Distributional, differential and integral problems: Equivalence and existence results
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Distributional, differential and integral problems: Equivalence and existence results
Original language description
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).
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
2017
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
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Volume of the periodical
2017
Issue of the periodical within the volume
7
Country of publishing house
HU - HUNGARY
Number of pages
26
Pages from-to
1-26
UT code for WoS article
000393037600001
EID of the result in the Scopus database
2-s2.0-85011019650