The functional formulation of second-order ordinary differential equations
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F05%3A%230000047" target="_blank" >RIV/47813059:19610/05:#0000047 - isvavai.cz</a>
Alternative codes found
RIV/60076658:12410/05:00008507
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
The functional formulation of second-order ordinary differential equations
Original language description
In this paper, the necessary and sufficient conditions in order that a smooth mapping $ff(ta,al,be,a,b)$ be a dependence of a complete solution $x(ta)$ of some second-order ordinary differential equation on Neumann conditions $x(al)=a$, $x(be)=b$, $al neq be$ are deduced. These necessary and sufficient conditions consist of functional equations for $ff$ and of a smooth extensibility condition. Illustrative examples are presented to demonstrate this result. In these examples, the mentionedfunctional equations for $ff$ are related to the functional equations for geodesics, to Jensen's equation, to the functional equations for conic sections and to Neuman's result for linear ordinary differential equations.
Czech name
Funkcionální formulace obyčejných funkcionálních rovnic druhého řádu
Czech description
V článku jsou odvozeny nutné a postačující podmínky pro existenci diferenciální rovnice, jejíž úplná řešení splňují zadanou funkcionální rovnici. Výsledek je doplňen ilustrativními příklady.
Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Aequationes Mathematicae
ISSN
0001-9054
e-ISSN
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Volume of the periodical
69
Issue of the periodical within the volume
3
Country of publishing house
CH - SWITZERLAND
Number of pages
8
Pages from-to
263-270
UT code for WoS article
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EID of the result in the Scopus database
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