Abstract
Consider the second order half--linear difference equation $$ \Delta(r_k|\Delta y_k|^{\alpha-1}\sgn\Delta y_k)+p_k|y_{k+1}|^{\alpha-1}\sgn y_{k+1}=0, \quad \alpha>1. $$ We give several various types of comparison theorems for this equation (included the so--called telescoping principle) and also for an associated generalized Riccati difference equation. In the second part we present strongly (non)oscillation criteria and related results. The paper is finished by an example, where oscillatory properties of a generalized discrete Euler equation are investigated.
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