On the logistic delay differential equations with piecewise constant argument and quasi-periodic time dependence
Complementing results due to \textit{G. Seifert} [J. Differ. Equations 164, No. 2, 451-458 (2000; Zbl 1009.34064)], it is shown that \(y'(t)= a(t)(a(t)- f(y[t]))\) admits on \(\mathbb{R}\) exactly one positive quasi-periodic solution \(y\) with frequencies \(1\), \(\omega_1,\dots,\omega_r\), which is then asymptotically stable, provided \(a\) is quasi-periodic with frequencies \(\omega_1,\dots,\omega_r\), \(f\) is entire with \(f(\mathbb{R})\subset\mathbb{R}\),with some additional involved conditions on \(f'\mid(0,\infty)\) and \(a\). No examples.
scientific article; zbMATH DE number 1866619