Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 2, Pages 169-178
doi:10.1155/S1048953399000179
Abstract
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 [8] 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.