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Convergence of Solutions for an Equation with State-Dependent Delay

✍ Scribed by Mária Bartha

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
189 KB
Volume
254
Category
Article
ISSN
0022-247X

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✦ Synopsis

A result of Smith and Thieme shows that if a semiflow is strongly order preserving, then a typical orbit converges to the set of equilibria. For the equation Ž .

Ž . Ž Ž Ž Ž .... with state-dependent delay x t s y x t q f x t y r x t , where ) 0 and f ˙Ž . and r are smooth real functions with f 0 s 0 and f Ј ) 0, we construct a semiflow which is monotone but not strongly order preserving. We prove a convergence result under a monotonicity condition different from the strong order preserving property, and apply it to the above equation to obtain generic convergence.

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