About: Nonnegativity and positivity of quadratic functionals in the discrete calculus of variations: Survey

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper we provide a survey of characterizations of the nonnegativity and positivity of discrete quadratic functionals which arise as the second variation for nonlinear discrete calculus of variations problems. These characterizations are in terms of (i) (strict) conjugate and (strict) coupled intervals, (ii) the conjoined bases of the associated Jacobi difference equation, and (iii) the solution of the corresponding Riccati difference equation. The results depend on the form of the boundary conditions of the quadratic functional and, basically, we distinguish three types: (a) separable endpoints with zero right endpoint (this of course includes the simplest case of both zero endpoints), (b) separable endpoints, and (c) jointly varying endpoints. In this paper we provide a survey of characterizations of the nonnegativity and positivity of discrete quadratic functionals which arise as the second variation for nonlinear discrete calculus of variations problems. These characterizations are in terms of (i) (strict) conjugate and (strict) coupled intervals, (ii) the conjoined bases of the associated Jacobi difference equation, and (iii) the solution of the corresponding Riccati difference equation. The results depend on the form of the boundary conditions of the quadratic functional and, basically, we distinguish three types: (a) separable endpoints with zero right endpoint (this of course includes the simplest case of both zero endpoints), (b) separable endpoints, and (c) jointly varying endpoints. (en)
Title	Nonnegativity and positivity of quadratic functionals in the discrete calculus of variations: Survey Nonnegativity and positivity of quadratic functionals in the discrete calculus of variations: Survey (en)
skos:prefLabel	Nonnegativity and positivity of quadratic functionals in the discrete calculus of variations: Survey Nonnegativity and positivity of quadratic functionals in the discrete calculus of variations: Survey (en)
skos:notation	RIV/00216224:14310/05:00012627!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(1K04001), P(GA201/04/0580)
http://linked.open...iv/cisloPeriodika	9
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Šimon Hilscher, Roman
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	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	533050
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/05:00012627
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Second variation; Euler-Lagrange difference equation; Discrete quadratic functional; Nonnegativity; Positivity; Linear Hamiltonian difference system; Conjugate interval; Coupled interval; Conjoined basis; Riccati difference equation (en)
http://linked.open.../riv/klicoveSlovo	Conjugate interval Coupled interval Linear Hamiltonian difference system Discrete quadratic functional Conjoined basis Nonnegativity Riccati difference equation Positivity Second variation Euler-Lagrange difference equation
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[A2DAB39EE975]
http://linked.open...i/riv/nazevZdroje	Journal of Difference Equations and Applications
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	Optimality conditions on time scales Difference equations and dynamic equations on time scales
http://linked.open...UplatneniVysledku	2005
http://linked.open...v/svazekPeriodika	11
http://linked.open...iv/tvurceVysledku	Šimon Hilscher, Roman Zeidan, Vera
http://linked.open...ain/vavai/riv/wos	000231705300006
issn	1023-6198
number of pages	19 (xsd:int)
http://localhost/t...ganizacniJednotka	14310
is http://linked.open...avai/riv/vysledek of	Nonnegativity and positivity of quadratic functionals in the discrete calculus of variations: Survey

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