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Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II
dc.creator | Caraballo Garrido, Tomás | es |
dc.creator | Cheban, David | |
dc.date.accessioned | 2015-04-08T10:27:06Z | |
dc.date.available | 2015-04-08T10:27:06Z | |
dc.date.issued | 2009 | es |
dc.identifier.citation | Caraballo Garrido, T. y Cheban, D. (2009). Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II. Journal of Differential Equations, 246 (3), 1164-1186. | es |
dc.identifier.issn | 0022-0396 | es |
dc.identifier.issn | 1553-5231 | es |
dc.identifier.uri | http://hdl.handle.net/11441/23637 | |
dc.description.abstract | In this paper we continue the research started in a previous paper, where we proved that the linear differential equation (1) x0 = A(t)x + f(t) with Levitan almost periodic coefficients has a unique Levitan almost periodic solution, if it has at least one bounded solution and the bounded solutions of the homogeneous equation (2) x0 = A(t)x are homoclinic to zero (i.e. lim jtj!+1 j'(t)j = 0 for all bounded solution ' of (2)). If the coefficients of (1) are Bohr almost periodic and all bounded solutions of equation (2) are homoclinic to zero, then the equation (1) admits a unique almost automorphic solution. In this second part we first generalise this result for linear functional differential equations (FDEs) of the form (3) x0 = A(t)xt + f(t); as well as for neutral FDEs. Analogous results for functional difference equations with finite delay and some classes of partial differential equations are also given. We study the problem of existence of Bohr/Levitan almost periodic solutions of differential equations of type (3) in the context of general semi-group non-autonomous dynamical systems (cocycles), in contrast with the group non-autonomous dynamical systems framework considered in the first part. | |
dc.format | application/pdf | es |
dc.language.iso | eng | es |
dc.relation.ispartof | Journal of Differential Equations, 246(3), 1164-1186 | es |
dc.rights | Atribución-NoComercial-SinDerivadas 4.0 España | es |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0 | es |
dc.subject | Almost periodic solution | |
dc.subject | Almost automorphic solutions | en |
dc.subject | Non-autonomous dynamical systems | en |
dc.subject | Favard's condition | en |
dc.subject | Cocycle | en |
dc.title | Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico | es |
dc.relation.publisherversion | https://ac.els-cdn.com/S0022039608003367/1-s2.0-S0022039608003367-main.pdf?_tid=37e435b0-05b9-11e8-a71d-00000aab0f02&acdnat=1517315550_6a217d765aeef3807c19df486d369656 | |
dc.identifier.doi | 10.1016/j.jde.2008.07.025 | es |
dc.journaltitle | Journal of Differential Equations | es |
dc.publication.volumen | 246 | es |
dc.publication.issue | 3 | es |
dc.publication.initialPage | 1164 | es |
dc.publication.endPage | 1186 | es |
dc.identifier.idus | https://idus.us.es/xmlui/handle/11441/23637 |
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