The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition
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 paramet...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1845 |
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| author | A. Nachaoui T. Shavadze T. Tadumadze |
| author_facet | A. Nachaoui T. Shavadze T. Tadumadze |
| author_sort | A. Nachaoui |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T15:30:00Z |
| format | Article |
| id | doaj.art-d4cdfee93db34c2193edeb119abc6731 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:30:00Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d4cdfee93db34c2193edeb119abc67312023-11-20T17:47:03ZengMDPI AGMathematics2227-73902020-10-01810184510.3390/math8101845The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial ConditionA. Nachaoui0T. Shavadze1T. Tadumadze2Jean Leray Laboratory of Mathematics, University of Nantes, CNRS UMR 6629 2 rue de Houssiniere, B.P. 92208, 44322 Nantes, FranceI. Vekua Institute of Applied Mathematics, 2 University St., 0186 Tbilisi, GeorgiaI. Vekua Institute of Applied Mathematics, 2 University St., 0186 Tbilisi, GeorgiaFor 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.https://www.mdpi.com/2227-7390/8/10/1845delay-controlled differential equationrepresentation of solutiondiscontinuous initial conditionperturbations |
| spellingShingle | A. Nachaoui T. Shavadze T. Tadumadze The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition Mathematics delay-controlled differential equation representation of solution discontinuous initial condition perturbations |
| title | The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition |
| title_full | The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition |
| title_fullStr | The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition |
| title_full_unstemmed | The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition |
| title_short | The Local Representation Formula of Solution for the Perturbed Controlled Differential Equation with Delay and Discontinuous Initial Condition |
| title_sort | local representation formula of solution for the perturbed controlled differential equation with delay and discontinuous initial condition |
| topic | delay-controlled differential equation representation of solution discontinuous initial condition perturbations |
| url | https://www.mdpi.com/2227-7390/8/10/1845 |
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