Positive solutions of fourth-order four-point boundary value problems with p-Laplacian operator ✩

In this paper, we consider the existence of positive solutions for the singular fourth-order p-Laplacian equation ϕp u (t) = f t,u(t) , 0 < t <1, with the four-point boundary conditions u(0) = 0, u(1) = au(ξ ), u (0) = 0, u (1) = bu (η), where ϕp(t) = |t |p−2t , p >1, 0 < ξ,η<1, f ∈ C((0, 1) × (0,+∞), [0,+∞)) may be singular at t = 0 and/or 1 and u = 0. By using the upper and lower solution method and fixed-point theorems, the existence of positive solutions to the above the boundary value problem is obtained. © 2007 Elsevier Inc. All rights reserved.