scholarly journals The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1845
Author(s):  
A. Nachaoui ◽  
T. Shavadze ◽  
T. Tadumadze
Keyword(s):  
Differential Equation ◽  
Representation Formula ◽  
Initial Vector ◽  
Initial Condition ◽  
Control Functions ◽  
Delay Differential ◽  
And Control ◽  
Nonlinear Delay Differential Equation ◽  
Equation With Delay ◽  
Nonlinear Delay

For the perturbed controlled nonlinear delay differential equation with the discontinuous initial condition, a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of the main interval. In the formula, the effects of perturbations of the delay parameter, the initial vector, the initial and control functions are detected.

The local formula of representation of a solution for a functional differential equation with the mixed initial condition considering perturbations of delays containing in the phase coordinates and in controls

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lela Alkhazishvili ◽  
Medea Iordanishvili
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Analytic Representation ◽  
Initial Vector ◽  
Initial Condition ◽  
Control Functions ◽  
Phase Coordinates ◽  
Functional Differential ◽  
And Control ◽  
Nonlinear Delay

Abstract For the perturbed controlled nonlinear delay functional differential equation with the mixed initial condition a formula of the analytic representation of solution is proved in the left neighborhood of the endpoint of main interval. In the formula the effects of perturbations of the delay parameters containing in the phase coordinates and controls, the initial vector, the initial and control functions are detected.

Numerical Dynamics of Nonstandard Finite Difference Method for Nonlinear Delay Differential Equation

2018 ◽  
Vol 28 (11) ◽  
pp. 1850133 ◽  
Author(s):  
Xiaolan Zhuang ◽  
Qi Wang ◽  
Jiechang Wen
Keyword(s):  
Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Delay Differential Equation ◽  
Difference Method ◽  
Discrete System ◽  
Delay Differential ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay ◽  
Nonstandard Finite Difference

In this paper, we study the dynamics of a nonlinear delay differential equation applied in a nonstandard finite difference method. By analyzing the numerical discrete system, we show that a sequence of Neimark–Sacker bifurcations occur at the equilibrium as the delay increases. Moreover, the existence of local Neimark–Sacker bifurcations is considered, and the direction and stability of periodic solutions bifurcating from the Neimark–Sacker bifurcation of the discrete model are determined by the Neimark–Sacker bifurcation theory of discrete system. Finally, some numerical simulations are adopted to illustrate the corresponding theoretical results.

A Necessary and Sufficient Condition for the Oscillation of an Even Order Nonlinear Delay Differential Equation

1973 ◽  
Vol 25 (5) ◽  
pp. 1078-1089 ◽  
Author(s):  
Bhagat Singh
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Oscillatory Behavior ◽  
Necessary And Sufficient Condition ◽  
Even Order ◽  
Image Position ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Nonlinear Delay Differential Equation ◽  
Nonlinear Delay

In this paper we study the oscillatory behavior of the even order nonlinear delay differential equation(1)where(i) denotes the order of differentiation with respect to t. The delay terms τi σi are assumed to be real-valued, continuous, non-negative, non-decreasing and bounded by a common constant M on the half line (t0, + ∞ ) for some t0 ≧ 0.

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