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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: $$U'=A(x)U+B(x)V,\ V'=C(x)U-A^*(x)V,\tag *$$ 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 {\it G. J. Etgen} and {\it J. F. Pawlowski} [Pacific J. Math. 66, 99-110 (1976; Zbl 0355.34017)] and theorems 1-7 of {\it L. H. Erbe}, {\it Q. Kong} and {\it 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 {\it F. Meng}, {\it J. Wang} and {\it 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.

34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A30Linear ODE and systems, general
Full Text: DOI
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