Multiple positive solutions for second-order four-point boundary value problem

Abstract

In this paper, we consider the following boundary value problem with a p-Laplacian (φ{symbol}p (x′ (t)))′ + f (t, x (t), x′ (t)) = 0, 0 < t < 1,α x (0) - β x′ (ξ) = 0, γ x (1) + δ x′ (η) = 0 . 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 problem. The emphasis is laid on how to deal with the new boundary condition to obtain the existence of positive solutions. © 2007 Elsevier Ltd. All rights reserved.