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.

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 Stability of a Functional Differential System with a Finite Number of Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Josef Rebenda ◽  
Zdeněk Šmarda
Keyword(s):  
Asymptotic Stability ◽  
Differential System ◽  
Asymptotic Properties ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Stability Of Solutions ◽  
Functional Differential ◽  
The Stability ◽  
Complex Valued ◽  
Functional Differential System

The paper is devoted to the study of asymptotic properties of a real two-dimensional differential system with unbounded nonconstant delays. The sufficient conditions for the stability and asymptotic stability of solutions are given. Used methods are based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties are studied by means of Lyapunov-Krasovskii functional. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one or more constant delays or one nonconstant delay were studied.

scholarly journals Positive solutions of functional-differential systems via the vector version of Krasnoselskii’s fixed point theorem in cones

2011 ◽  
Vol 27 (2) ◽  
pp. 165-172
Author(s):  
SORIN BUDISAN ◽  
◽  
RADU PRECUP ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Functional Differential Systems ◽  
Existence Of Positive Solutions ◽  
Vector Version ◽  
Functional Differential ◽  
Functional Differential System

We study the existence of positive solutions of the functional-differential system ... (0 < t < 1), subject to linear boundary conditions. We prove the existence of at least one positive solution by using the vector version of Krasnoselskii’s fixed point theorem in cones.

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