Oscillation and nonoscillation of solutions of second order linear dynamic equations with integrable coefficients on time scales
The authors present so-called Willett-Wong-type oscillation and nonoscillation theorems for second order linear dynamic equations on time scales by means of a ``second-level Riccati equation''. Applying these results, they give the complete classification of oscillation and nonoscillation for the difference equation \[ \Delta^2x(n)+\left[\frac{a}{t^{c+1}}+b\frac{(-1)^n}{t^c}\right]x(n+1)=0 \] for \(t\in\mathbb{N}\), \(a,b,c\in\mathbb{R}\) in cases \(a=0\) and \(a\neq 0\). The results obtained in the paper extend and improve some earlier results.
scientific article; zbMATH DE number 5648696
scientific article