On pairs of positive solutions for a singular boundary value

Abstract

In this paper, we study the existence of multiple solutions of some singular boundary value problems where p can be equal to zero at t = 0 and t = T, the function g can be singular at t = 0, t = T and a h for u = 0. Such singularities generalize Emden-Fowler equations. We consider the case where the “slope” is larger than the first eigenvalue near 0 and near infinity. In between the slope is controlled from the existence of a strict upper solution. To prove our result we extend to the singular case the theory of lower and upper solutions a;nd its relation with the Leray-Schauder degree.