Copyright © 2012 Yulin Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem (-1)n-kun(t)=f(t,ut), 0<t<1, n≥2, 1≤k≤n-1, u(0)=∑i=1m-2‍aiu(ξi), u(i)(0)=u(j)(1)=θ, 1≤i≤k−1, 0≤j≤n−k−1 in a real Banach space E, where θ is the zero element of E, 0 < ξ1 < ξ2<⋯<ξm-2<1,ai∈[0,+∞),i=1,2,…,m-2. As an application, we give two examples to demonstrate our results.