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

The authors give some oscillation criteria for the linear matrix Hamiltonian system: \[ U'=A(x)U+B(x)V,\;V'=C(x)U-A^*(x)V,\tag{*} \] where \(A(x)\), \(B(x)=B^* (x)>0\) and \(C(x)=C^*(x)\) are real continuous \(n\times n\)-matrix functions on the interval \([a,\infty)\).
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.


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