About: Time scale embedding theorem and coercivity of quadratic functionals

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper we study the relation between the coercivity and positivity of a time scale quadratic functional J, which could be a second variation for a nonlinear time scale calculus of variations problem (P). We prove for the case of general jointly varying endpoints that J is coercive if and only if it is positive definite and the time scale version of the strengthened Legendre condition holds. In order to prove this, we establish a time scale embedding theorem and apply it to the Riccati matrix equation associated with the quadratic functional J. Consequently, we obtain sufficiency criteria for the nonlinear problem (P) in terms of the positivity of J or in terms of the time scale Riccati equation. This result is new even for the continuous time case when the endpoints are <i> jointly varying </i>. In this paper we study the relation between the coercivity and positivity of a time scale quadratic functional J, which could be a second variation for a nonlinear time scale calculus of variations problem (P). We prove for the case of general jointly varying endpoints that J is coercive if and only if it is positive definite and the time scale version of the strengthened Legendre condition holds. In order to prove this, we establish a time scale embedding theorem and apply it to the Riccati matrix equation associated with the quadratic functional J. Consequently, we obtain sufficiency criteria for the nonlinear problem (P) in terms of the positivity of J or in terms of the time scale Riccati equation. This result is new even for the continuous time case when the endpoints are <i> jointly varying </i>. (en)
Title	Time scale embedding theorem and coercivity of quadratic functionals Time scale embedding theorem and coercivity of quadratic functionals (en)
skos:prefLabel	Time scale embedding theorem and coercivity of quadratic functionals Time scale embedding theorem and coercivity of quadratic functionals (en)
skos:notation	RIV/00216224:14310/08:00024155!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1K04001), P(GA201/04/0580), P(KJB100190701), P(KJB1019407), P(ME 891), Z(MSM0021622409)
http://linked.open...iv/cisloPeriodika	1
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	400064
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/08:00024155
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Time scale; Time scale embedding theorem; Quadratic functional; Positivity; Coercivity; Riccati equation; Legendre condition; Calculus of variations; Weak local extremum (en)
http://linked.open.../riv/klicoveSlovo	Riccati equation Legendre condition Time scale embedding theorem Weak local extremum Time scale Calculus of variations Quadratic functional Coercivity Positivity
http://linked.open...odStatuVydavatele	DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV	[C431C7FB26A7]
http://linked.open...i/riv/nazevZdroje	Analysis (Munich)
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 Asymptotics, oscillation, and quadratic functionals in theory of dynamic equations http://linked.opendata.cz/resource/domain/vavai/projekt/ME%20891 Difference equations and dynamic equations on time scales Linear Hamiltonian dynamic systems and half-linear dynamic equations
http://linked.open...UplatneniVysledku	2008
http://linked.open...v/svazekPeriodika	28
http://linked.open...iv/tvurceVysledku	Šimon Hilscher, Roman Zeidan, Vera
http://linked.open...n/vavai/riv/zamer	Matematické struktury a jejich fyzikální aplikace
issn	0174-4747
number of pages	28 (xsd:int)
http://localhost/t...ganizacniJednotka	14310
is http://linked.open...avai/riv/vysledek of	Time scale embedding theorem and coercivity of quadratic functionals Time scale embedding theorem and coercivity of quadratic functionals Time scale embedding theorem and coercivity of quadratic functionals Time scale embedding theorem and coercivity of quadratic functionals

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