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A note on multivalued differential equations on proximate retracts

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  • Donal O'Regan

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.

Suggested Citation

  • Donal O'Regan, 1999. "A note on multivalued differential equations on proximate retracts," International Journal of Stochastic Analysis, Hindawi, vol. 12, pages 1-10, January.
    • Handle: RePEc:hin:jnijsa:689250
    DOI: 10.1155/S1048953399000179
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