On unbounded oscillation of fourth order functional difference equations

Abstract

In this work, an illustrative discussion have been made on unbounded oscillation properties of a class of fourth order neutral functional difference equations of the form: Δ2(r(n)Δ2(y(n)+ p(n)y(n− τ)))+g(n)G(y(n−σ))−h(n)H(y(n−α)) = 0 under the assumptions ∞ ∑ n=0 n r(n) = ∞, ∞ ∑ n=0 n r(n) < ∞. New oscillation criteria have been established for different ranges of p(n) with |p(n)| < ∞ . Mathematics subject classification (2010): 39A10, 39A12.