On regularity of mild solutions for autonomous linear retarded functional differential equations
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929422303494144 |
|---|---|
| author | Nishiguchi, Junya |
| author_facet | Nishiguchi, Junya |
| contents | The notion of mild solutions for autonomous linear retarded functional differential equations (RFDEs) has been introduced in [J. Nishiguchi, Electron.\ J. Qual.\ Theory Differ.\ Equ.\ \textbf{2023}, No.~32, 1--77] for the purpose of defining fundamental matrix solutions and obtaining a variation of constants formula for the RFDEs. This notion gives a straightforward definition of solutions to the RFDEs under discontinuous history functions compared with previous studies in the literature. For a given autonomous linear RFDE, it holds that the fundamental matrix solutions are locally Lipschitz continuous on the interval $[0, \infty)$. However, it is not apparent whether a similar property is true for the mild solutions. Here we obtain a result which shows the regularity of mild solutions on $[0, \infty)$ for autonomous linear RFDEs. The result makes clear a connection between the mild solutions and solution concepts in previous studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11777 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On regularity of mild solutions for autonomous linear retarded functional differential equations Nishiguchi, Junya Dynamical Systems Primary 34K05, 34K06, Secondary 34K99, 26A42 The notion of mild solutions for autonomous linear retarded functional differential equations (RFDEs) has been introduced in [J. Nishiguchi, Electron.\ J. Qual.\ Theory Differ.\ Equ.\ \textbf{2023}, No.~32, 1--77] for the purpose of defining fundamental matrix solutions and obtaining a variation of constants formula for the RFDEs. This notion gives a straightforward definition of solutions to the RFDEs under discontinuous history functions compared with previous studies in the literature. For a given autonomous linear RFDE, it holds that the fundamental matrix solutions are locally Lipschitz continuous on the interval $[0, \infty)$. However, it is not apparent whether a similar property is true for the mild solutions. Here we obtain a result which shows the regularity of mild solutions on $[0, \infty)$ for autonomous linear RFDEs. The result makes clear a connection between the mild solutions and solution concepts in previous studies. |
| title | On regularity of mild solutions for autonomous linear retarded functional differential equations |
| topic | Dynamical Systems Primary 34K05, 34K06, Secondary 34K99, 26A42 |
| url | https://arxiv.org/abs/2407.11777 |