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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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