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

Abstract

The paper is concerned with the existence of an almost-periodic solution of the systemwith deviating argument soldx(t)/dt = A (t) x (t) + ƒ (t, x(t)), x(t − τ 1(t)), , x(t−τ κ(t)) , 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.