Some oscillation and non-oscillation theorems for fourth order difference equations

Sufficient conditions are established for oscillation of all solutions of t he fourth order difference equation Delta (a(n)Delta>(*) over bar * (b(n)Delta>(*) over bar * (c(n)Deltay(n)))) + q(n)f(y(n+1)) = h(n) (n is an element of N-0) where Delta is the forward difference operator Deltay(n) = y(n+1) - y(n), { a(n)}, {b(n)}, {c(n)}, {q(n)}, {h(n)} are real sequences, and f is a real-v alued continuous function. Also, sufficient conditions are provided which e nsure that all non-oscillatory solutions of the equation approach zero as n --> infinity. Examples are inserted to illustrate the results.