New results on critical oscillation constants depending on a graininess

Kód výsledku v IS VaVaI

RIV/67985840:_____/10:00349242 - isvavai.cz

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

New results on critical oscillation constants depending on a graininess

Popis výsledku v původním jazyce

We establish criteria of Hille-Nehari type for the half-linear second order dynamic equation (r(t)Phi(y(Delta)))(Delta) +p(t)Phi(y(sigma)) = 0, Phi(u) = |u|(alpha-1) sgn u, alpha > 1, on time scales, under the condition integral(infinity) r(1/(1-alpha))(s)Delta s < infinity. As a particular important case we get that there is a (non-improvable) critical oscillation constant which may be different from the one known from the continuous case, and its value depends on the graininess of a time scale and onthe coefficient r. Along with the results of the previous paper by the author, which dealt with the condition integral(infinity) r(1/(1-alpha))(s)Delta s = infinity, a quite complete discussion on generalized Hille-Nehari type criteria involving the bestpossible constants is provided. To prove these criteria, appropriate modifications of the approaches known from the linear case (alpha = 2) or the continuous case (T = R) cannot be used in a general case, and thus we apply a new method.

Název v anglickém jazyce

New results on critical oscillation constants depending on a graininess

Popis výsledku anglicky

We establish criteria of Hille-Nehari type for the half-linear second order dynamic equation (r(t)Phi(y(Delta)))(Delta) +p(t)Phi(y(sigma)) = 0, Phi(u) = |u|(alpha-1) sgn u, alpha > 1, on time scales, under the condition integral(infinity) r(1/(1-alpha))(s)Delta s < infinity. As a particular important case we get that there is a (non-improvable) critical oscillation constant which may be different from the one known from the continuous case, and its value depends on the graininess of a time scale and onthe coefficient r. Along with the results of the previous paper by the author, which dealt with the condition integral(infinity) r(1/(1-alpha))(s)Delta s = infinity, a quite complete discussion on generalized Hille-Nehari type criteria involving the bestpossible constants is provided. To prove these criteria, appropriate modifications of the approaches known from the linear case (alpha = 2) or the continuous case (T = R) cannot be used in a general case, and thus we apply a new method.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

KJB100190701: Asymptotika, oscilace a kvadratické funkcionály v teorii dynamických rovnic

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2010

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Dynamic Systems and Applications

ISSN

1056-2176

e-ISSN

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Svazek periodika

19

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

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Kód UT WoS článku

000282916600005

EID výsledku v databázi Scopus

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