A critical oscillation constant as a variable of time scales for half-linear dynamic equations

0340554 - MÚ 2010 RIV SK eng J - Článek v odborném periodiku
Řehák, Pavel
A critical oscillation constant as a variable of time scales for half-linear dynamic equations.
Mathematica Slovaca. Roč. 60, č. 2 (2010), s. 237-256. ISSN 0139-9918. E-ISSN 1337-2211
Grant CEP: GA AV ČR KJB100190701
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: dynamic equation * time scale * half-linear equation * (non)oscillation criteria * Hille-Nehari criteria * Kneser criteria * critical constant * oscillation constant * Hardy inequality
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.316, rok: 2010
http://link.springer.com/article/10.2478%2Fs12175-010-0009-7

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.
Trvalý link: http://hdl.handle.net/11104/0183768