A relaxation theorem for a differential inclusion with “maxima”

Author:

Cernea Aurelian12

Affiliation:

1. Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest , Romania

2. Academy of Romanian Scientists, Splaiul Independenƫei 54, 050094 Bucharest , Romania

Abstract

Abstract We consider a Cauchy problem associated to a nonconvex differential inclusion with “maxima” and we prove a Filippov type existence result. This result allows to obtain a relaxation theorem for the problem considered.

Publisher

Walter de Gruyter GmbH

Reference14 articles.

1. [1] Aubin, J.P., Frankowska, H., Set-valued Analysis, Birkhauser, Basel, 1990.

2. [2] Bainov, D.D., Hristova, S., Differential equations with maxima, Chapman and Hall/CRC, Boca Raton, 2011.

3. [3] Cernea, A., On the existence of solutions for differential inclusions with "maxima", Libertas Mathematica, New Series 35 (2015), 89-98.

4. [4] Filippov, A.F., Classical solutions of differential equations with multivalued right hand side, SIAM J. Control 5 (1967), 609-621.10.1137/0305040

5. [5] Georgiev, L., Angelov, V.G., On the existence and uniqueness of solutions for maximum equations, Glasnik Mat. 37 (2002), 275-281.

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