dc.contributor.author Kamenskii, M. dc.contributor.author Makarenkov, O. dc.date.accessioned 2016-12-14T16:52:26Z dc.date.available 2016-12-14T16:52:26Z dc.date.issued 2016-12-01 dc.identifier.issn 1877-0533 dc.identifier.uri http://hdl.handle.net/20.500.11824/335 dc.description.abstract If $x_0$ is an equilibrium of an autonomous differential equation $\dot x=f(x)$ and $\det \|f'(x_0)\|\not=0$, then $x_0$ persists under autonomous perturbations and $x_0$ transforms into a $T$-periodic solution under non-autonomous $T$-periodic perturbations. In this paper we discover a similar structural stability for Moreau sweeping processes of the form $-\dot u\in N_B(u)+f_0(u),$ $u\in\mathbb{R}^2,$ i. e. we consider the simplest case where the derivative is taken with respect to the Lebesgue measure and where the convex set $B$ of the reduced system is a non-moving unit ball of $\mathbb{R}^2.$ We show that an equilibrium $\|u_0\|=1$ persists under periodic perturbations, if the projection $\overline{f}:\partial B\to\mathbb{R}^2$ of $f_0$ on the tangent to the boundary $\partial B$ is nonsingular at $u_0$. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Sweeping process en_US dc.subject Perturbation theory en_US dc.subject Continuation principle en_US dc.subject Periodic solution en_US dc.title On the response of autonomous sweeping processes to periodic perturbations en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.1007/s11228-015-0348-1 dc.relation.publisherversion http://link.springer.com/article/10.1007/s11228-015-0348-1 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/acceptedVersion en_US dc.journal.title Set-Valued and Variational Analysis en_US
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