## Oscillatory nonautonomous Lucas sequences.(English)Zbl 1203.39009

Summary: The oscillatory behavior of the solutions of the second-order linear nonautonomous equation $$x(n+1)=a(n)x(n) - b(n)x(n - 1), n\in \mathbb N_{0},$$ where $$a,b:\mathbb N_{0}\rightarrow \mathbb R$$, is studied. Under the assumption that the sequence $$b(n)$$ dominates somehow $$a(n)$$, the amplitude of the oscillations and the asymptotic behavior of its solutions are also analyzed.

### MSC:

 39A21 Oscillation theory for difference equations 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 39A06 Linear difference equations 39A22 Growth, boundedness, comparison of solutions to difference equations
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### References:

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