On the non-uniqueness of continuous solutions to differential equations with a discrete state-dependent delay
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914466057158656 |
|---|---|
| author | Rezounenko, Alexander |
| author_facet | Rezounenko, Alexander |
| contents | We discuss the non-uniqueness of continuous solutions to differential equations with a {\it discrete } state-dependent delay and continuous initial functions. We are interested not only in the fact (conditions) of non-uniqueness, but in additional information on the number of non-unique solutions and discuss an approach to classify them. We provide a few explicit (easy to verify) examples of the non-uniqueness of continuous solutions and propose an approach to their classification. This partial classification may be illustrated by using just three collors and their simple and intuitive combination. We recognize that this initial classification is not exhaustive, and further study is necessary to build a complete picture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10265 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the non-uniqueness of continuous solutions to differential equations with a discrete state-dependent delay Rezounenko, Alexander Classical Analysis and ODEs Dynamical Systems 34K43, 34A12, 34K05 We discuss the non-uniqueness of continuous solutions to differential equations with a {\it discrete } state-dependent delay and continuous initial functions. We are interested not only in the fact (conditions) of non-uniqueness, but in additional information on the number of non-unique solutions and discuss an approach to classify them. We provide a few explicit (easy to verify) examples of the non-uniqueness of continuous solutions and propose an approach to their classification. This partial classification may be illustrated by using just three collors and their simple and intuitive combination. We recognize that this initial classification is not exhaustive, and further study is necessary to build a complete picture. |
| title | On the non-uniqueness of continuous solutions to differential equations with a discrete state-dependent delay |
| topic | Classical Analysis and ODEs Dynamical Systems 34K43, 34A12, 34K05 |
| url | https://arxiv.org/abs/2604.10265 |