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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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References:
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