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Short note on oscillation of matrix Hamiltonian systems. (English) Zbl 1062.34032

The authors study the linear matrix system

U ' =A(x)U+B(x)V,V ' =C(x)U+(μ(x)I-A * (x))V,(1)

where A(x), B(x), C(x) are continuous real-valued n×n-matrix functions on the interval J=[a,) and μ(x) is a real-valued continuous function on J. The matrices B and C are supposed to be symmetric and B is supposed to be either positive definite or negative definite. The authors transform the system by a transformation preserving oscillatory properties into a Hamiltonian system and use an oscillation criterion due to I. Kumari and S. Umamaheswaram [J. Differ. Equations 165, No.1, 174-198 (2000; Zbl 0970.34025)] to derive a new oscillation criterion for system (1).

MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A30Linear ODE and systems, general