Constantin Buse & Oprea Jitianu
We consider a mild solution of a well-posed inhomogeneous Cauchy problem
on a complex Banach space , where is a 1-periodic operator-valued function. We prove that if belongs to for each then for each the solution of the well-posed Cauchy problem
is uniformly exponentially stable. The converse statement is also true. Details about the space are given in the section 1, below. Our approach is based on the spectral theory of evolution semigroups.
Submitted November 13, 2002. Published February 11, 2003.
Math Subject Classifications: 26D10, 34A35, 34D05, 34B15, 45M10, 47A06.
Key Words: Almost periodic functions, exponential stability, periodic evolution families of operators, integral inequality, differential inequality on Banach spaces.
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|Constantin Buse |
Department of Mathematics
West University of Timisoara
Bd. V. Parvan 4
1900 Timisoara, Romania
|Oprea Jitianu |
Department of Applied Mathematics
University of Craiova
Bd. A. I. Cuza 13,
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