Distributional, differential and integral problems: Equivalence and existence results

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00471069" target="_blank" >RIV/67985840:_____/17:00471069 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.14232/ejqtde.2017.1.7" target="_blank" >http://dx.doi.org/10.14232/ejqtde.2017.1.7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14232/ejqtde.2017.1.7" target="_blank" >10.14232/ejqtde.2017.1.7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Distributional, differential and integral problems: Equivalence and existence results

Popis výsledku v původním jazyce

We are interested in studying the matter of equivalence of the following problems: Dx = f (t, x)Dg x(0) = x0 (1) where Dx and Dg stand for the distributional derivatives of x and g, respectively, x'g(t) = f (t, x(t)), mg-a.e. x(0) = x0 (2) where x'g denotes the g-derivative of x (in a sense to be specified in Section 2) and mg is the variational measure induced by g, and x(t) = x0 + ...t 0 f (s, x(s))dg(s), (3) where the integral is understood in the Kurzweil-Stieltjes sense. We prove that, for regulated functions g, (1) and (3) are equivalent if f satisfies a bounded variation assumption. The relation between problems (2) and (3) is described for very general f, though, more restrictive assumptions over the function g are required. We provide then two existence results for the integral problem (3) and, using the correspondences established with the other problems, we deduce the existence of solutions for (1) and (2).

Název v anglickém jazyce

Distributional, differential and integral problems: Equivalence and existence results

Popis výsledku anglicky

We are interested in studying the matter of equivalence of the following problems: Dx = f (t, x)Dg x(0) = x0 (1) where Dx and Dg stand for the distributional derivatives of x and g, respectively, x'g(t) = f (t, x(t)), mg-a.e. x(0) = x0 (2) where x'g denotes the g-derivative of x (in a sense to be specified in Section 2) and mg is the variational measure induced by g, and x(t) = x0 + ...t 0 f (s, x(s))dg(s), (3) where the integral is understood in the Kurzweil-Stieltjes sense. We prove that, for regulated functions g, (1) and (3) are equivalent if f satisfies a bounded variation assumption. The relation between problems (2) and (3) is described for very general f, though, more restrictive assumptions over the function g are required. We provide then two existence results for the integral problem (3) and, using the correspondences established with the other problems, we deduce the existence of solutions for (1) and (2).

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

2017

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

—

Svazek periodika

2017

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

HU - Maďarsko

Počet stran výsledku

26

Strana od-do

1-26

Kód UT WoS článku

000393037600001

EID výsledku v databázi Scopus

2-s2.0-85011019650