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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

  • DOI - Digital Object Identifier

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

Result continuities

  • Project

  • 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

  • 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

  • EID of the result in the Scopus database