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Stability and almost periodic solutions of neutral functional differential equations with infinite delay

Stability and almost periodic solutions of neutral functional differential equations with... For the operatorD(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect toH D,f + (ξ), then Eq.(1) has anmω-periodic solutionp(t), for some integerm ≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance fromH +(ξ,D,f), then Eq.(1) has an almost periodic solution. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Stability and almost periodic solutions of neutral functional differential equations with infinite delay

Acta Mathematicae Applicatae Sinica , Volume 14 (1) – Jul 3, 2007

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Publisher
Springer Journals
Copyright
Copyright © 1998 by Science Press
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02677350
Publisher site
See Article on Publisher Site

Abstract

For the operatorD(t), we prove the inherence theorem, Theorem 2. Basing on it, we study the stability with respect to the hull for neutral functional differential equations with infinite delay. We prove that if periodic Eq.(1) possesses the solution ξ(t) that is uniformly asymptotically stable with respect toH D,f + (ξ), then Eq.(1) has anmω-periodic solutionp(t), for some integerm ≥1. Furthermore, we prove that if the almost periodic Eq.(1) possesses the solution ξ(t) that is stable under disturbance fromH +(ξ,D,f), then Eq.(1) has an almost periodic solution.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 3, 2007

References