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Uniqueness and Stability of Slowly Oscillating Periodic Solutions of Delay Equations with Unbounded Nonlinearity

✍ Scribed by X.W. Xie

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
752 KB
Volume
103
Category
Article
ISSN
0022-0396

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✦ Synopsis

We study uniqueness and stability problems of slowly oscillating periodic solutions of delay equations with sinall parameters. If the nonlinearity decays to a negative number at (-\infty) and blows up at (+\infty) or vice versa, we show that, for sufficiently small parameters, the slowly oscillating periodic solutions are unique and asymptotically stable provided that the decay rate can dominate the growth rate in an appropriate sense. This result particularly implies that Wright's equation has a unique and asymptotically stable slowly oscillating periodic solution for large parameter (\alpha). 1993 Academic Press, Inc

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## Abstract In this paper, we use the coincidence degree theory to establish new results on the existence and uniqueness of __T__ ‐periodic solutions for a class of nonlinear __n__ ‐th order differential equations with delays of the form __x__^(__n__)^(__t__) + __f__ (__x__^(__n‐__ 1)^(__t__)) + _