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

被引：1

作者：

Nachaoui, A. ^{[1
]}

Shavadze, T. ^{[2
]}

Tadumadze, T. ^{[2
,3
]}

机构：

[1] Univ Nantes, Jean Leray Lab Math, CNRS UMR 6629, 2 Rue Houssiniere,BP 92208, F-44322 Nantes, France

[2] I Vekua Inst Appl Math, 2 Univ St, GE-0186 Tbilisi, Georgia

[3] Iv Javakhishvili Tbilisi State Univ, Dept Math, GE-0186 Tbilisi, Georgia

来源：

MATHEMATICS | 2020年 / 8卷 / 10期

基金：

美国国家科学基金会;

关键词：

delay-controlled differential equation; representation of solution; discontinuous initial condition; perturbations;

D O I：

10.3390/math8101845

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1 / 12

页数：12

共 12 条

[1] ON THE REPRESENTATION OF SOLUTION OF THE PERTURBED CONTROLLED DIFFERENTIAL EQUATION WITH DELAY AND CONTINUOUS INITIAL CONDITION
Tadumadze, Tamaz
Dvalishvili, Phridon
Shavadze, Tea
APPLIED AND COMPUTATIONAL MATHEMATICS, 2019, 18 (03) : 305 - 315
[2] On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition
Nachaoui, Abdeljalil
Shavadze, Tea
Tadumadze, Tamaz
GEORGIAN MATHEMATICAL JOURNAL, 2024, 31 (05) : 847 - 860
[3] 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
Alkhazishvili, Lela
Iordanishvili, Medea
GEORGIAN MATHEMATICAL JOURNAL, 2022, 29 (01) : 1 - 12
[4] Uniformly convergent numerical method for two parameter singularly perturbed parabolic differential equations with discontinuous initial condition
Kumari, Neha
Gowrisankar, S.
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2024,
[5] A robust B-spline method for two parameter singularly perturbed parabolic differential equations with discontinuous initial condition
Kumari, Neha
Gowrisankar, S.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2024, 70 (06) : 5379 - 5403
[6] Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition
J. L. Gracia
E. O’Riordan
Numerical Algorithms, 2021, 88 : 1851 - 1873
[7] Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition
Gracia, J. L.
O'Riordan, E.
NUMERICAL ALGORITHMS, 2021, 88 (04) : 1851 - 1873
[8] Optimization of Initial Data for Linear Neutral Functional-Differential Equations with the Discontinuous Initial Condition
Tadumadze, T.
AZERBAIJAN JOURNAL OF MATHEMATICS, 2012, 2 (02): : 84 - 93
[9] Parameter-uniform approximations for a singularly perturbed convection-diffusion problem with a discontinuous initial condition
Luis Gracia, Jose
O'Riordan, Eugene
APPLIED NUMERICAL MATHEMATICS, 2021, 162 (162) : 106 - 123
[10] A RELIABLE NUMERICAL METHOD FOR THE SINGULARLY PERTURBED NONLINEAR DIFFERENTIAL EQUATION WITH AN INTEGRAL BOUNDARY CONDITION
Cakir, Musa
Gurbuz, Bahar
Gunes, Baransel
TRANSACTIONS OF A RAZMADZE MATHEMATICAL INSTITUTE, 2024, 178 (03) : 381 - 391

← 1 2 →