Czechoslovak Mathematical Journal

, Volume 51, Issue 2, pp 303–321 | Cite as

Oscillatory Properties of Second Order Half-Linear Difference Equations

  • Pavel Rehak
Article

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.
half-linear difference equation Picone identity Reid Roundabout Theorem oscillation criteria 

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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2001

Authors and Affiliations

  • Pavel Rehak
    • 1
  1. 1.Department of Mathematics, Faculty of SciencesMasaryk University BrnoBrnoCzech Republic

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