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dc.contributor.authorKamenskii, M.
dc.contributor.authorMakarenkov, O.
dc.date.accessioned2016-12-14T16:52:26Z
dc.date.available2016-12-14T16:52:26Z
dc.date.issued2016-12-01
dc.identifier.issn1877-0533
dc.identifier.urihttp://hdl.handle.net/20.500.11824/335
dc.description.abstractIf $x_0$ 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.formatapplication/pdfen_US
dc.language.isoengen_US
dc.rightsReconocimiento-NoComercial-CompartirIgual 3.0 Españaen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjectSweeping processen_US
dc.subjectPerturbation theoryen_US
dc.subjectContinuation principleen_US
dc.subjectPeriodic solutionen_US
dc.titleOn the response of autonomous sweeping processes to periodic perturbationsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.identifier.doi10.1007/s11228-015-0348-1
dc.relation.publisherversionhttp://link.springer.com/article/10.1007/s11228-015-0348-1en_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US
dc.type.hasVersioninfo:eu-repo/semantics/acceptedVersionen_US
dc.journal.titleSet-Valued and Variational Analysisen_US


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