On the existence and uniqueness of almost periodic solutions for delay logistic equations. (Q1856049)

Extending an earlier result due to \textit{G. Seifert} [Differ. Integral Equ. 9, 335--342 (1996; Zbl 0838.34083)], by means of a Lyapunov functional, it is shown that \[ N'(t)= N(t)\Biggl(a(t)- b(t) \int^\infty_0 K(s)\,N(t-s)\,ds\Biggr) \] has exactly one almost-periodic solution on \([0,\infty)\), which is asymptotically stable, provided \(a\) and \(b\) are real-valued \(ap\geq b_0> 0\), \(\int^\infty_0 s^2 K(s)\,ds< \infty\) (with \(K\geq 0\)) and \(b_0\) is not too small. (It is not clear to the reviewer whether the assumption of uniform almost-periodicity of \(f\) used in the (Lyapunov) theorem \(A\) is fulfilled here).