Electronic Journal of Differential Equations,
Vol. 1999(1999), No. 46, pp. 1-9.

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

Author: D. N. Cheban (State Univ. of Moldova, Moldova)

Abstract: 
 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.