Oscillatory Nonautonomous Lucas Sequences

Abstract

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∈ℕ0, where a,b:ℕ0→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.