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Oscillation of second order nonlinear delay difference equations. (English) Zbl 1035.39008

Consider the nonlinear delay difference equation

Δ(p n Δx n )+q n f(x n-σ )=0,n=0,1,2,(*)

where Δu n =u n+1 -u n for any sequence {u n } of real numbers, σ is a nonnegative integer, {p n } n=0 and {q n } n=0 are sequences of real numbers such that p n >0, 1 p n <, q n 0 and q n has a positive subsequence, and f is a continuous nondecreasing real valued function which satisfies uf(u)>0 for u0 and f(u)/uγ>0· The author establishes some sufficient conditions which guarantee that every solution of (*) is oscillatory or converges to zero.

39A11Stability of difference equations (MSC2000)