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Comparison Theorems of Liapunov-Razumikhin Type for NFDEs With Infinite Delay

Published online by Cambridge University Press:  20 November 2018

John R. Haddock ,
Shigui Ruan ,
Jianhong Wu  and
Huaxing Xia
John R. Haddock
Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152, U.S.A.
Shigui Ruan
Affiliation:
Department of Mathematics, Statistics and Computing Science, Dalhousie University, Halifax, Nova Scotia, B3H3J5
Jianhong Wu
Affiliation:
Department of Mathematics and Statistics, York University, North York, Ontario, M3J 1P3
Huaxing Xia
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S4K1
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Abstract

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Some comparison theorems of Liapunov-Razumikhin type are provided for uniform (asymptotic) stability and uniform (ultimate) boundedness of solutions to neutral functional differential equations with infinite delay with respect to a given phase space pair. Examples are given to illustrate how the comparison theorems and stability and boundedness of solutions depend on the choice(s) of phase space(s) and are related to asymptotic behavior of solutions to some difference and integral equations.

Keywords

34K4034K2034D40stability and boundednessLiapunov-Razumikhin techniqueNFDEs with infinite delaycomparison method
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 3 , 01 June 1995 , pp. 500 - 526
Copyright
Copyright © Canadian Mathematical Society 1995

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