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Sufficient conditions are established for oscillation of all solutions of the fourth order difference equation ∆ an∆(bn∆(cn∆yn)) + qnf(yn+1) = hn (n ∈ N0) where ∆ is the forward difference operator ∆yn = yn+1 − yn, {an}, {bn}, {cn}, {qn}, {hn} are real sequences, and f is a real-valued continuous function. Also, sufficient conditions are provided which ensure that all non-oscillatory solutions of the equation approach zero as n →∞. Examples are inserted to illustrate the results.

Some Oscillation and Non-Oscillation Theorems for Fourth Order Difference Equations