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dc.contributor.authorBuse, Constantin ( )
dc.contributor.authorLupulescu, Vasile ( Orcid Icon 0000-0001-9145-5163 )
dc.identifier.citationBuse, C., & Lupulescu, V. (2003). Exponential stability of linear and almost periodic systems on Banach spaces. Electronic Journal of Differential Equations, 2003(125), pp. 1-7.en_US

Let vƒ(·, 0) the mild solution of the well-posed inhomogeneous Cauchy problem

v̇(t) = A(t)v(t) + ƒ(t), v(0) = 0 t ≥ 0

on a complex Banach space X, where A(·) is an almost periodic (possible unbounded) operator-valued function. We prove that vƒ(·, 0) belongs to a suitable subspace of bounded and uniformly continuous functions if and only if for each x ∈ X the solution of the homogeneous Cauchy problem

u̇(t) = A(t)u(t), u(0) = x t ≥ 0

is uniformly exponentially stable. Our approach is based on the spectral theory of evolution semigroups.

dc.format.extent7 pages
dc.format.medium1 file (.pdf)
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.subjectUniform exponential stabilityen_US
dc.subjectEvolution semigroupsen_US
dc.titleExponential stability of linear and almost periodic systems on Banach spacesen_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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