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Asymptotic behavior of volterra integrodifferential equations

Asymptotic behavior of volterra integrodifferential equations Vol.13 No.1 ACTA MATHEMATICAE APPLICATAE SINICA Jan., 1997 Study Bulletin ASYMPTOTIC BEHAVIOR OF VOLTERRA INTEGRODIFFERENTIAL EQUATIONS* XU DAoYI (f~'i~) (Department of Mathematics, Sichuan Normal University, Chengdu 610066, China) The purpose of this paper is to study the asymptotic behavior and boundedness of the Volterra integrodifferential equation z'(t) = A(t)z(t) + C(t, s)z(s) ds + G (t, s, x(s)) ds + f(t), (1) /0 /0 where z e R '~, A(t) and C(t, s) are continuous n x n matrices, and ](t) is continuous n-vectors. The function G(t,s,x(s)) is unknown and represents the nonlinear parameter perturbation with respect to the state z(s) in the linear integral term. In general, it is assumed that G is bounded in the form IG(t,s,z(s))l<d(t,s)Jx(s)], Vt>0, VzeR ~, (2) where I " ] is any vector or matrix norm and d(t, s) > 0 is a continuous function. The perturbation often occurs in dynamical systems due to modelling errors, measurement errors, linearization approximations, and so on. Asymptotic behavior of differential equations with bounded delays and nonlinear perturbation have been intensively investigated by numerous authors [i] . However to the best of the present author's knowledge, most of the known works on integrodifferential equations only deal http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Asymptotic behavior of volterra integrodifferential equations

Xu, Daoyi
Acta Mathematicae Applicatae Sinica , Volume 13 (1) – Jul 16, 2005
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References (6)

Publisher
Springer Journals
Copyright
Copyright © 1997 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02020486
Publisher site
See Article on Publisher Site

Abstract

Vol.13 No.1 ACTA MATHEMATICAE APPLICATAE SINICA Jan., 1997 Study Bulletin ASYMPTOTIC BEHAVIOR OF VOLTERRA INTEGRODIFFERENTIAL EQUATIONS* XU DAoYI (f~'i~) (Department of Mathematics, Sichuan Normal University, Chengdu 610066, China) The purpose of this paper is to study the asymptotic behavior and boundedness of the Volterra integrodifferential equation z'(t) = A(t)z(t) + C(t, s)z(s) ds + G (t, s, x(s)) ds + f(t), (1) /0 /0 where z e R '~, A(t) and C(t, s) are continuous n x n matrices, and ](t) is continuous n-vectors. The function G(t,s,x(s)) is unknown and represents the nonlinear parameter perturbation with respect to the state z(s) in the linear integral term. In general, it is assumed that G is bounded in the form IG(t,s,z(s))l<d(t,s)Jx(s)], Vt>0, VzeR ~, (2) where I " ] is any vector or matrix norm and d(t, s) > 0 is a continuous function. The perturbation often occurs in dynamical systems due to modelling errors, measurement errors, linearization approximations, and so on. Asymptotic behavior of differential equations with bounded delays and nonlinear perturbation have been intensively investigated by numerous authors [i] . However to the best of the present author's knowledge, most of the known works on integrodifferential equations only deal

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Jul 16, 2005

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