Oscillatory and Asymptotic Behaviour of Fourth Order Nonlinear Difference Equations

This paper considers a class of fourth order nonlinear difference equations .² (r..² y.)+ f(n, y.) = 0, n . (n.), where f(n,y) may be classified as superlinear, sublinear, strongly superlinear and strongly sublinear. In superlinear and sublinear cases, necessary and sufficient conditions are obtained for the difference equation to admit the existence of nonoscillatory solutions with special asymptotic properties. In strongly superlinear and strongly sublinear cases, sufficient conditions are given for all solutions to be oscillatory.