuous and A satisfies some appropriate conditions. The main results is the existence and the uniqueness of a strictly positive regular solution of the problem (*). Moreover, we study the behaviour of this solution in a neighbourhood of #omega#. Our approach is based on the use of the Green's function of the homogeneous equation and Schauder's fixed point theorem.