Asymptotic properties of solutions to discrete Volterra type equations

2021 ◽  
Author(s):  
Janusz Migda ◽  
Magdalena Nockowska‐Rosiak ◽  
Malgorzata Migda
Keyword(s):  
Asymptotic Properties ◽  
Volterra Type

scholarly journals Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Janusz Migda ◽  
Małgorzata Migda ◽  
Magdalena Nockowska-Rosiak
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Type Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Volterra Type ◽  
Order Difference ◽  
Prescribed Asymptotic Behavior

We consider the discrete Volterra type equation of the form Δ(rnΔxn)=bn+∑k=1nK(n,k)f(xk). We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use o(ns), for given nonpositive real s, as a measure of approximation.

Existence and properties of semi-bounded global solutions to the functional differential equation with Volterra-type operators on the real line

2017 ◽  
Vol 147 (6) ◽  
pp. 1119-1168
Author(s):  
Maitere Aguerrea ◽  
Robert Hakl
Keyword(s):  
Real Line ◽  
Asymptotic Properties ◽  
Global Solutions ◽  
Continuous Operator ◽  
Volterra Type ◽  
Existence Of A Solution ◽  
Carathéodory Conditions ◽  
Functional Differential ◽  
Image Position ◽  
Continuous Operators

Consider the equationwhere are linear positive continuous operators and f : Cloc(ℝ;ℝ) → Lloc(ℝ;ℝ) is a continuous operator satisfying the local Carathéodory conditions. Efficient conditions guaranteeing the existence of a global solution, which is bounded and non-negative in the neighbourhood of –∞, to the equation considered are established provided that ℓ0, ℓ1 and f are Volterra-type operators. The existence of a solution that is positive on the whole real line is discussed as well. Furthermore, the asymptotic properties of such solutions are studied in the neighbourhood of –∞. The results are applied to certain models appearing in the natural sciences.

scholarly journals Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
M. De la Sen
Keyword(s):  
Asymptotic Properties ◽  
Distributed Delays ◽  
Asymptotic Convergence ◽  
Time Varying ◽  
Volterra Type ◽  
Linear Dynamics ◽  
Functional Differential Systems ◽  
Functional Differential ◽  
Functional Differential System ◽  
Rassias Stability

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

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