New results on critical oscillation constants depending on a graininess

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F10%3A00349242" target="_blank" >RIV/67985840:_____/10:00349242 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
New results on critical oscillation constants depending on a graininess
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/KJB100190701" target="_blank" >KJB100190701: Asymptotics, oscillation, and quadratic functionals in theory of dynamic equations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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