About: On disconjugacy for vector linear Hamiltonian systems on time scales

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this work we present a unified treatment of continuous and discrete vector linear Hamiltonian systems on a general time scale T, with the matrix B<sub>t</sub> not necessarily invertible. This contains as special cases the Sturm-Liouville differential and difference equations of higher order. We define generalized zeros for vector solutions (x,u) of the Hamiltonian system. From this we read off the corresponding definition of generalized zero points for solutions of the Sturm-Liouville equations, so that the well known continuous case (T=R) and recently developed discrete one (T=Z) are unified. We show that disconjugacy of the equation implies positivity of the corresponding quadratic functional. In this work we present a unified treatment of continuous and discrete vector linear Hamiltonian systems on a general time scale T, with the matrix B<sub>t</sub> not necessarily invertible. This contains as special cases the Sturm-Liouville differential and difference equations of higher order. We define generalized zeros for vector solutions (x,u) of the Hamiltonian system. From this we read off the corresponding definition of generalized zero points for solutions of the Sturm-Liouville equations, so that the well known continuous case (T=R) and recently developed discrete one (T=Z) are unified. We show that disconjugacy of the equation implies positivity of the corresponding quadratic functional. (en) In this work we present a unified treatment of continuous and discrete vector linear Hamiltonian systems on a general time scale T, with the matrix B<sub>t</sub> not necessarily invertible. This contains as special cases the Sturm-Liouville differential and difference equations of higher order. We define generalized zeros for vector solutions (x,u) of the Hamiltonian system. From this we read off the corresponding definition of generalized zero points for solutions of the Sturm-Liouville equations, so that the well known continuous case (T=R) and recently developed discrete one (T=Z) are unified. We show that disconjugacy of the equation implies positivity of the corresponding quadratic functional. (cs)
Title	On disconjugacy for vector linear Hamiltonian systems on time scales On disconjugacy for vector linear Hamiltonian systems on time scales (en) On disconjugacy for vector linear Hamiltonian systems on time scales (cs)
skos:prefLabel	On disconjugacy for vector linear Hamiltonian systems on time scales On disconjugacy for vector linear Hamiltonian systems on time scales (en) On disconjugacy for vector linear Hamiltonian systems on time scales (cs)
skos:notation	RIV/00216224:14310/00:00008159!RIV08-GA0-14310___
http://linked.open.../vavai/riv/strany	181-188
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GA201/96/0410), P(GA201/98/0677)
http://linked.open...vai/riv/dodaniDat	2008
http://linked.open...aciTvurceVysledku	Šimon Hilscher, Roman
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
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	720343
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/00:00008159
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	time scale; linear Hamiltonian system; disconjugacy; generalized zero; quadratic functional (en)
http://linked.open.../riv/klicoveSlovo	linear Hamiltonian system time scale disconjugacy generalized zero quadratic functional
http://linked.open...ontrolniKodProRIV	[2024B9A3D59C]
http://linked.open...v/mistoKonaniAkce	Poznan
http://linked.open...i/riv/mistoVydani	Amsterdam
http://linked.open...i/riv/nazevZdroje	Communications in Difference Equations: Proceedings of the Fourth International Conference on Difference Equations
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Differential and functional - differential equations Difference equations and their applications
http://linked.open...UplatneniVysledku	2000
http://linked.open...iv/tvurceVysledku	Hilscher, Roman
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	1998-01-01 (xsd:date)
number of pages	8 (xsd:int)
http://purl.org/ne...btex#hasPublisher	Gordon and Breach
https://schema.org/isbn	90-5699-688-6
http://localhost/t...ganizacniJednotka	14310

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