On the kernel of the Stieltjes derivative and the space of bounded Stieltjes-differentiable functions

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On the kernel of the Stieltjes derivative and the space of bounded Stieltjes-differentiable functions

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the kernel of the Stieltjes derivative and the space of bounded Stieltjes-differentiable functions

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Journal of Qualitative Theory of Differential Equations

ISSN

1417-3875

e-ISSN

1417-3875

Svazek periodika

2025

Číslo periodika v rámci svazku

36

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

41

Strana od-do

1-41

Kód UT WoS článku

001568527900001

EID výsledku v databázi Scopus

2-s2.0-105013885095