Instability of nonautonomous state-dependent delay integro-differential systems
type: Item
instance of: scholarly article
title: Instability of nonautonomous state-dependent delay integro-differential systems
zbMATH Open document ID: 1112.34053
author: Bashir Ahmad
author: Seenith Sivasundaram
published in: Nonlinear Analysis. Real World Applications
publication date: 2007-01-16T00:00:00Z
review text: Consider the system with state-dependent time delay \[ \begin{multlined} u^\prime(t)=A(t)\left( u(t)+\int_{t_0}^t G(t,s)u(s)\,ds\right) \\+B(t)\left( u(t-r(t,u(t)))+\int_{t_0}^t G(t,s)u(s-r(s,u(s)))\,ds \right), \end{multlined} \] \[ u_{t_0}=\phi, \] where \(G(t,s)\) is continuous on \([t_0,\infty)\times [t_0,\infty)\), \(r(t,u(t))\) is a nonnegative bounded delay function, \(A,\,B\in C([t_0-\tau,\infty],\mathbb{R}^{n\times n})\) for \(\tau>0\), \(\phi\in C([-\tau,\,0],\mathbb{R}^n)\). The authors derive sufficient conditions for the instability of the zero solution based for the concept of \((h,k)\) dichotomies.
reviewed by: Ivan Ginchev
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 5116302
zbMATH Keywords: integro-differential systems
zbMATH Keywords: Lyapunov instability
zbMATH Keywords: \((h, k)\)-dichotomies
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2005.04.003
OpenAlex ID: W1977622708
cites work: Q5533446
cites work: Dichotomies in stability theory
cites work: Ordinary and delay differential equations
cites work: Asymptotic integration of nonautonomous delay-differential systems
cites work: Q4003237
cites work: Stability criteria for linear delay differential equations
cites work: Theory of functional differential equations. 2nd ed
cites work: Q4872463
cites work: Ordinary dichotomy and perturbations of the coefficient matrix of the linear impulsive differential equation
cites work: Q4525531
cites work: On the instability of differential systems with varying delay
cites work: On the Instability of Linear Nonautonomous Delay Systems
cites work: Q4308708
cites work: Dichotomies and asymptotic solutions of nonlinear differential systems
cites work: Roughness of \((h,k)\)-dichotomies
cites work: Stability of Discrete Dichotomies for Linear Difference Systems
cites work: Q3839820
cites work: Discrete dichotomies
DOI: 10.1016/J.NONRWA.2005.04.003
description: scientific article; zbMATH DE number 5116302