Multiple positive solutions for fourth-order three-point p-Laplacian boundary-value problems

Abstract

In this paper, we study the three-point boundary-value problem for a fourth-order one-dimensional p-Laplacian differential equation (φp(u″(t)))″ + α(t)ƒ(u(t)) = 0, t ∈ (0, 1), subject to the nonlinear boundary conditions: u(0) = ξu(1), u′(1) = ηu′(0), (φp(u″(0))′ = α1(φp(u″(δ))′, u″(1) = p-1√β1u″(δ), where φp(s) = |s|p-2s, p > 1. Using the five functional fixed point theorem due to Avery, we obtain sufficient conditions for the existence of at least three positive solutions.