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Oscillatory Properties of Second Order Half-Linear Difference Equations

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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.

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Authors and Affiliations

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

    Pavel Rehak

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  1. Pavel Rehak
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Rehak, P. Oscillatory Properties of Second Order Half-Linear Difference Equations. Czechoslovak Mathematical Journal 51, 303–321 (2001). https://doi.org/10.1023/A:1013790713905

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