Oscillatory properties of second order half-linear difference equations
| Autoři | |
|---|---|
| Rok publikování | 2001 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Czechoslovak Mathematical Journal |
| Fakulta / Pracoviště MU | |
| Citace | |
| Doi | http://dx.doi.org/10.1023/A:1013790713905 |
| Obor | Obecná matematika |
| Klíčová slova | Half-linear difference equation; Picone identity; Reid Roundabout Theorem; oscillation criteria |
| Popis | 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. |
| Související projekty: |