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Oscillatory Properties of Second Order Half-Linear Difference Equations

Authors:

Institution:

(1) Department of Mathematics, Faculty of Sciences, Masaryk University Brno, Janackovo nam. 2a, CZ-662 95 Brno, Czech Republic

Abstract:

We study oscillatory properties of the second order half-linear difference equation

$\Delta (r_k |\Delta yk|^{\alpha - 2} \Delta yk) - pk|yk + 1|^{\alpha - 2} yk + 1 = 0,\alpha > 1$

. It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation

$\Delta (r_k \Delta yk) - pkyk + 1 = 0.$

. We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.

Keywords:

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