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Oscillation criteria for linear matrix Hamiltonian systems. (English) Zbl 0970.34025

The authors give some oscillation criteria for the linear matrix Hamiltonian system:

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

where A(x), B(x)=B * (x)>0 and C(x)=C * (x) are real continuous n×n-matrix functions on the interval [a,).

The results given stand for extensions to the systems of the form (*), of the following oscillation criteria earlier derived by other authors: theorems 1 and 2 for the system (**) Y '' +Q(x)Y=0 due to G. J. Etgen and J. F. Pawlowski [Pacific J. Math. 66, 99-110 (1976; Zbl 0355.34017)] and theorems 1-7 of L. H. Erbe, Q. Kong and S. Ruan [Proc. Am. Math. Soc. 117, No. 4, 957-962 (1993; Zbl 0777.34024)] for selfadjoint systems (***) (P(x)U ' ) ' +Q(x)U=0 as well as the theorem 1 for (**) given by F. Meng, J. Wang and Z. Zheng [Proc. Am. Math. Soc. 126, No. 2, 391-395 (1998; Zbl 0891.34037)]. Finally, the authors present a set of six examples illustrating the established theorems.


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