Multiple positive solutions to a class of singular boundary value problems for the one-dimensional p-laplacian

In this paper, we establish the existence of multiple positive solutions to the singular nonlinear boundary value problem (φ(u′))′+ q(t)f(u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) + B(u′(1)) = 0, by using the Leray-Schauder alternative and the fixed-point theorem in cones, where φ(s) = s p−2s, p > 1. The singularity may appear at u = 0 and T = 0