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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.

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