Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Oscillation criteria for Hamiltonian matrix difference systems

Authors: L. H. Erbe and Peng Xiang Yan
Journal: Proc. Amer. Math. Soc. 119 (1993), 525-533
MSC: Primary 39A10; Secondary 34C10
MathSciNet review: 1172949
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Abstract: We obtain some oscillation criteria for the Hamiltonian difference system

$\displaystyle \left\{ \begin{gathered}\Delta Y(t) = B(t)Y(t + 1) + C(t)Z(t), \h... ...lta Z(t) = - A(t)Y(t + 1) - {B^{\ast}}(t)Z(t), \hfill \\ \end{gathered} \right.$

where $ A,B,C,Y,Z$ are $ d \times d$ matrix functions. As a corollary, we establish the validity of an earlier conjecture for a second-order matrix difference system.

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Keywords: Disconjugacy, difference system, Riccati system
Article copyright: © Copyright 1993 American Mathematical Society