Boundary Value Problems
Volume 2009 (2009), Article ID 978605, 22 pages
doi:10.1155/2009/978605
Research Article

Positive Solutions of Singular Multipoint Boundary Value Problems for Systems of Nonlinear Second-Order Differential Equations on Infinite Intervals in Banach Spaces

Xingqiu Zhang

School of Mathematics, Liaocheng University, Liaocheng, Shandong 252059, China

Received 27 April 2009; Accepted 12 June 2009

Academic Editor: Donal O'Regan

Copyright © 2009 Xingqiu Zhang. 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

The cone theory together with Mönch fixed point theorem and a monotone iterative technique is used to investigate the positive solutions for some boundary problems for systems of nonlinear second-order differential equations with multipoint boundary value conditions on infinite intervals in Banach spaces. The conditions for the existence of positive solutions are established. In addition, an explicit iterative approximation of the solution for the boundary value problem is also derived.