About: The Helmholtz conditions for systems of second order homogeneous differential equations

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Variationality of systems of second order ordinary differential equations is studied within the class of positive homogeneous systems. The concept of a higher order positive homogeneous function, related to Finsler geometry, is represented by the well-known Zermelo conditions, and applied to the theory of variational equations. In particular, it is shown that every system of m+1 second order variational and positive homogeneous differential equations is linearly dependent and admits subsystems of m differential equations which are variational in sense of parameter-invariant variational problems, and vice versa. An example of a positive homogeneous variational system of second order differential equations is given. Variationality of systems of second order ordinary differential equations is studied within the class of positive homogeneous systems. The concept of a higher order positive homogeneous function, related to Finsler geometry, is represented by the well-known Zermelo conditions, and applied to the theory of variational equations. In particular, it is shown that every system of m+1 second order variational and positive homogeneous differential equations is linearly dependent and admits subsystems of m differential equations which are variational in sense of parameter-invariant variational problems, and vice versa. An example of a positive homogeneous variational system of second order differential equations is given. (en)
Title	The Helmholtz conditions for systems of second order homogeneous differential equations The Helmholtz conditions for systems of second order homogeneous differential equations (en)
skos:prefLabel	The Helmholtz conditions for systems of second order homogeneous differential equations The Helmholtz conditions for systems of second order homogeneous differential equations (en)
skos:notation	RIV/61988987:17310/13:A1401A0H!RIV14-GA0-17310___
http://linked.open...avai/predkladatel	Přírodovědecká fakulta
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(EE2.3.30.0058), P(GA201/09/0981)
http://linked.open...iv/cisloPeriodika	1-2
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Krupka, Demeter
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ostravská univerzita v Ostravě / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	77203
http://linked.open...ai/riv/idVysledku	RIV/61988987:17310/13:A1401A0H
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	variational differential equation; Helmholtz conditions; Lagrangian; positive homogeneous function; Zermelo conditions; Finsler geometry (en)
http://linked.open.../riv/klicoveSlovo	Lagrangian Helmholtz conditions Zermelo conditions Finsler geometry positive homogeneous function variational differential equation
http://linked.open...odStatuVydavatele	HU - Maďarsko
http://linked.open...ontrolniKodProRIV	[03AF875F9412]
http://linked.open...i/riv/nazevZdroje	PUBL MATH-DEBRECEN
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Global Analysis and the Geometry of Fibred Spaces Development of Research Teams at the University of Pardubice
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	83
http://linked.open...iv/tvurceVysledku	Krupka, Demeter Urban, Z.
issn	0033-3883
number of pages	14 (xsd:int)
http://localhost/t...ganizacniJednotka	17310

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