scholarly journals Modified Wiener equations

2001 ◽  
Vol 27 (6) ◽  
pp. 347-356 ◽  
Author(s):  
Will Watkins
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Initial Value Problem ◽  
Initial Conditions ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Initial Value ◽  
Order Ordinary Differential Equation ◽  
First Case ◽  
Functional Differential

This paper is concerned with a class of functional differential equations whose argument transforms are involutions. In contrast to the earlier works in this area, which have used only involutions with a fixed point, we also admit involutions without a fixed point. In the first case, an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. In our case, either two initial conditions or two boundary conditions are necessary for a solution; the equation is then reduced to a boundary value problem for a higher order ODE.

scholarly journals The System of Differential Equations Associated With Involutions

2021 ◽  
Author(s):  
Farrukh Nuriddin ugli Dekhkonov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Initial Value Problem ◽  
Initial Conditions ◽  
Higher Order ◽  
System Of Differential Equations ◽  
Initial Value ◽  
Order Ordinary Differential Equation

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

scholarly journals Asymptotic Dichotomy in a Class of Third-Order Nonlinear Differential Equations with Impulses

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Kun-Wen Wen ◽  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Nonlinear Differential Equation ◽  
Nonlinear Differential Equations ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Third Order ◽  
Order Nonlinear Differential Equation ◽  
Functional Differential

Solutions of quite a few higher-order delay functional differential equations oscillate or converge to zero. In this paper, we obtain several such dichotomous criteria for a class of third-order nonlinear differential equation with impulses.

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.

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.

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 Solving a well-posed fractional initial value problem by a complex approach

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Arran Fernandez ◽  
Sümeyra Uçar ◽  
Necati Özdemir
Keyword(s):  
Fixed Point ◽  
Initial Value Problem ◽  
Complex Analysis ◽  
Fixed Point Theory ◽  
Initial Conditions ◽  
Point Theory ◽  
Initial Value ◽  
Complex Approach ◽  
Set Up ◽  
Well Posed

AbstractNonlinear fractional differential equations have been intensely studied using fixed point theorems on various different function spaces. Here we combine fixed point theory with complex analysis, considering spaces of analytic functions and the behaviour of complex powers. It is necessary to study carefully the initial value properties of Riemann–Liouville fractional derivatives in order to set up an appropriate initial value problem, since some such problems considered in the literature are not well-posed due to their initial conditions. The problem that emerges turns out to be dimensionally consistent in an unexpected way, and therefore suitable for applications too.

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