Oscillation criteria for Hamiltonian matrix difference systems
Lynn Erbe, Pengxiang Yan · Proceedings of the American Mathematical Society · 1993
We obtain some oscillation criteria for the Hamiltonian difference system \[ { Δ Y ( t ) = B ( t ) Y ( t + 1 ) + C ( t ) Z ( t ) , Δ Z ( t ) = − A ( t ) Y ( t + 1 ) − B ∗ ( t ) Z ( t ) , \left \{ \begin {gathered} \Delta Y(t) = B(t)Y(t + 1) + C(t)Z(t), \hfill \\ \Delta Z(t) = - A(t)Y(t + 1) - {B^{\ast }}(t)Z(t), \hfill \\ \end {gathered} \right . \] where A , B , C , Y , Z A,B,C,Y,Z are d × d d \times d matrix functions. As a corollary, we establish the validity of an earlier conjecture for a second-order matrix difference system.