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Statements

Subject Item
n2:RIV%2F00216224%3A14310%2F05%3A00012627%21RIV10-MSM-14310___
rdf:type
n3:Vysledek skos:Concept
dcterms: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.
dcterms: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
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
skos:notation
RIV/00216224:14310/05:00012627!RIV10-MSM-14310___
n4:aktivita
n10:P
n4:aktivity
P(1K04001), P(GA201/04/0580)
n4:cisloPeriodika
9
n4:dodaniDat
n15:2010
n4:domaciTvurceVysledku
n7:6860591
n4:druhVysledku
n18:J
n4:duvernostUdaju
n13:S
n4:entitaPredkladatele
n17:predkladatel
n4:idSjednocenehoVysledku
533050
n4:idVysledku
RIV/00216224:14310/05:00012627
n4:jazykVysledku
n16:eng
n4: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
n4:klicoveSlovo
n5:Riccati%20difference%20equation n5:Conjugate%20interval n5:Euler-Lagrange%20difference%20equation n5:Discrete%20quadratic%20functional n5:Positivity n5:Second%20variation n5:Nonnegativity n5:Linear%20Hamiltonian%20difference%20system n5:Coupled%20interval n5:Conjoined%20basis
n4:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n4:kontrolniKodProRIV
[A2DAB39EE975]
n4:nazevZdroje
Journal of Difference Equations and Applications
n4:obor
n8:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
2
n4:projekt
n14:1K04001 n14:GA201%2F04%2F0580
n4:rokUplatneniVysledku
n15:2005
n4:svazekPeriodika
11
n4:tvurceVysledku
Zeidan, Vera Šimon Hilscher, Roman
n4:wos
000231705300006
s:issn
1023-6198
s:numberOfPages
19
n11:organizacniJednotka
14310