Publication details

Oscillatory properties of second order half-linear difference equations

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Year of publication 2001
Type Article in Periodical
Magazine / Source Czechoslovak Mathematical Journal
MU Faculty or unit

Faculty of Education

Field General mathematics
Keywords Half-linear difference equation; Picone identity; Reid Roundabout Theorem; oscillation criteria
Description 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.
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