Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 2, Pages 169-178
A note on multivalued differential equations on proximate retracts
National University of Ireland, Department of Mathematics, Galway, Ireland
Received 1 October 1997; Revised 1 July 1998
Copyright © 1999 Donal O'Regan. 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.
This paper discusses viable solutions for differential inclusions in Banach
spaces. Existence will be established in two steps. In step 1, a nonlinear
alternative of Leray-Schauder type  for maps with closed graphs will be
used to establish a variety of existence principles for the Cauchy differential inclusion. Step 2 involves using the results in step 1 together with
some tricks involving the Bouligand cone (and sometimes the Urysohn
function) so that new existence criteria can be established for multivalued
differential equations on proximate retracts.