Fernández Francisco J. and Márquez Albés Ignacio and Tojo F. Adrián F. and Villanueva Mariz Carlos: On the kernel of the Stieltjes derivative and the space of bounded Stieltjes-differentiable functions. (2025)
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Abstract
We investigate the existence and uniqueness of solutions to first-order Stieltjes differential problems, focusing on the role of the Stieltjes derivative and its kernel. Unlike the classical case, the kernel of the Stieltjes derivative operator is nontrivial, leading to non-uniqueness issues in Cauchy problems. We characterize this kernel by providing necessary and sufficient conditions for a function to have a zero Stieltjes derivative. To address the implications of this nontrivial kernel, we introduce a function space which serves as a suitable framework for studying Stieltjes differential problems. We explore its topological structure and propose a metric that facilitates the formulation of existence and uniqueness results. Our findings demonstrate that solutions to firstorder Stieltjes differential equations are, in general, not unique, underscoring the need for a refined analytical approach to such problems.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2025 |
| Number: | 36 |
| ISSN: | 1417-3875 |
| Number of Pages: | 41 |
| Language: | English |
| Place of Publication: | Szeged |
| DOI: | 10.14232/ejqtde.2025.1.36 |
| Uncontrolled Keywords: | Stieltjes-differenciálegyenlet |
| Additional Information: | Bibliogr.: p. 40-41. ; összefoglalás angol nyelven |
| Subjects: | 01. Natural sciences 01. Natural sciences > 01.01. Mathematics |
| Date Deposited: | 2025. Nov. 19. 15:49 |
| Last Modified: | 2025. Nov. 19. 15:49 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/88916 |
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