A relaxation theorem for a differential inclusion with “maxima”

Aurelian Cernea

doi:10.1515/auom-2017-0005

.blurhash-client-img { display: none !important; }

A relaxation theorem for a differential inclusion with “maxima”

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 25 (2017): Issue 1 (January 2017)

By: Aurelian Cernea

Open Access

|Sep 2017

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.

References

[1] Aubin, J.P., Frankowska, H., Set-valued Analysis, Birkhauser, Basel, 1990.
Search in Google Scholar Back to article
[2] Bainov, D.D., Hristova, S., Differential equations with maxima, Chapman and Hall/CRC, Boca Raton, 2011.10.1201/b10877
Search in Google Scholar Back to article
[3] Cernea, A., On the existence of solutions for differential inclusions with "maxima", Libertas Mathematica, New Series 35 (2015), 89-98.
Search in Google Scholar Back to article
[4] Filippov, A.F., Classical solutions of differential equations with multivalued right hand side, SIAM J. Control 5 (1967), 609-621.10.1137/0305040
Open DOI Search in Google Scholar Back to article
[5] Georgiev, L., Angelov, V.G., On the existence and uniqueness of solutions for maximum equations, Glasnik Mat. 37 (2002), 275-281.
Search in Google Scholar Back to article
[6] Gonzalez, P., Pinto, M., Convergent solutions of certain nonlinear differential equations with maxima, Math. Comput. Modelling 45 (2007), 1-10.10.1016/j.mcm.2005.03.008
Search in Google Scholar Back to article
[7] Hiai, F., Umegaki, H., Integrals, Conditional Expectations and Martin- gales of Multivalued Functions, J. Multivariate Anal. 7 (1977), 149-182.10.1016/0047-259X(77)90037-9
Open DOI Search in Google Scholar Back to article
[8] Ivanov, A., Liz, E., Trofimchuk, S., Halanay inequality, Yorke 3/2 stability criteria and differential equations with maxima, Tohoku Math. J. 54 (2002), 277-295.10.2748/tmj/1113247567
Search in Google Scholar Back to article
[9] Malgorzata, M., Zhang, G., On unstable neutral difference equations with "maxima", Math. Slovaca 56 (2006), 451-463.
Search in Google Scholar Back to article
[10] Otrocol, D., Systems of functional differential equations with maxima, of mixed type, Electronic J. Qual. Theory Differ. Equations 2014 (2014), no. 5, 1-9.10.14232/ejqtde.2014.1.5
Search in Google Scholar Back to article
[11] Otrocol, D., Rus, I.A., Functional-differential equations with "maxima" via weakly Picard operator theory, Bull. Math. Soc. Sci. Math. Roumanie 51(99) (2008), 253-261.
Search in Google Scholar Back to article
[12] Otrocol, D., Rus, I.A., Functional-differential equations with "maxima", of mixed type, Fixed Point Theory 9 (2008), 207-220.
Search in Google Scholar Back to article
[13] Popov, E.P., Automatic regulation and control, Nauka, Moskow, 1966 (in Russian).
Search in Google Scholar Back to article
[14] Stepanov, E., On solvability of some boundary value problems for differential equations with "maxima", Topol. Meth. Nonlin. Anal. 8 (1996), 315-326.10.12775/TMNA.1996.035
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.1515/auom-2017-0005 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

Journal RSS Feed

Language: English

Page range: 61 - 68

Submitted on: Feb 20, 2016

Accepted on: Apr 25, 2016

Published on: Sep 21, 2017

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Set-valued map,

differential inclusion,

relaxation

Related subjects:

Mathematics,

General mathematics

© 2017 Aurelian Cernea, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 25 (2017): Issue 1 (January 2017)