Oscillation and Nonoscillation for Systems of Self-Adjoint Second-Order Difference Equations

Abstract

The self-adjoint second-order difference system (1) $\Delta (R_n \Delta Y_n ) + P_n Y_{n + 1} = 0$, $n \geqq 0$, where $\Delta Y_n = Y_{n + 1} - Y_n ,\{ {R_n } \}_{n = 0}^\infty ,\{ {P_n } \}_{n = 0}^\infty $ are sequences of $d \times d$ Hermitian matrices with $R_n > 0$ (positive definite) are considered. Oscillation and nonoscillation criteria for solutions of (1) are obtained by Riccati and averaging techniques.