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dc.contributor.authorMaroto Camarena, Ismael
dc.contributor.authorNúñez Jiménez, María del Carmen 
dc.contributor.authorObaya, Rafael 
dc.date.accessioned2017-09-19T18:38:34Z
dc.date.available2017-09-19T18:38:34Z
dc.date.issued2017
dc.identifier.citationDiscrete and Continuous Dynamical Systems 37 (7), 3939-3961es
dc.identifier.issn1078-0947es
dc.identifier.urihttp://uvadoc.uva.es/handle/10324/25757
dc.description.abstractThe properties of stability of a compact set $K$ which is positively invariant for a semiflow $(\W\times W^\infty([-r,0],\mathbb{R}^n),\Pi,\mathbb{R}^+)$ determined by a family of nonautonomous FDEs with state-dependent delay taking values in $[0,r]$ are analyzed. The solutions of the variational equation through the orbits of $K$ induce linear skew-product semiflows on the bundles $K\times W^\infty([-r,0],\R^n)$ and $K\times C([-r,0],\R^n)$. The coincidence of the upper-Lyapunov exponents for both semiflows is checked, and it is a fundamental tool to prove that the strictly negative character of this upper-Lyapunov exponent is equivalent to the exponential stability of $\mK$ in $\W\times W^\infty([-r,0],\R^n)$ and also to the exponential stability of this compact set when the supremum norm is taken in $W^\infty([-r,0],\R^n)$. In particular, the existence of a uniformly exponentially stable solution of a uniformly almost periodic FDE ensures the existence of exponentially stable almost periodic solutions.es
dc.format.mimetypeapplication/pdfes
dc.language.isoenges
dc.publisherAmerican Institute of Mathematical Scienceses
dc.rights.accessRightsinfo:eu-repo/semantics/openAccesses
dc.titleDynamical properties of nonautonomous functional differential equations with state-dependent delayes
dc.typeinfo:eu-repo/semantics/articlees
dc.identifier.doi10.3934/dcds.2017167es
dc.peerreviewedSIes
dc.description.projectMinisterio de Economía, Industria y Competitividad (MTM2015-66330-P)
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/643073


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