Existence and stability of almost-periodic solutions of quasi-linear differential equations with deviating argument

The paper is concerned with the existence of an almost-periodic solution of the system with deviating argument dx(t)/dt = A(t)x(t) + f(t,x(t)),x(t - r(1)(t)),...,x(t - r(k) (t)), (1) such that the associated homogeneous linear system satisfies exponential dichotomy and deviations of the argument are not restricted by any sign assumption. The exponential stability of the solution when the system is with delay argument is considered. (C) 2004 Elsevier Ltd. All rights reserved.