Bouakkaz, Ahlème; Khemis, Rabah Positive periodic solutions for a class of second-order differential equations with state-dependent delays. (English) Zbl 1459.34157 Turk. J. Math. 44, No. 4, 1412-1426 (2020). The following class of second-order differential equations with iterative state-dependent delays is considered: \[ x''(t)+p(t)x'(t)+q(t)x(t) = \frac{d}{dt}\left[f(t, x(t), x^{[2]}(t), \ldots, x^{[n]}(t))\right] +\sum^n_{j=1}c_j(t)x^{[j]}(t), \] where \(p\) and \(q\) are positive continuous real-valued functions, \(f: \mathbb{R}^{n+1} \to \mathbb{R}\) is continuous, \(x^{[0]}(t)=t, x^{[1]}(t) = x(t), x^{[2]}(t)=x(x(t)), \ldots, x^{[n]}(t)=x(x^{[n-1]}(t))\). By virtue of a Krasnoselskii fixed point theorem and some useful properties of a Green’s function, sufficient conditions are obtained for existence of positive periodic solutions. This is inspired by similar results available in literature. Reviewer: Zhanyuan Hou (London) Cited in 13 Documents MSC: 34K13 Periodic solutions to functional-differential equations 34K43 Functional-differential equations with state-dependent arguments Keywords:positive periodic solutions; nonlinear differential equation; fixed point theorem; Green’s function PDFBibTeX XMLCite \textit{A. Bouakkaz} and \textit{R. Khemis}, Turk. J. Math. 44, No. 4, 1412--1426 (2020; Zbl 1459.34157) Full Text: DOI