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Disconjugacy for linear Hamiltonian difference systems. (English) Zbl 0762.39003
Using Riccati methods, disconjugacy criteria are obtained for the linear Hamiltonian difference system (1) $\Delta y(t)=B(t)y(t+1)+C(t)z(t)$, $\Delta z(t)=-A(t)y(t+1)-B\sp*(t)z(t)$, 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 $y\sp*(p)C\sp{-1}(p)(I-B(p))y(p+1)\le 0$ for any nontrivial solution $y(t)$, $z(t)$ of (1).
Reviewer: H.Länger (Wien)

##### MSC:
 39A10 Additive difference equations 39A12 Discrete version of topics in analysis
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##### References:
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