scholarly journals Nonlinear Volterra difference equations in spacelp

2004 ◽  
Vol 2004 (2) ◽  
pp. 301-306 ◽  
Author(s):  
Michael I. Gil' ◽  
Rigoberto Medina
Keyword(s):  
Discrete Time ◽  
Difference Equations ◽  
Volterra Equations ◽  
Stability Conditions ◽  
Lyapunov Functionals ◽  
Volterra Difference Equations

We consider a class of vector nonlinear discrete-time Volterra equations in spacelpand derive estimates for the norms of solutions. These estimates give us explicit stability conditions, which allow us to avoid finding Lyapunov functionals.

scholarly journals Boundedness of solutions of matrix nonlinear volterra difference equations

2002 ◽  
Vol 7 (1) ◽  
pp. 19-22
Author(s):  
Michael I. Gil' ◽  
Rigoberto Medina
Keyword(s):  
Euclidean Space ◽  
Discrete Time ◽  
Difference Equations ◽  
Volterra Equations ◽  
Boundedness Of Solutions ◽  
Volterra Operators ◽  
Norm Of The Resolvent ◽  
Volterra Difference Equations

Nonlinear discrete-time Volterra equations in a Euclidean space are considered. Conditions for the boundedness of solutions are established by virtue of recent estimates for the norm of the resolvent of Volterra operators. The conditions are formulated in the terms of coefficients of considered equations. In addition, estimates for thec0- andl2-norms of solutions are derived.

scholarly journals Existence and Boundedness of Solutions for Nonlinear Volterra Difference Equations in Banach Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Rigoberto Medina
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Discrete Time ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Volterra Equations ◽  
Boundedness Of Solutions ◽  
Nilpotent Operators ◽  
All Solutions ◽  
Volterra Difference Equations

We consider a class of nonlinear discrete-time Volterra equations in Banach spaces. Estimates for the norm of operator-valued functions and the resolvents of quasi-nilpotent operators are used to find sufficient conditions that all solutions of such equations are elements of an appropriate Banach space. These estimates give us explicit boundedness conditions. The boundedness of solutions to Volterra equations with infinite delay is also investigated.

GENERAL METHOD OF LYAPUNOV FUNCTIONALS CONSTRUCTION IN STABILITY INVESTIGATIONS OF NONLINEAR STOCHASTIC DIFFERENCE EQUATIONS WITH CONTINUOUS TIME

2005 ◽  
Vol 05 (02) ◽  
pp. 175-188 ◽  
Author(s):  
LEONID SHAIKHET
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Continuous Time ◽  
Type Theorem ◽  
Volterra Equations ◽  
Lyapunov Functionals ◽  
Stochastic Difference Equation ◽  
Stochastic Difference Equations ◽  
After Effect ◽  
General Method

The general method of Lyapunov functionals construction has been developed during the last decade for stability investigations of stochastic differential equations with after-effect and stochastic difference equations. After some modification of the basic Lyapunov type theorem this method was successfully used also for difference Volterra equations with continuous time. The latter often appear as useful mathematical models. Here this method is used for a stability investigation of some nonlinear stochastic difference equation with continuous time.

scholarly journals Some stability conditions for scalar Volterra difference equations

2016 ◽  
Vol 36 (4) ◽  
pp. 459 ◽  
Author(s):  
Leonid Berezansky ◽  
Małgorzata Migda ◽  
Ewa Schmeidel
Keyword(s):  
Difference Equations ◽  
Stability Conditions ◽  
Volterra Difference Equations

scholarly journals Mittag-Leffler stability analysis of fractional discrete-time neural networks via fixed point technique

2019 ◽  
Vol 24 (6) ◽  
Author(s):  
Guo-Cheng Wu ◽  
Thabet Abdeljawad ◽  
Jinliang Liu ◽  
Dumitru Baleanu ◽  
Kai-Teng Wu
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Discrete Time ◽  
Difference Equations ◽  
Complete Solution ◽  
Solution Space ◽  
Stability Conditions ◽  
Fractional Difference ◽  
Finite Time Stability ◽  
Fractional Difference Equations

A class of semilinear fractional difference equations is introduced in this paper. The fixed point theorem is adopted to find stability conditions for fractional difference equations. The complete solution space is constructed and the contraction mapping is established by use of new equivalent sum equations in form of a discrete Mittag-Leffler function of two parameters. As one of the application, finite-time stability is discussed and compared. Attractivity of fractional difference equations is proved, and Mittag-Leffler stability conditions are provided. Finally, the stability results are applied to fractional discrete-time neural networks with and without delay, which show the fixed point technique’s efficiency and convenience.

scholarly journals Stability for Linear Volterra Difference Equations in Banach Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Rigoberto Medina
Keyword(s):  
Banach Spaces ◽  
Difference Equations ◽  
Stability Conditions ◽  
Freezing Method ◽  
Existence And Stability ◽  
Volterra Difference Equations

This paper is devoted to studying the existence and stability of implicit Volterra difference equations in Banach spaces. The proofs of our results are carried out by using an appropriate extension of the freezing method to Volterra difference equations in Banach spaces. Besides, sharp explicit stability conditions are derived.

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