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On the oscillation of self-adjoint matrix Hamiltonian systems. (English) Zbl 1048.34073
The authors consider the linear selfadjoint Hamiltonian matrix system $U'(x)= A(x)U(x)+B(x)V(x),\qquad V'(x)=C(x)U(x)-A^*(x)V(x), \tag{1}$ where $$A(x)$$, $$B(x)$$ and $$C(x)$$ are real continuous $$n\times n$$-matrix functions. The matrices $$B(x)$$ and $$C(x)$$ are supposed to be symmetric and the matrix $$B(x)$$ is positive definite. Using the averaging technique, introduced by Ch. G. Philos [Arch. Math. 53, 482–492 (1989; Zbl 0661.34030)] in the case of second-order linear differential equation, the authors prove new oscillation criteria for system $$(1)$$. These criteria include several known criteria as special cases.

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34A30 Linear ordinary differential equations and systems
##### Keywords:
Hamiltonian system; oscillation; linear system
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