On the solutions of fourth order difference equations
The authors study the behavior of nonoscillatory solutions of the fourth order difference equation \(\Delta^4 y_n= f(n, y_{n+2})\), \(n\in \mathbb{N}\), where \(f: \mathbb{N}\times \mathbb{R}\to \mathbb{R}\) satisfies \(x\cdot f(n, x)< 0\) for all \(n\in \mathbb{N}\), \(x\neq 0\). For related results see the papers of \textit{B. Smith} and \textit{W. E. Taylor jun.} [Rocky Mt. J. Math. 16, 403-406 (1986; Zbl 0602.39003)] and \textit{W. E. Taylor jun.} [Port. Math. 45, No. 1, 105-114 (1988; Zbl 0652.39004)].
scientific article; zbMATH DE number 894663