Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1993-1172949-2
MathSciNet review: 1172949
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] Calvin D. Ahlbrandt, Dominant and recessive solutions of symmetric three term recurrences, J. Differential Equations (to appear). MR 1264521 (95f:39002)
  • [2] W. Coppel, Disconjugacy, Lecture Notes in Math., vol. 220, Springer, New York, 1971. MR 0460785 (57:778)
  • [3] L. Erbe and P. Yan, Weighted averaging techniques in oscillation theory for second order difference equations, Canad. Math. Bull. 35 (1992), 61-69. MR 1157465 (93a:39010)
  • [4] -, Disconjugacy for linear Hamiltonian difference systems, J. Math. Anal. Appl. 167 (1992), 355-367. MR 1168594 (93f:39001)
  • [5] -, Qualitative properties of Hamiltonian difference systems, J. Math. Anal. Appl. (to appear). MR 1194083 (94d:39005)
  • [6] P. Lancaster and M. Tismenetsky, The theory of matrices, Academic Press, New York, 1985, pp. 286-289. MR 792300 (87a:15001)
  • [7] A. Peterson and J. Ridenhour, Oscillation of second order linear matrix difference equations, J. Differential Equations 89 (1991), 69-88. MR 1088335 (92e:39010)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 39A10, 34C10

Retrieve articles in all journals with MSC: 39A10, 34C10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1172949-2
Keywords: Disconjugacy, difference system, Riccati system
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society