Oscillation for Higher Order Superlinear Delay Difference Equations with Unstable Type

摘要

This paper investigates the oscillatory behavior of the following higher order superlinear delay difference equation with unstable type Δ~m x_n = p_n|x_(n-k)|~(α-1) x_(n-k), n ≥ n_0, (*) where α > 1 and m is an even integer. The existence of unbounded and nonoscillatory solution for superlinear Eq.(*) is proved. Then an almost sharp criterion for bounded oscillation and nonoscillation is obtained.