On the kernel of the Stieltjes derivative and the space of bounded Stieltjes-differentiable functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00639044" target="_blank" >RIV/67985840:_____/25:00639044 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.14232/ejqtde.2025.1.36" target="_blank" >https://doi.org/10.14232/ejqtde.2025.1.36</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.14232/ejqtde.2025.1.36" target="_blank" >10.14232/ejqtde.2025.1.36</a>
Alternative languages
Result language
angličtina
Original language name
On the kernel of the Stieltjes derivative and the space of bounded Stieltjes-differentiable functions
Original language description
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 first-order Stieltjes differential equations are, in general, not unique, underscoring the need for a refined analytical approach to such problems.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Electronic Journal of Qualitative Theory of Differential Equations
ISSN
1417-3875
e-ISSN
1417-3875
Volume of the periodical
2025
Issue of the periodical within the volume
36
Country of publishing house
HU - HUNGARY
Number of pages
41
Pages from-to
1-41
UT code for WoS article
001568527900001
EID of the result in the Scopus database
2-s2.0-105013885095