<i>D</i>-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations
This paper presents a method of establishing the <i>D</i>-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/11/1761 |
| _version_ | 1797549961135521792 |
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| author | Natalia Dilna Michal Fečkan Mykola Solovyov |
| author_facet | Natalia Dilna Michal Fečkan Mykola Solovyov |
| author_sort | Natalia Dilna |
| collection | DOAJ |
| description | This paper presents a method of establishing the <i>D</i>-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functional differential equations. Here, we show the conditions of the symmetric property of the unique solution of symmetric functional differential equations. Furthermore, in this paper, an illustration of a particular symmetric equation is presented. In this example, all theoretical investigations referred to earlier are demonstrated. In addition, we graphically demonstrate two possible linear functions with the required symmetry properties. |
| first_indexed | 2024-03-10T15:22:28Z |
| format | Article |
| id | doaj.art-322c763b233f4f2eb37d84c654143339 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T15:22:28Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-322c763b233f4f2eb37d84c6541433392023-11-20T18:19:51ZengMDPI AGSymmetry2073-89942020-10-011211176110.3390/sym12111761<i>D</i>-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential EquationsNatalia Dilna0Michal Fečkan1Mykola Solovyov2Mathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, SlovakiaMathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, SlovakiaSuperconductors Department, Institute of Electrical Engineering, Slovak Academy of Sciences, Dúbravská cesta 9, 841 01 Bratislava, SlovakiaThis paper presents a method of establishing the <i>D</i>-stability terms of the symmetric solution of scalar symmetric linear and nonlinear functional differential equations. We determine the general conditions of the unique solvability of the initial value problem for symmetric functional differential equations. Here, we show the conditions of the symmetric property of the unique solution of symmetric functional differential equations. Furthermore, in this paper, an illustration of a particular symmetric equation is presented. In this example, all theoretical investigations referred to earlier are demonstrated. In addition, we graphically demonstrate two possible linear functions with the required symmetry properties.https://www.mdpi.com/2073-8994/12/11/1761symmetric solutionCauchy problemunique solution<i>D</i>-stability |
| spellingShingle | Natalia Dilna Michal Fečkan Mykola Solovyov <i>D</i>-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations Symmetry symmetric solution Cauchy problem unique solution <i>D</i>-stability |
| title | <i>D</i>-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations |
| title_full | <i>D</i>-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations |
| title_fullStr | <i>D</i>-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations |
| title_full_unstemmed | <i>D</i>-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations |
| title_short | <i>D</i>-Stability of the Initial Value Problem for Symmetric Nonlinear Functional Differential Equations |
| title_sort | i d i stability of the initial value problem for symmetric nonlinear functional differential equations |
| topic | symmetric solution Cauchy problem unique solution <i>D</i>-stability |
| url | https://www.mdpi.com/2073-8994/12/11/1761 |
| work_keys_str_mv | AT nataliadilna idistabilityoftheinitialvalueproblemforsymmetricnonlinearfunctionaldifferentialequations AT michalfeckan idistabilityoftheinitialvalueproblemforsymmetricnonlinearfunctionaldifferentialequations AT mykolasolovyov idistabilityoftheinitialvalueproblemforsymmetricnonlinearfunctionaldifferentialequations |