About: How the constants in Hille-Nehari theorems depend on time scales

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We present criteria of Hille--Nehari type for the linear dynamic equation $(r(t)y\del)\del+p(t)y\sig=0$, i.e., the criteria in terms of the limit behavior of $\left(\int_a^t 1/r(s)\,\dd s\right)\int_t^\infty p(s)\,\dd s$ as $t\to\infty$. As a particular important case, we get that there is a (sharp) critical constant in those criteria which belongs to the interval $[0,1/4]$, and its value depends on the graininess $\mu$ and the coefficient $r$. Also we offer some applications, e.g., criteria for strong (non)oscillation and Kneser type criteria, comparison with existing results (our theorems turn out to be new even in the discrete case as well as in many other situations), and comments with examples. We present criteria of Hille--Nehari type for the linear dynamic equation $(r(t)y\del)\del+p(t)y\sig=0$, i.e., the criteria in terms of the limit behavior of $\left(\int_a^t 1/r(s)\,\dd s\right)\int_t^\infty p(s)\,\dd s$ as $t\to\infty$. As a particular important case, we get that there is a (sharp) critical constant in those criteria which belongs to the interval $[0,1/4]$, and its value depends on the graininess $\mu$ and the coefficient $r$. Also we offer some applications, e.g., criteria for strong (non)oscillation and Kneser type criteria, comparison with existing results (our theorems turn out to be new even in the discrete case as well as in many other situations), and comments with examples. (en)
Title	How the constants in Hille-Nehari theorems depend on time scales How the constants in Hille-Nehari theorems depend on time scales (en)
skos:prefLabel	How the constants in Hille-Nehari theorems depend on time scales How the constants in Hille-Nehari theorems depend on time scales (en)
skos:notation	RIV/00216224:14410/06:00015479!RIV10-GA0-14410___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/01/0079), P(GA201/04/0580), P(GP201/01/P041), P(KJB1019407), Z(AV0Z10190503)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Řehák, Pavel
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 / Pedagogická fakulta
http://linked.open...dnocenehoVysledku	478288
http://linked.open...ai/riv/idVysledku	RIV/00216224:14410/06:00015479
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Hille-Nehari criteria; oscillation criteria; time scales; dynamic equation on time scales (en)
http://linked.open.../riv/klicoveSlovo	oscillation criteria time scales Hille-Nehari criteria dynamic equation on time scales
http://linked.open...odStatuVydavatele	EG - Egyptská arabská republika
http://linked.open...ontrolniKodProRIV	[885AD2002B7D]
http://linked.open...i/riv/nazevZdroje	Advances in 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	Qualitative theory of solutions of difference equations Difference equations and dynamic equations on time scales Qualitative theory of half-linear differential and difference equations Linear Hamiltonian dynamic systems and half-linear dynamic equations
http://linked.open...UplatneniVysledku	2006
http://linked.open...v/svazekPeriodika	2006
http://linked.open...iv/tvurceVysledku	Řehák, Pavel
http://linked.open...ain/vavai/riv/wos	000241658400001
http://linked.open...n/vavai/riv/zamer	Rozvoj a prohloubení obecných matematických poznatků a jejich užití v dalších vědních oborech a v praxi
issn	1687-1839
number of pages	15 (xsd:int)
http://localhost/t...ganizacniJednotka	14410

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