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Bounded solutions of third order nonlinear difference equations. (English) Zbl 1140.39305
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 \(x\neq 0\). We obtain sufficient conditions for the boundedness of all nonoscillatory solutions of the above equation. Some examples are also given.

MSC:
39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
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References:
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