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