Geodesic
Oscillatory properties of second order half-linear difference equations
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 2, pp. 303-321.

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We study oscillatory properties of the second order half-linear difference equation \[ \Delta (r_k|\Delta y_k|^{\alpha -2}\Delta y_k)-p_k|y_{k+1}|^{\alpha -2}y_{k+1}=0, \quad \alpha >1. \qquad \mathrm{(HL)}\] It will be shown that the basic facts of oscillation theory for this equation are essentially the same as those for the linear equation \[ \Delta (r_k\Delta y_k)-p_ky_{k+1}=0. \] We present here the Picone type identity, Reid Roundabout Theorem and Sturmian theory for equation (HL). Some oscillation criteria are also given.
Classification : 39A10, 39A11
Keywords: half-linear difference equation; Picone identity; Reid Roundabout Theorem; oscillation criteria 
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     author = {\v{R}eh\'ak, Pavel},
     title = {Oscillatory properties of second order half-linear difference equations},
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Řehák, Pavel. Oscillatory properties of second order half-linear difference equations. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 2, pp. 303-321. http://geodesic.mathdoc.fr/item/CMJ_2001__51_2_a6/