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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) \(\Delta y(t)=B(t)y(t+1)+C(t)z(t)\), \(\Delta z(t)=-A(t)y(t+1)-B^*(t)z(t)\), 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)

MSC:

39A10 Additive difference equations
39A12 Discrete version of topics in analysis
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