<abstract xmlns="http://www.w3.org/1999/xhtml">. We establish the so-called “<italic>telescoping principle</italic>” for oscillation of the second order half-linear dynamic equation [<italic>r</italic>(<italic>t</italic>)Φ(<italic>x&lt;sup></italic>Δ&lt;/sup>)]&lt;sup>Δ&lt;/sup> + <italic>c</italic>(<italic>t</italic>)Φ(<italic>x&lt;sup>σ&lt;/sup></italic>) = 0 on a time scale. This principle provides a method enabling us to construct many new oscillatory equations. Unlike previous works concerning the telescoping principle, we formulate some oscillation results under the weaker assumption <italic>r</italic>(<italic>t</italic>) ≠ 0 (instead <italic>r</italic>(<italic>t</italic>) <italic>> </italic>0). </abstract>

. We establish the so-called “telescoping principle” for oscillation of the second order half-linear dynamic equation [r(t)Φ(xΔ)]Δ + c(t)Φ(xσ) = 0 on a time scale. This principle provides a method enabling us to construct many new oscillatory equations. Unlike previous works concerning the telescoping principle, we formulate some oscillation results under the weaker assumption r(t) ≠ 0 (instead r(t) > 0).

A telescoping principle for oscillation of the second order half-linear dynamic equations on time scales

Department of Mathematical Analysis Faculty of Science Masaryk University Brno Kotl´aˇrsk´a 2 CZ–611-37 Brno CZECH REPUBLIC

Tatra Mountains Mathematical Publications

. We establish the so-called “telescoping principle” for oscillation of the second order half-linear dynamic equation [r(t)Φ(xΔ)]Δ + c(t)Φ(xσ) = 0 on a time scale. This principle provides a method enabling us to construct many new oscillatory equations. Unlike previous works concerning the telescoping principle, we formulate some oscillation results under the weaker assumption r(t) ≠ 0 (instead r(t) > 0).

. We establish the so-called “telescoping principle” for oscillation of the second order half-linear dynamic equation [r(t)Φ(xΔ)]Δ +...

A telescoping principle for oscillation of the second order half-linear dynamic equations on time scales

Published Online: Nov 12, 2012

Page range: 243 - 255

DOI: https://doi.org/10.2478/v10127-009-0041-6

Keywords
half-linear dynamic equation, telescoping principle, oscillation criteria

This content is open access.

A telescoping principle for oscillation of the second order half-linear dynamic equations on time scales

Published Online: Nov 12, 2012

Page range: 243 - 255

DOI: https://doi.org/10.2478/v10127-009-0041-6

Keywordshalf-linear dynamic equation, telescoping principle, oscillation criteria

This content is open access.

Keywords
half-linear dynamic equation, telescoping principle, oscillation criteria