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

Jiří Vítovec

doi:10.2478/v10127-009-0041-6

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

Tatra Mountains Mathematical Publications

Volume 43 (2009): Issue 1 (August 2009)

By: Jiří Vítovec

Open Access

|Nov 2012

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).

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