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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.

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

Citations:

Zbl 0745.00045
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