Erbe, Lynn H.; Yan, Pengxiang Disconjugacy for linear Hamiltonian difference systems. (English) Zbl 0762.39003 J. Math. Anal. Appl. 167, No. 2, 355-367 (1992). Using Riccati methods, disconjugacy criteria are obtained for the linear Hamiltonian difference system (1) \(\Delta y(t)=B(t)y(t+1)+C(t)z(t)\), \(\Delta z(t)=-A(t)y(t+1)-B^*(t)z(t)\), where \(\Delta y(t)=y(t+1)-y(t)\), \(A,C\) are \(d\times d\) Hermitian matrices and \(B\) is a \(d\times d\) matrix such that \(I-B\) and \(C\) are regular. Here (1) is said to be disconjugate on \([M-1,N+1]\) if there exists at most one integer \(p\in[M-1,N]\) such that \(y^*(p)C^{-1}(p)(I-B(p))y(p+1)\leq 0\) for any nontrivial solution \(y(t)\), \(z(t)\) of (1). Reviewer: H.Länger (Wien) Cited in 5 ReviewsCited in 43 Documents MSC: 39A10 Additive difference equations 39A12 Discrete version of topics in analysis Keywords:Riccati methods; disconjugacy; linear Hamiltonian difference system PDFBibTeX XMLCite \textit{L. H. Erbe} and \textit{P. Yan}, J. Math. Anal. Appl. 167, No. 2, 355--367 (1992; Zbl 0762.39003) Full Text: DOI References: [1] Ahlbrandt, C.; Hooker, J., Recessive solutions of symmetric three term recurrence relations, (Canad. Math. Soc., Conference Proceeding, 8 (1987)), 3-42 [2] Ahlbrandt, C.; Hooker, J., Riccati matrix difference equations and disconjugacy of discrete linear systems, SIAM J. Math. Anal., 19, 1183-1197 (1988) · Zbl 0655.39001 [3] Coppel, W. A., Disconjugacy, (Lecture Notes in Mathematics (1971), Springer-Verlag: Springer-Verlag New York/Berlin), 34-80 · Zbl 0224.34003 [4] Chen, S.; Erbe, L., Riccati techniques and discrete oscillations, J. Math. Anal. Appl., 142, 468-487 (1989) · Zbl 0686.39001 [5] Chen, S.; Erbe, L., Oscillation and nonoscillation for systems of self-adjoint second-order difference equations, SIAM J. Math. Anal., 20, 939-949 (1989) · Zbl 0687.39001 [6] A. Peterson and J. Ridenhour; A. Peterson and J. Ridenhour · Zbl 0731.39005 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.