Multiple positive solutions for boundary value problems of second order delay differential equations with one-dimensional p-Laplacian

We consider the boundary value problems: (φp(x (t))) + q(t)f (t,x(t),x(t − 1), x (t)) = 0, φp(s) = |s|p−2s, p >1, t ∈ (0, 1), subject to some boundary conditions. By using a generalization of the Leggett– Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions to the above problems. © 2006 Elsevier Inc. All rights reserved