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On the solutions of fourth order difference equations. (English) Zbl 0851.39003

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 B. Smith and W. E. Taylor jun. [Rocky Mt. J. Math. 16, 403-406 (1986; Zbl 0602.39003)] and W. E. Taylor jun. [Port. Math. 45, No. 1, 105-114 (1988; Zbl 0652.39004)].

MSC:

39A10 Additive difference equations
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References:

[1] B. Smith and W.E. Taylor, Jr., Oscillatory and asymptotic behavior of certain fourth order difference equations , Rocky Mountain J. Math. 16 (1986), 403-406. · Zbl 0602.39003 · doi:10.1216/RMJ-1986-16-2-403
[2] W.E. Taylor, Jr., Oscillation properties of fourth order difference equations , Portugal Math. 45 (1988), 105-114. · Zbl 0652.39004
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