Boundary Value Problems
Volume 2011 (2011), Article ID 567054, 14 pages
doi:10.1155/2011/567054
Research Article

New Fixed Point Theorems of Mixed Monotone Operators and Applications to Singular Boundary Value Problems on Time Scales

Huiye Xu

College of Economics and Management, North University of China, Taiyuan, Shanxi 030051, China

Received 3 July 2010; Accepted 13 December 2010

Academic Editor: Daniel Franco

Copyright © 2011 Huiye Xu. 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

Some new existence and uniqueness theorems of fixed points of mixed monotone operators are obtained, and then they are applied to a nonlinear singular second-order three-point boundary value problem on time scales. We prove the existence and uniqueness of a positive solution for the above problem which cannot be solved by using previously available methods.