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

[21] A NEW APPROACH TO THE METHOD OF NONLINEAR VARIATION OF PARAMETERS FOR A PERTURBED NONLINEAR NEUTRAL FUNCTIONAL-DIFFERENTIAL EQUATION
VENTURA, A
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1989, 138 (01) : 59 - 74
[22] REPRESENTATION AND APPROXIMATION OF GENERALIZED SOLUTIONS OF A NON-LINEAR FUNCTIONAL-DIFFERENTIAL EQUATION
PARROTT, ME
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1982, 6 (04) : 307 - 318
[23] ON THE OSCILLATION OF THIRD-ORDER QUASI-LINEAR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS
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Li, Tongxing
ARCHIVUM MATHEMATICUM, 2011, 47 (03): : 181 - 199
[24] NUMERICAL-SOLUTION OF A QUASI-LINEAR 2ND-ORDER SINGULARLY PERTURBED EQUATION
ZADORIN, AI
IGNATYEV, VI
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1991, 31 (01) : 112 - 116
[25] VARIATION FORMULAS OF SOLUTION FOR A CONTROLLED FUNCTIONAL-DIFFERENTIAL EQUATION CONSIDERING DELAY PERTURBATION
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Nachaoui, A.
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[26] Generalized solutions of local initial problems for quasi-linear hyperbolic functional differential systems
Czlapinski, T
Kamont, Z
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 1999, 35 (1-2) : 185 - 206
[27] FINITE-DIFFERENCE METHOD FOR A NONLINEAR PARABOLIC FUNCTIONAL-DIFFERENTIAL EQUATION WITH AN INITIAL CAUCHY CONDITION
MALEC, M
SCHIAFFINO, A
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1987, 1B (01): : 99 - 109
[28] SOLUTION OF A MIXED PROBLEM WITH PERIODIC BOUNDARY CONDITION FOR A QUASI-LINEAR EULER-BERNOULLI EQUATION
Halilov, H.
Kutlu, K.
Guler, B. O.
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2010, 39 (03): : 417 - 428
[29] A finite difference method for quasi-linear and nonlinear differential functional parabolic equations with Dirichlet's condition
Sapa, Lucjan
ANNALES POLONICI MATHEMATICI, 2008, 93 (02) : 113 - 133
[30] Probabilistic representation and local existence for the quasi-linear partial integro-differential equations with Sobolev initial value
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