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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.

39A11 Stability of difference equations (MSC2000)
39A10 Additive difference equations
Full Text: DOI Euclid
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