On Exponential Stability of Volterra Difference Equations with Infinite Delay

2014 ◽  
Vol 62 (2) ◽  
pp. 125-137
Author(s):  
Pham Huu Anh Ngoc ◽  
Le Trung Hieu
Keyword(s):  
Exponential Stability ◽  
Difference Equations ◽  
Infinite Delay ◽  
Volterra Difference Equations

scholarly journals Stability of the positive steady-state solutions of systems of nonlinear Volterra difference equations of population models with diffusion and infinite delay

2000 ◽  
Vol 23 (4) ◽  
pp. 261-270 ◽  
Author(s):  
B. Shi
Keyword(s):  
Steady State ◽  
Difference Equations ◽  
Infinite Delay ◽  
Steady State Solution ◽  
Population Models ◽  
Monotone Iterative ◽  
Positive Steady State ◽  
Infinite Delays ◽  
Steady State Solutions ◽  
Volterra Difference Equations

An open problem given by Kocic and Ladas in 1993 is generalized and considered. A sufficient condition is obtained for each solution to tend to the positive steady-state solution of the systems of nonlinear Volterra difference equations of population models with diffusion and infinite delays by using the method of lower and upper solutions and monotone iterative techniques.

ASYMPTOTIC EXPANSION FOR DIFFERENCE EQUATIONS WITH INFINITE DELAY

2009 ◽  
Vol 02 (01) ◽  
pp. 19-40
Author(s):  
Claudio Cuevas ◽  
Luis del Campo
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Asymptotic Expansion ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Difference Equations ◽  
Infinite Delay ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Volterra Difference Equations

Using summable dichotomies and Schauder's fixed point theorem, we obtain existence, asymptotic behavior and compactness properties, of convergent solutions for difference equations with infinite delay. Applications on Volterra difference equations with infinite delay are shown.

New criteria for global exponential stability of linear time-varying volterra difference equations

2016 ◽  
Vol 66 (6) ◽  
Author(s):  
Trung Hieu Le
Keyword(s):  
Exponential Stability ◽  
Difference Equations ◽  
Global Exponential Stability ◽  
Linear Time ◽  
Time Varying ◽  
Novel Approach ◽  
New Criteria ◽  
Volterra Difference Equations ◽  
Explicit Criteria

AbstractLinear time-varying Volterra difference equations are considered. By a novel approach, we get some new explicit criteria for global exponential stability. Some examples are given to illustrate the obtained results. To the best of our knowledge, the obtained results are new.

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