Abstract and Applied Analysis
Volume 2004 (2004), Issue 5, Pages 425-434

On a nonlocal Cauchy problem for differential inclusions

E. Gatsori, S. K. Ntouyas, and Y. G. Sficas

Department of Mathematics, University of Ioannina, Ioannina 45110, Greece

Received 3 September 2002

Copyright © 2004 E. Gatsori et al. 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 establish sufficient conditions for the existence of solutions for semilinear differential inclusions, with nonlocal conditions. We rely on a fixed-point theorem for contraction multivalued maps due to Covitz and Nadler andon the Schaefer's fixed-point theorem combined with lower semicontinuous multivalued operators with decomposable values.