Oscillatory Nonautonomous Lucas Sequences

Abstract

The oscillatory behavior of the solutions of the second-order linear nonautonomous equation $x\left(n+1\right)=a\left(n\right)x\left(n\right)-b\left(n\right)x\left(n-1\right),n\in {\mathbb{N}}_0,$ where $a,b:{\mathbb{N}}_0\to ℝ$, 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 analized.