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

Abstract

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−2 s, p > 1. The singularity may appear at u = 0 and t = 0