Total Stability in Nonlinear Discrete Volterra Equations with Unbounded Delay

Almost Periodic Solutions of Nonlinear Discrete Volterra Equations with Unbounded Delay

In this paper we study the existence of almost periodic solution for nonlinear discrete Volterra equation with unbounded delay, as a discrete version of the results for integro-differential equations. 1. Almost periodic sequences and difference equations Bohr’s theory of almost periodic functions has been extensively studied, especially in connection with differential equations. Almost periodic...

Almost Periodic Solutions of Nonlinear Volterra Difference Equations with Unbounded Delay

In order to obtain the conditions for the existence of periodic and almost periodic solutions of Volterra difference equations, x(n+1) = f(n, x(n))+ ∑n s=−∞ F (n, s, x(n+ s), x(n)), we consider certain stability properties, which are referred to as (K, ρ)-weakly uniformly-asymptotic stability and (K, ρ)-uniformly asymptotic stability. Moreover, we discuss the relationship between the ρ-separati...

Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

Boundedness and stability of discrete Volterra equations

Lyapunov Functionals and Stability in Nonlinear Finite Delay Volterra Discrete Systems

In this research, we utilize Lyapunov functionals and obtain sufficient conditions for the stability of the zero solution of the discrete Volterra system of the form x(t+ 1) = Px(t) + t−1 ∑ s=t−r C(t, s)g(x(s)). Due to the nature of the Lyapunov functional, we will be able to show that all solutions are l ( [t0,∞) ∩ Z ) . AMS Subject Classifications: 3K20, 45J05.