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Some new oscillation results for linear Hamiltonian systems. (English) Zbl 1161.34002
The authors consider linear Hamiltonian systems of the form \(X^\prime = A(t)X+B(t)Y, Y^\prime=C(t)X-A^\ast (t)Y\), where \(A, B=B^\ast >0, C=C^\ast, X, Y\) are \(n \times n\)-matrices and \(t \in [t_0,\infty)\). It is said that such a system is oscillatory if for any solution \((X,Y)\) such that its Wronskian vanishes: \(X^\ast (t)Y(t) - Y^\ast (t)X(t) =0\), and \(\det X(t_1) \neq 0\) for some \(t_1\in [t_0,\infty)\) the determinant \(X(t)\) has arbitrary large zeros. By using the standard integral average technique they derive some new criteria for such a system to be oscillatory.

MSC:
34A30 Linear ordinary differential equations and systems
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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