About: Comparison theorems and strong oscillation in the half-linear discrete oscillation theory

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Consider the second order half--linear difference equation $$ \Delta(r_k\|\Delta y_k\|^{\alpha-1}\sgn\Delta y_k)+p_k\|y_{k+1}\|^{\alpha-1}\sgn y_{k+1}=0, \quad \alpha>1. $$ We give several various types of comparison theorems for this equation (included the so--called telescoping principle) and also for an associated generalized Riccati difference equation. In the second part we present strongly (non)oscillation criteria and related results. The paper is finished by an example, where oscillatory properties of a generalized discrete Euler equation are investigated. Consider the second order half--linear difference equation $$ \Delta(r_k\|\Delta y_k\|^{\alpha-1}\sgn\Delta y_k)+p_k\|y_{k+1}\|^{\alpha-1}\sgn y_{k+1}=0, \quad \alpha>1. $$ We give several various types of comparison theorems for this equation (included the so--called telescoping principle) and also for an associated generalized Riccati difference equation. In the second part we present strongly (non)oscillation criteria and related results. The paper is finished by an example, where oscillatory properties of a generalized discrete Euler equation are investigated. (en) Consider the second order half--linear difference equation $$ \Delta(r_k\|\Delta y_k\|^{\alpha-1}\sgn\Delta y_k)+p_k\|y_{k+1}\|^{\alpha-1}\sgn y_{k+1}=0, \quad \alpha>1. $$ We give several various types of comparison theorems for this equation (included the so--called telescoping principle) and also for an associated generalized Riccati difference equation. In the second part we present strongly (non)oscillation criteria and related results. The paper is finished by an example, where oscillatory properties of a generalized discrete Euler equation are investigated. (cs)
Title	Comparison theorems and strong oscillation in the half-linear discrete oscillation theory Comparison theorems and strong oscillation in the half-linear discrete oscillation theory (en) Comparison theorems and strong oscillation in the half-linear discrete oscillation theory (cs)
skos:prefLabel	Comparison theorems and strong oscillation in the half-linear discrete oscillation theory Comparison theorems and strong oscillation in the half-linear discrete oscillation theory (en) Comparison theorems and strong oscillation in the half-linear discrete oscillation theory (cs)
skos:notation	RIV/00216224:14410/03:00007885!RIV08-GA0-14410___
http://linked.open.../vavai/riv/strany	333-352
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/98/0677), P(GA201/99/0295), Z(AV0Z1019905)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2008
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	601815
http://linked.open...ai/riv/idVysledku	RIV/00216224:14410/03:00007885
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Half-linear difference equation; generalized discrete Riccati and Euler equation; comparison theorems (en)
http://linked.open.../riv/klicoveSlovo	Half-linear difference equation generalized discrete Riccati and Euler equation comparison theorems
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[252FC3C375DF]
http://linked.open...i/riv/nazevZdroje	Rocky Mountain Journal of Mathematics
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	Difference equations and their applications Qualitative theory of differential equations
http://linked.open...UplatneniVysledku	2003
http://linked.open...v/svazekPeriodika	33
http://linked.open...iv/tvurceVysledku	Řehák, Pavel
http://linked.open...n/vavai/riv/zamer	Complex development of all branches of mathematics with regard to the needs of physics and technology
issn	0035-7596
number of pages	20 (xsd:int)
http://localhost/t...ganizacniJednotka	14410

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