Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators

M. I. Gil'

doi:10.1016/j.jmaa.2004.11.018

Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators

M. I. Gil'

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.

Original language	English
Pages (from-to)	140-158
Number of pages	19
Journal	Journal of Mathematical Analysis and Applications
Volume	308
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2004.11.018
State	Published - 1 Aug 2005

Keywords

Absolute stability
Abstract nonlinear differential-delay equations
Boundedness of solutions
Input-output stability
Lyapunov stability

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2004.11.018

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title = "Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators",

abstract = "We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.",

keywords = "Absolute stability, Abstract nonlinear differential-delay equations, Boundedness of solutions, Input-output stability, Lyapunov stability",

author = "Gil', {M. I.}",

note = "Funding Information: ✩ This research was supported by the Kamea Fund of the Israel. E-mail address: gilmi@black.bgu.ac.il.",

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PY - 2005/8/1

Y1 - 2005/8/1

N2 - We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.

AB - We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.

KW - Absolute stability

KW - Abstract nonlinear differential-delay equations

KW - Boundedness of solutions

KW - Input-output stability

KW - Lyapunov stability

UR - http://www.scopus.com/inward/record.url?scp=19044397052&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2004.11.018

DO - 10.1016/j.jmaa.2004.11.018

M3 - Article

AN - SCOPUS:19044397052

VL - 308

SP - 140

EP - 158

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -

Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators

Abstract

Keywords

ASJC Scopus subject areas

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