Abstract
In this paper we begin a study of the differential-delay equation
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We prove the existence of periodic solutions for 0<ɛ<ɛ 0, where ɛ 0 is an optimal positive number. We investigate regularity and monotonicity properties of solutions x(t) which are defined for all t and of associated functions like η(t)=t−r(x(t)). We begin the development of a Poincaré-Bendixson theory and phase-plane analysis for such equations. In a companion paper these results will be used to investigate the limiting profile and corresponding boundary layer phenomena for periodic solutions as ɛ approaches zero.
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Mallet-Paret, J., Nussbaum, R.D. Boundary layer phenomena for differential-delay equations with state-dependent time lags, I.. Arch. Rational Mech. Anal. 120, 99–146 (1992). https://doi.org/10.1007/BF00418497
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DOI: https://doi.org/10.1007/BF00418497