Hartman Wintner Type Lemma, Oscillation, and Conjugacy Criteria for Half-Linear Difference Equations

We discuss oscillatory properties of the second order half-linear difference equation Žrk yk 2 yk. pk yk 1 2yk 1 0, where 1. In particular, we establish the discrete half-linear extension of the Hartman Wintner lemma and oscillatory and conjugacy criteria as an application of this lemma. The proofs of all these results and also of most of the other statements in this paper are based on the Riccati technique.