Electron. J. Diff. Eqns., Vol. 1999(1999), No. 46, pp. 1-9.

Relationship between different types of stability for linear almost periodic systems in Banach spaces

D. N. Cheban (State University of Moldova, Moldova)

For the linear equation $x'= A(t)x$ with recurrent (almost periodic) coefficients in an arbitrary Banach space, we prove that the asymptotic stability of the null solution and of all limit equations implies the uniform stability of the null solution.

Submitted June 18, 1999. Published November 27, 1999.
Math Subject Classifications: 34C35, 34C27, 34K15, 34K20, 58F27, 34G10.
Key Words: non-autonomous linear dynamical systems, global attractors, almost periodic system, stability, asymptotic stability.

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David N. Cheban
State University of Moldova
Faculty of Mathematics and Informatics
60, A. Mateevich str.
Chisinau, MD-2009, Moldova
e-mail: cheban@usm.md

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