On the representation of solution for the perturbed quasi-linear controlled neutral functional-differential equation with the discontinuous initial condition

被引：0

作者：

Nachaoui, Abdeljalil ^{[3
]}

Shavadze, Tea ^{[1
,2
]}

Tadumadze, Tamaz ^{[2
,4
]}

机构：

[1] Business & Technol Univ, 82 I Chavchavadze Ave, GE-0162 Tbilisi, Georgia

[2] Iv Javakhishvili Tbilisi State Univ, I Vekua Inst Appl Math, 11 Univ St, GE-0186 Tbilisi, Georgia

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

[4] Javakhishvili Tbilisi State Univ, Dept Math, 11 Univ St, GE-0186 Tbilisi, Georgia

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2024年 / 31卷 / 05期

基金：

美国国家科学基金会;

关键词：

Neutral functional-differential equation; perturbations; representation of solution; discontinuous initial condition;

D O I：

10.1515/gmj-2023-2122

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The analytic relation between solutions of the original Cauchy problem and a corresponding perturbed problem is established. In the representation formula of solution, the effects of the discontinuous initial condition and perturbation of the initial data are revealed.

引用

页码：847 / 860

页数：14

共 47 条

[1] VARIATION FORMULAS OF A SOLUTION AND INITIAL DATA OPTIMIZATION PROBLEMS FOR QUASI-LINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS INITIAL CONDITION
Tadumadze, Tamaz
Gorgodze, Nika
MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2014, 63 : 1 - 77
[2] The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition
Nachaoui, A.
Shavadze, T.
Tadumadze, T.
MATHEMATICS, 2020, 8 (10) : 1 - 12
[3] 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
[4] ON THE REPRESENTATION OF SOLUTION OF THE PERTURBED CONTROLLED DIFFERENTIAL EQUATION WITH DELAY AND CONTINUOUS INITIAL CONDITION
Tadumadze, Tamaz
Dvalishvili, Phridon
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APPLIED AND COMPUTATIONAL MATHEMATICS, 2019, 18 (03) : 305 - 315
[5] PERIODIC-SOLUTIONS OF LINEAR AND QUASI-LINEAR NEUTRAL FUNCTIONAL-DIFFERENTIAL EQUATIONS
ZHANG, M
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 189 (02) : 378 - 392
[6] ASYMPTOTIC-BEHAVIOR OF A PERTURBED NEUTRAL FUNCTIONAL-DIFFERENTIAL EQUATION RELATED TO THE SOLUTION OF THE UNPERTURBED LINEAR-SYSTEM
IZE, AF
VENTURA, A
PACIFIC JOURNAL OF MATHEMATICS, 1984, 111 (01) : 57 - 91
[7] CLASSICAL SOLUTION OF THE CAUCHY PROBLEM FOR A QUASI-LINEAR WAVE EQUATION WITH DISCONTINUOUS INITIAL CONDITIONS
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Rudzko, Jan, V
DOKLADY NATSIONALNOI AKADEMII NAUK BELARUSI, 2023, 67 (03): : 183 - 188
[8] OPTIMAL CONTROL OF THE QUASI-LINEAR NEUTRAL DIFFERENTIAL EQUATION
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PROCEEDINGS OF THE 6TH INTERNATIONAL CONFERENCE ON CONTROL AND OPTIMIZATION WITH INDUSTRIAL APPLICATIONS, VOL I, 2018, : 173 - 175
[9] OSCILLATION CRITERIA FOR SECOND-ORDER QUASI-LINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATION
Moaaz, Osama
Bazighifan, Omar
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2020, 13 (09): : 2465 - 2473
[10] QUASI-LINEAR MULTISTEP METHODS AND VARIABLE STEP PREDICTOR CORRECTOR METHODS FOR NEUTRAL FUNCTIONAL-DIFFERENTIAL EQUATIONS
JACKIEWICZ, Z
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1986, 23 (02) : 423 - 452

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