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Asymptotic analysis of differential-delay equations and nonuniqueness of periodic solutions (1985)

Chapin, S. ; Payne, L. E.

Chichester, West Sussex : Wiley-Blackwell

Mathematical Methods in the Applied Sciences 7 (1985), S. 223-237

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ISSN: 0170-4214

Keywords: Mathematics and Statistics ; Applied Mathematics

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Mathematics

Notes: We study the differential-delay equation x′(t) = -αf(x(t-1)), where α is a positive parameter and f is an odd function which decays like x-r at infinity. In particular, we consider the case r ≤ 2, and prove the existence of periodic solutions with special symmetries which are different from previously known periodic solutions of minimal period 4. For r = 2 we prove sharp asymptotic estimates for the minimal periods of these solutions.Our results disprove a conjecture of R. D. Nussbaum.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1002/mma.1670070114

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