Geodesic
Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation
Electronic journal of differential equations, Tome 2000 (2000)
In this paper, we prove a uniqueness theorem for rapidly oscillating periodic solutions of the singularly perturbed differential-delay equation $\varepsilon \dot{x}(t)=-x(t)+f(x(t-1))$. 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.
Classification : 34K26, 37G10
Keywords: delay equation, rapidly oscillating, singularly perturbed 
@article{EJDE_2000__2000__a138,
     author = {Krishnan,  Hari P.},
     title = {Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0957.34070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a138/}
}
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VL  - 2000
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%0 Journal Article
%A Krishnan,  Hari P.
%T Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation
%J Electronic journal of differential equations
%D 2000
%V 2000
%U http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a138/
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Krishnan,  Hari P. Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation. Electronic journal of differential equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a138/