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A critical oscillation constant as a variable of time scales for half-linear dynamic equations. (English) Zbl 1240.34478
The author establishes Hille-Nehari criteria for the half-linear time scale analogue of the classical second order linear differential equation. A very important special case of the main result in this paper is the existence of a (sharp) critical constant which may be different from what is known in the continuous case. This constant depends on the graininess of the time scale and the leading coefficient in the half-linear dynamic equation. Criteria for strong (non)oscillation and of Kneser type are given. Also, a Hardy-type inequality is presented. Many interesting examples are given to illustrate the significance of the results in this paper.

MSC:
34N05 Dynamic equations on time scales or measure chains
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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