Uniqueness of Rapidly Oscillating Periodic Solutions to a Singularly Perturbed Differential-delay Equation
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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.