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.
Highlights
In this paper we study the existence of solutions y: [O, T]--.K C_E to the differential inclusion y’(t) e (t,y(t)) e a.e. t e [0, T]
The technique to establish the existence of viable solutions to (1.1) will be in two steps
Our goal will be to establish some general existence principles for (1.2) which will automatically lead to new criteria for the existence of viable solutions to (1.1)
Summary
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
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