Copyright © 2010 Yujun Cui and 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.
We obtain some new existence theorems of the maximal and minimal
fixed points for discontinuous monotone operator on an order interval in an ordered normed
space. Moreover, the maximal and minimal fixed points can be achieved by monotone iterative
method under some conditions. As an example of the application of our results, we show the
existence of extremal solutions to a class of discontinuous initial value problems.