Oscillatory and asymptotic behavior of fourth order nonlinear delay difference equations

The authors consider the nonlinear difference equation (E) delta2 ((delta(bn delta yn))+f(n,yn-t)=0, n należy N(no)={no,no+1,...}, here {an} and {bn} are positive real sequences, I is a nonnegative integer, f: N(no) x R R is a continuous function with uf(n, u) > 0 for all u nierówne 0. They obtain necessary and sufficient conditions for the existence of nonoscillatory solutions with a specified asymptotic behavior. They also obtain sufficient conditions for all solutions to be oscillatory if/ is either strongly sublinear or strongly superlinear. Examples of their results are also included.