On the approximation of continuous functions by analytic solutions of universal functional-differential equations

2004 ◽  
Vol 41 (1) ◽  
pp. 1-15 ◽  
Author(s):  
C. Elsner
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Analytic Solutions ◽  
Continuous Functions ◽  
Functional Differential ◽  
Approximation Of Continuous Functions

Periodic solutions to functional differential equations

1985 ◽  
Vol 101 (3-4) ◽  
pp. 253-271 ◽  
Author(s):  
O. A. Arino ◽  
T. A. Burton ◽  
J. R. Haddock
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Continuous Functions ◽  
Ultimate Boundedness ◽  
Space Of Continuous Functions ◽  
Uniform Ultimate Boundedness ◽  
Functional Differential ◽  
Image Position

SynopsisWe consider a system of functional differential equationswhere G: R × B → Rn is T periodic in t and B is a certain phase space of continuous functions that map (−∞, 0[ into Rn. The concepts of B-uniform boundedness and B-uniform ultimate boundedness are introduced, and sufficient conditions are given for the existence of a T-periodic solution to (1.1). Several examples are given to illustrate the main theorem.

On the existence of periodic solutions for autonomous retarded functional differential equations on R2

1986 ◽  
Vol 102 (3-4) ◽  
pp. 259-262 ◽  
Author(s):  
J. G. Dos Reis ◽  
R. L. S. Baroni
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Retarded Functional Differential Equations ◽  
Existence Of Periodic Solutions ◽  
Functional Differential

SynopsisLet Ca be the set of all the continuous functions from the interval [−r, 0] on the sphere of radius a, on the plane. We prove, under certains conditions, that a retarded autonomous differential equation that leaves Ca invariant has a non-constant periodic solution.

scholarly journals The Kneser property for abstract retarded functional differential equations with infinite delay

2003 ◽  
Vol 2003 (26) ◽  
pp. 1645-1661 ◽  
Author(s):  
Hernán R. Henríquez
Keyword(s):  
Differential Equations ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Space Of Continuous Functions ◽  
First Order ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

We establish existence of mild solutions for a class of semilinear first-order abstract retarded functional differential equations (ARFDEs) with infinite delay and we prove that the set consisting of mild solutions for this problem is connected in the space of continuous functions.

scholarly journals Practical Stability with Respect to h-Manifolds for Impulsive Control Functional Differential Equations with Variable Impulsive Perturbations

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 656 ◽  
Author(s):  
Gani Stamov ◽  
Ivanka Stamova ◽  
Xiaodi Li ◽  
Ekaterina Gospodinova
Keyword(s):  
Differential Equations ◽  
Impulsive Control ◽  
Functional Differential Equations ◽  
Cellular Neural Network ◽  
Continuous Functions ◽  
Practical Stability ◽  
Piecewise Continuous ◽  
Impulsive Perturbations ◽  
Functional Differential ◽  
Control Functional

The present paper is devoted to the problems of practical stability with respect to h-manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumikhin method of piecewise continuous functions. The new results are applied to an impulsive control cellular neural network model with variable impulsive perturbations.

Asymptotic behaviour of functional-differential equations with proportional time delays

1996 ◽  
Vol 7 (1) ◽  
pp. 11-30 ◽  
Author(s):  
Yunkang Liu
Keyword(s):  
Differential Equations ◽  
Asymptotic Behaviour ◽  
Initial Value Problem ◽  
Time Delays ◽  
Functional Differential Equations ◽  
Analytic Solutions ◽  
Comprehensive Analysis ◽  
Initial Value ◽  
Functional Differential ◽  
Image Position

This paper discusses the initial value problemwhereA, BiandCiared × dcomplex matrices,pi,qi∈ (0, 1),i= 1, 2, …, andy0is a column vector in ℂd. By using ideas from the theory of ordinary differential equations and the theory of functional equations, we give a comprehensive analysis of the asymptotic behaviour of analytic solutions of this initial value problem.

scholarly journals LINEAR AUTONOMOUS NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS IN THE PHASE SPACE OF REGULATED FUNCTIONS

1994 ◽  
Vol 25 (3) ◽  
pp. 195-207
Author(s):  
LUIZ FICHMANN
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Linear Equation ◽  
Functional Differential Equations ◽  
Continuous Functions ◽  
Neutral Functional Differential Equations ◽  
Functional Differential ◽  
Regulated Functions ◽  
Natural Description

We extend the natural description of the spectrum for the flow of the linear equation $\frac{d}{dt}Dx_t=Lx_t$ from the context of continuous functions to the context of regulated right-continuous functions.

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