Oscillation of fourth order nonlinear neutral difference equations I

Abstract

Oscillatory and asymptotic behaviour of solutions of a class ofnonlinear fourth order neutral difference equations of the form∆2(r(n)∆2(y(n)+p(n)y(n−m))) +q(n)G(y(n−k)) = 0and(NH) ∆2(r(n)∆2(y(n)+p(n)y(n−m))) +q(n)G(y(n−k)) =f(n)are studied under the assumption∞∑n=0nr(n)=∞, for various ranges ofp(n).Sufficient conditions are obtained for the existence of bounded positive solutionsof (NH