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Zbl 1140.39305
Andruch-Sobiło, Anna; Migda, Małgorzata
Bounded solutions of third order nonlinear difference equations. (English)
[J] Rocky Mt. J. Math. 36, No. 1, 23-34 (2006). ISSN 0035-7596

Summary: We consider the nonlinear difference equation $$\Delta(a_n\Delta(b_n\Delta x_n)) = q_nf(x_{n+2}),\quad n\in N,$$ where $\{a_n\}$, $\{b_n\}$, $\{q_n\}$ are positive real sequences, $f$ is a real function with $xf(x) > 0$ for all $x\ne 0$. We obtain sufficient conditions for the boundedness of all nonoscillatory solutions of the above equation. Some examples are also given.

MSC 2000:: *39A11 Stability of difference equations
39A10 Difference equations

Keywords: bounded solutions; oscillatory solutions; nonoscillatory solutions; quickly oscillatory solutions; third order nonlinear difference equations

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