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- Title
Perron-Type Criterion for Linear Difference Equations with Distributed Delay.
- Authors
Alzabut, Jehad O.; Abdeljawad, Thabet
- Abstract
The article focuses on Perron's theorem for linear difference equations with distributed delay. It is well known in theory of ordinary differential equations that if for every continuous function F(t) bounded on [0, ∞), the solution of a given equation satisfying x(0) = 0 is bounded on [0, infin;), then the trivial solution of the corresponding homogenous equation is uniformly asymptotically stable. This result is referred as Perron's criterion, which has been extended to differential equations with distributed delay. One of the ways of deriving discrete time version of dynamical systems corresponding to continuous time formulations is based on appropriate modifications of the models.
- Subjects
DIFFERENCE equations; LINEAR systems; DISTRIBUTED algorithms; DIFFERENTIAL equations; CONTINUOUS functions; EQUATIONS; DISCRETE-time systems
- Publication
Discrete Dynamics in Nature & Society, 2007, p1
- ISSN
1026-0226
- Publication type
Article
- DOI
10.1155/2007/10840