Existence and uniqueness of solution for Stieltjes differential equations with several derivators
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910780846243840 |
|---|---|
| author | Albés, Ignacio Márquez Tojo, F. Adrián F. |
| author_facet | Albés, Ignacio Márquez Tojo, F. Adrián F. |
| contents | In this paper, we study some existence and uniqueness results for systems of differential equations in which each of equations of the system involves a different Stieltjes derivative. Specifically, we show that this problems can only have one solution under the Osgood condition, or even, the Montel-Tonelli condition. We also explore some results guaranteeing the existence of solution under these conditions. Along the way, we obtain some interesting properties for the Lebesgue-Stieltjes integral associated to a finite sum of nondecreasing and left-continuous maps, as well as a characterization of the pseudometric topologies defined by this type of maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06627 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness of solution for Stieltjes differential equations with several derivators Albés, Ignacio Márquez Tojo, F. Adrián F. Classical Analysis and ODEs In this paper, we study some existence and uniqueness results for systems of differential equations in which each of equations of the system involves a different Stieltjes derivative. Specifically, we show that this problems can only have one solution under the Osgood condition, or even, the Montel-Tonelli condition. We also explore some results guaranteeing the existence of solution under these conditions. Along the way, we obtain some interesting properties for the Lebesgue-Stieltjes integral associated to a finite sum of nondecreasing and left-continuous maps, as well as a characterization of the pseudometric topologies defined by this type of maps. |
| title | Existence and uniqueness of solution for Stieltjes differential equations with several derivators |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2501.06627 |