International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 727468, 18 pages
Research Article

Positive Solutions for (k, nk) Conjugate Multipoint Boundary Value Problems in Banach Spaces

School of Science, Hunan University of Technology, Zhuzhou 412007, China

Received 20 March 2012; Revised 20 May 2012; Accepted 3 June 2012

Academic Editor: Mohamed-Aziz Taoudi

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.


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, n2, 1kn-1, u(0)=i=1m-2aiu(ξi), u(i)(0)=u(j)(1)=θ, 1ik1, 0jnk1 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.