Smith, H. L.; Kuang, Y. Periodic solutions of differential delay equations with threshold-type delays. (English) Zbl 0762.34044 Oscillation and dynamics in delay equations, Proc. Spec. Sess. AMS, San Francisco/CA (USA) 1991, Contemp. Math. 129, 153-176 (1992). [For the entire collection see Zbl 0745.00045.]Motivated by biological models, a theorem on existence of periodic solutions is proved by a fixed-point argument for an autonomous delay-differential equation with the delay depending upon the state, in the function space; a specific situation is the one where the delay is implicitly defined by an integral relation, the threshold-type delay appearing in biological applications. The result is obtained by hard work; some details have to be found in a preprint of the authors (#23 in the references). References include 35 titles. Reviewer: A.Halanay (Bucureşti) Cited in 39 Documents MSC: 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34C25 Periodic solutions to ordinary differential equations 92D25 Population dynamics (general) 92D30 Epidemiology Keywords:biological models; periodic solutions; autonomous delay-differential equation; threshold-type delay Citations:Zbl 0745.00045 PDFBibTeX XMLCite \textit{H. L. Smith} and \textit{Y. Kuang}, Contemp. Math. 129, 153--176 (1992; Zbl 0762.34044)