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A critical oscillation constant as a variable of time scales for half-linear dynamic equations
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SYSNO ASEP 0340554 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A critical oscillation constant as a variable of time scales for half-linear dynamic equations Author(s) Řehák, Pavel (MU-W) RID, SAI, ORCID Source Title Mathematica Slovaca. - : Walter de Gruyter - ISSN 0139-9918
Roč. 60, č. 2 (2010), s. 237-256Number of pages 20 s. Language eng - English Country SK - Slovakia Keywords dynamic equation ; time scale ; half-linear equation ; (non)oscillation criteria ; Hille-Nehari criteria ; Kneser criteria ; critical constant ; oscillation constant ; Hardy inequality 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 000274746900009 EID SCOPUS 77951284058 DOI 10.2478/s12175-010-0009-7 Annotation We present criteria of Hille-Nehari type for the half-linear dynamic equation (r(t)I broken vertical bar(y (Delta)))(Delta)+p(t)I broken vertical bar(y (sigma) ) = 0 on time scales. As a particular important case we get that there is a a (sharp) critical constant which may be different from what is known from the continuous case, and its value depends on the graininess of a time scale and on the coefficient r. As applications we state criteria for strong (non)oscillation, examine generalized Euler type equations, and establish criteria of Kneser type. Examples from q-calculus, a Hardy type inequality with weights, and further possibilities for study are presented as well. Our results unify and extend many existing results from special cases, and are new even in the well-studied discrete case. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2010
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