Oscillatory properties of second order half-linear difference equations. (English) Zbl 0982.39004

Řehák, Pavel

Czech. Math. J. 51, No. 2, 303-321 (2001).

Summary: We study oscillatory properties of the second order half-linear difference equation \[ \Delta(r_k|\Delta y_k|^{\alpha -2}\Delta y_k)-p_k|y_{k+1}|^{\text{ad}}y_{k+1}=0, \quad \alpha >1. \tag{HL} \] It is 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.

MSC:

39A11

Stability of difference equations (MSC2000)

Keywords:

half-linear difference equation; Picone identity; Reid Roundabout theorem; oscillation criteria

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