Copyright © 2012 Ying Chen and Shihuang Hong. 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

This paper presents sufficient conditions for the existence of positive solutions for a class of integral inclusions. Our results are obtained via a new fixed point theorem for multivalued operators developed in the paper, in which some nonnegative function is used to describe the cone expansion and compression instead of the classical norm-type, and lead to new existence principles.