Oscillation results for second order scalar and matrix difference equations (Q1334562)

The authors consider the selfadjoint second order scalar difference equations \(\Delta (r_ n \Delta x_ n) + p_ n x_{n + 1} = 0\) and the matrix system \(\Delta (R_ n \Delta x_ n) + P_ n x_{n + 1} = 0\), where \(\{r_ n\}^ \infty_ 0\), \(\{p_ n\}^ \infty_ 0\), \((\{\mathbb{R}_ n \}^ \infty_ n\), \(\{\mathbb{P}_ n\}^ \infty_ 0)\) are sequences of real numbers \((d \times d\) Hermitian matrices) with \(r_ n > 0\) \((R_ n > 0)\). They obtain some new oscillation criteria through change of variable techniques combined with consideration of the equation as perturbations of the cases \(p_ n = 0\) \((P_ n = 0)\).