Publication details

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



Year of publication 2010
Type Article in Periodical
Magazine / Source Mathematica Slovaca
MU Faculty or unit

Faculty of Education

Field General mathematics
Keywords dynamic equation; time scale; half-linear equation; (non)oscillation criteria; Hille-Nehari criteria; Kneser criteria; critical constant; oscillation constant; Hardy inequality
Description We present criteria of Hille-Nehari type for the half-linear dynamic equation 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 at the differential term. 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.
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