About: Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	A time scale quadratic problem J with piecewise right-dense continuous coefficients and one varying endpoint is considered. Such problems are ``hybrid'', since they include mixing of continuous- and discrete-time problems. A new notion of a generalized conjugate point involving ``dynamic'' (hybrid) systems and comprising as special cases those known for the continuous- and discrete-time settings is introduced. A type of a strengthened Legendre condition is identified and used to establish characterizations of the nonnegativity and positivity of J in terms of (i) the nonexistence of such conjugate points, (ii) the natural conjoined basis of the associated time scale Jacobi equation, and (iii) a solution of the corresponding time scale Riccati equation. These results furnish second order necessary optimality conditions for a nonlinear time scale variational problem. A time scale quadratic problem J with piecewise right-dense continuous coefficients and one varying endpoint is considered. Such problems are ``hybrid'', since they include mixing of continuous- and discrete-time problems. A new notion of a generalized conjugate point involving ``dynamic'' (hybrid) systems and comprising as special cases those known for the continuous- and discrete-time settings is introduced. A type of a strengthened Legendre condition is identified and used to establish characterizations of the nonnegativity and positivity of J in terms of (i) the nonexistence of such conjugate points, (ii) the natural conjoined basis of the associated time scale Jacobi equation, and (iii) a solution of the corresponding time scale Riccati equation. These results furnish second order necessary optimality conditions for a nonlinear time scale variational problem. (en)
Title	Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application (en)
skos:prefLabel	Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application (en)
skos:notation	RIV/00216224:14310/07:00019435!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(1K04001), P(GA201/04/0580), P(KJB1019407)
http://linked.open...iv/cisloPeriodika	3
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	430788
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/07:00019435
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Time scale quadratic functional; Nonnegativity; Positivity; Jacobi equation; Linear Hamiltonian system; Conjugate point; Conjoined basis; Riccati matrix equation; Strengthened Legendre condition; Time-dependent impulsive dynamical system (en)
http://linked.open.../riv/klicoveSlovo	Jacobi equation Conjugate point Strengthened Legendre condition Time scale quadratic functional Time-dependent impulsive dynamical system Conjoined basis Linear Hamiltonian system Nonnegativity Riccati matrix equation Positivity
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[77B8F326CE91]
http://linked.open...i/riv/nazevZdroje	Dynamic Systems 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 Linear Hamiltonian dynamic systems and half-linear dynamic equations
http://linked.open...UplatneniVysledku	2007
http://linked.open...v/svazekPeriodika	16
http://linked.open...iv/tvurceVysledku	Šimon Hilscher, Roman Zeidan, Vera
http://linked.open...ain/vavai/riv/wos	000250040200004
issn	1056-2176
number of pages	30 (xsd:int)
http://localhost/t...ganizacniJednotka	14310

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