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dc.contributor.authorBuse, Constantin ( )
dc.contributor.authorJitianu, Oprea ( )
dc.date.accessioned2020-09-14T19:20:15Z
dc.date.available2020-09-14T19:20:15Z
dc.date.issued2003-02-11
dc.identifier.citationBuse, C., & Jitianu, O. (2003). A new theorem on exponential stability of periodic evolution families on Banach spaces. Electronic Journal of Differential Equations, 2003(14), pp. 1-10.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/12605
dc.description.abstractWe consider a mild solution vf (·, 0) of a well-posed inhomogeneous Cauchy problem v̇(t) = A(t)v(t) + ƒ(t), v(0) = 0 on a complex Banach space X, where A(·) is a 1-periodic operator-valued function. We prove that if vƒ (·, 0) belongs to AP0 (ℝ+, X) for each ƒ ∈ AP0(ℝ+, X) then for each x ∈ X the solution of the well-posed Cauchy problem u̇(t) = A(t)v(t), u(0) = x is uniformly exponentially stable. The converse statement is also true. Details about the space AP0(ℝ+, X) are given in the section 1, below. Our approach is based on the spectral theory of evolution semigroups.en_US
dc.formatText
dc.format.extent10 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2003, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectAlmost periodic functionsen_US
dc.subjectExponential stabilityen_US
dc.subjectPeriodic evolution families of operatorsen_US
dc.subjectIntegral inequalityen_US
dc.subjectDifferential inequality on Banach spacesen_US
dc.titleA new theorem on exponential stability of periodic evolution families on Banach spacesen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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