International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 4, Pages 699-706

Regular and singular perturbations of upper semicontinuous differential inclusion

Tzanko Donchev and Vasil Angelov

Department of Mathematics, University of Mining and Geology, SOFIA 1100, Bulgaria

Received 13 November 1995; Revised 11 April 1996

Copyright © 1997 Tzanko Donchev and Vasil Angelov. 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.


In the paper we study the continuity properties of the solution set of upper semicontinuous differential inclusions in both regularly and singularly perturbed case. Using a kind of dissipative type of conditions introduced in [1] we obtain lower semicontinuous dependence of the solution sets. Moreover new existence result for lower semicontinuous differential inclusions is proved.