Existence, uniqueness, variation-of-constant formula and controllability for linear dynamic equations with Perron -integrals
| Autor: | F. Andrade da Silva, M. Federson, E. Toon |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Bulletin of Mathematical Sciences, Vol 12, Iss 03 (2022) |
| Druh dokumentu: | article |
| ISSN: | 16643607 1664-3615 1664-3607 |
| DOI: | 10.1142/S1664360721500119 |
| Popis: | In this paper, we investigate the existence and uniqueness of a solution for a linear Volterra-Stieltjes integral equation of the second kind, as well as for a homogeneous and a nonhomogeneous linear dynamic equations on time scales, whose integral forms contain Perron [Formula: see text]-integrals defined in Banach spaces. We also provide a variation-of-constant formula for a nonhomogeneous linear dynamic equations on time scales and we establish results on controllability for linear dynamic equations. Since we work in the framework of Perron [Formula: see text]-integrals, we can handle functions not only having many discontinuities, but also being highly oscillating. Our results require weaker conditions than those in the literature. We include some examples to illustrate our main results. |
| Databáze: | Directory of Open Access Journals |
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