Asymptotic behavior of third order delay difference equations with a negative middle term

Abstract

In this paper, we establish some sufficient conditions which ensure that the solutions of the third order delay difference equation with a negative middle term

Delta(a(n) Delta(Delta w(n))(alpha)) p(n)(Delta w(n+1))(alpha) - q(n)h(w(n-1)) = 0, n >= n(0),

are oscillatory. Moreover, we study the asymptotic behavior of the nonoscillatory solutions. Two illustrative examples are included for illustration.