A note on multivalued differential equations on proximate retracts. (1999)

• Record Type: Journal Article
• Authors: O'Regan, Donal
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 12:Number 2(1999)
• Page Start: 169
• Page End: 178
• Publication Date: 1999
• Subjects: viable solutions -- multivalued -- differential inclusions -- proximate retracts; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953399000179
• Languages: English
• ISSNs: 1048-9533

Abstract

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.