Uniqueness of Rapidly Oscillating Periodic Solutions to a Singularly Perturbed Differential-delay Equation
Date
2000-07-24
Authors
Krishnan, Hari P.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
In this paper, we prove a uniqueness theorem for rapidly oscillating periodic solutions of the singularly perturbed differential-delay equation εẋ(t) = -x(t) + ƒ(x(t - 1)). In particular, we show that, for a given oscillation rate, there exists exactly one periodic solution to the above equation. Our proof relies upon a generalization of Lin's method, and is valid under generic conditions.
Description
Keywords
Delay equation, Rapidly oscillating, Singularly perturbed
Citation
Krishnan, H. P. (2000). Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation. <i>Electronic Journal of Differential Equations, 2000</i>(56), pp. 1-18.
Rights
Attribution 4.0 International