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New results on critical oscillation constants depending on a graininess
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SYSNO ASEP 0349242 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title New results on critical oscillation constants depending on a graininess Author(s) Řehák, Pavel (MU-W) RID, SAI, ORCID Source Title Dynamic Systems and Applications - ISSN 1056-2176
Roč. 19, č. 2 (2010), s. 271-287Number of pages 17 s. Language eng - English Country US - United States Keywords half-linear dynamic equation ; time scale ; (non)oscillation ; Hille-Nehari criterion ; Riccati technique Subject RIV BA - General Mathematics R&D Projects KJB100190701 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000282916600005 EID SCOPUS 77958054658 Annotation 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 on the 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 best possible 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2011
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