Effect of a small delay in almost-periodic linear systems of high order (Q792532)

The author obtains several sufficient conditions for the existence of almost periodic (a.p.) solutions to equations with small delay of the form \(x''(t)=B(t)x(t-\tau)+f(t), x\in {\mathbb{R}}^ n\), \(\tau =const\). in which B(t) is an \(n\times n\) a. p. matrix, and \(f(t)\in {\mathbb{R}}^ n\) is an a. p. function (in the sense of Bohr). He also shows that the existence of a. p. solutions of these equations depends on the existence of the delay \(\tau\neq 0\) which can be arbitrarily small.