scholarly journals Resolvent of nonautonomous linear delay functional differential equations

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Joël Blot ◽  
Mamadou I. Koné
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Differentiable Function ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Complete Proof ◽  
Right Hand ◽  
Linear Delay ◽  
Functional Differential ◽  
The Right

AbstractThe aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

scholarly journals Existence and Asymptotic Behavior of Positive Solutions of Functional Differential Equations of Delayed Type

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
J. Diblík ◽  
M. Kúdelčíková
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Positive Solutions ◽  
Linear Functional ◽  
Linear Equations ◽  
Functional Differential Equations ◽  
Right Hand ◽  
Functional Differential ◽  
The Right

Solutions of the equationy˙(t)= −f(t,yt)are considered fort→∞. The existence of two classes of positive solutions which are asymptotically different is proved using the retract method combined with Razumikhin's technique. With the aid of two auxiliary linear equations, which are constructed using upper and lower linear functional estimates of the right-hand side of the equation considered, inequalities for both types of positive solutions are given as well.

scholarly journals Generalized quasilinearization method for nonlinear functional differential equations

2003 ◽  
Vol 16 (1) ◽  
pp. 33-43 ◽  
Author(s):  
Bashir Ahmad ◽  
Rehmat Ali Khan ◽  
S. Sivasundaram
Keyword(s):  
Differential Equations ◽  
Rate Of Convergence ◽  
Initial Value Problems ◽  
Functional Differential Equations ◽  
Approximate Solutions ◽  
Monotone Sequence ◽  
Quasilinearization Method ◽  
Initial Value ◽  
Nonlinear Functional ◽  
Functional Differential

We develop a generalized quasilinearization method for nonlinear initial value problems involving functional differential equations and obtain a sequence of approximate solutions converging monotonically and quadratically to the solution of the problem. In addition, we obtain a monotone sequence of approximate solutions converging uniformly to the solution of the problem, possessing the rate of convergence higher than quadratic.

scholarly journals Differential Transform Algorithm for Functional Differential Equations with Time-Dependent Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Josef Rebenda ◽  
Zuzana Pátíková
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Recurrence Relation ◽  
Numerical Solutions ◽  
Functional Differential Equations ◽  
Neutral System ◽  
Initial Value ◽  
Differential Transformation ◽  
Functional Differential

An algorithm using the differential transformation which is convenient for finding numerical solutions to initial value problems for functional differential equations is proposed in this paper. We focus on retarded equations with delays which in general are functions of the independent variable. The delayed differential equation is turned into an ordinary differential equation using the method of steps. The ordinary differential equation is transformed into a recurrence relation in one variable using the differential transformation. Approximate solution has the form of a Taylor polynomial whose coefficients are determined by solving the recurrence relation. Practical implementation of the presented algorithm is demonstrated in an example of the initial value problem for a differential equation with nonlinear nonconstant delay. A two-dimensional neutral system of higher complexity with constant, nonconstant, and proportional delays has been chosen to show numerical performance of the algorithm. Results are compared against Matlab function DDENSD.

scholarly journals A singular initial value problem for some functional differential equations

2004 ◽  
Vol 2004 (3) ◽  
pp. 261-270 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O'Regan ◽  
Oleksandr E. Zernov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Asymptotic Properties ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Singular Initial Value Problem ◽  
Functional Differential

For the initial value problem trx′(t)=at+b1x(t)+b2x(q1t)+b3trx′(q2t)+φ(t,x(t),x(q1t),x′(t),x′(q2t)), x(0)=0, where r>1, 0<qi≤1, i∈{1,2}, we find a nonempty set of continuously differentiable solutions x:(0,ρ]→ℝ, each of which possesses nice asymptotic properties when t→+0.

Continuous dependence of a solution of a neutral functional differential equation on the right-hand side and initial data taking into account perturbations of variable delays

2016 ◽  
Vol 23 (4) ◽  
pp. 519-535
Author(s):  
Nika Gorgodze ◽  
Ia Ramishvili ◽  
Tamaz Tadumadze
Keyword(s):  
Initial Data ◽  
Continuous Dependence ◽  
Functional Differential Equations ◽  
Initial Vector ◽  
Initial Moment ◽  
Neutral Functional Differential Equations ◽  
Variable Delays ◽  
Right Hand ◽  
Functional Differential ◽  
The Right

AbstractTheorems on the continuous dependence of a solution of the Cauchy problem with respect to the nonlinear term of the right-hand side and initial data are proved for neutral functional differential equations whose right-hand sides are linear with respect to the prehistory of the phase velocity. Under the initial data we imply a collection of initial moment, variable delays entering in the phase coordinates, initial vector and initial functions. In this paper, an essential novelty is that perturbations of variable delays are taken into account in proving the main theorems.

Bounded solutions of functional differential equations of the neutral type with infinite delays

1982 ◽  
Vol 93 (1-2) ◽  
pp. 33-39 ◽  
Author(s):  
V. G. Angelov ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Functional Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Bounded Solutions ◽  
Initial Value ◽  
Infinite Delays ◽  
Functional Differential

SynopsisIn this paper the authors obtain sufficient conditions for the existence and uniqueness of the initial value problem of functional differential equations of neutral type with infinite delays, making use of some earlier results of the present authors.

scholarly journals D-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1761
Author(s):  
Natalia Dilna ◽  
Michal Fečkan ◽  
Mykola Solovyov
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Functional Differential Equations ◽  
Linear Functions ◽  
Initial Value ◽  
Nonlinear Functional ◽  
Symmetry Properties ◽  
Theoretical Investigations ◽  
Functional Differential ◽  
Symmetric Property

This paper presents a method of establishing the D-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functional differential equations. Here, we show the conditions of the symmetric property of the unique solution of symmetric functional differential equations. Furthermore, in this paper, an illustration of a particular symmetric equation is presented. In this example, all theoretical investigations referred to earlier are demonstrated. In addition, we graphically demonstrate two possible linear functions with the required symmetry properties.

Periodic solutions of ordinary differential equations with one-sided growth restrictions

1978 ◽  
Vol 82 (1-2) ◽  
pp. 95-106 ◽  
Author(s):  
J. Mawhin ◽  
W. Walter
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Functional Differential Equations ◽  
First Order ◽  
Asymptotic Nature ◽  
Special Cases ◽  
Existence Of Periodic Solutions ◽  
Growth Restrictions ◽  
Functional Differential ◽  
The Right

SynopsisThe existence of periodic solutions is proved for first order vector ordinary and functional differential equations when the right-hand side satisfies a one-sided growth restriction of Wintner type together with some conditions of asymptotic nature. Special cases in the line of Landesman-Lazer and of Winston are explicited.

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