Existence of multiple positive solutions for one-dimensional p-Laplacian

In this paper we consider the multipoint boundary value problem for one-dimensional p-Laplacian φp(u ) +f (t,u) = 0, t∈ (0, 1), subject to the boundary value conditions: φp u (0) = n−2 i=1 aiφp u (ξi ) , u(1) = n−2 i=1 biu(ξi ), where φp(s) = |s|p−2s, p >1, ξi ∈ (0, 1) with 0 < ξ1 < ξ2 < ··· < ξn−2 < 1, and ai, bi satisfy ai, bi ∈ [0,∞], 0 < n−2 i=1 ai < 1, and n−2 i=1 bi < 1. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem.  2005 Elsevier Inc. All rights reserved