# Masaryk University

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# Oscillatory properties of second order half-linear difference equations

Authors 2001 Article in Periodical Czechoslovak Mathematical Journal http://dx.doi.org/10.1023/A:1013790713905 General mathematics Half-linear difference equation; Picone identity; Reid Roundabout Theorem; oscillation criteria We study oscillatory properties of the second order half-linear difference equation \begin{equation*} \trr(r_k|\trr y_k|^{\alpha-2}\trr y_k)-p_k|y_{k+1}|^{\ad}y_{k+1}=0, \ \alpha>1. \tag{HL} \end{equation*} It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation $$\trr(r_k\trr y_k)-p_ky_{k+1}=0.$$ We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.