On the oscillation of self-adjoint matrix Hamiltonian systems. (English) Zbl 1048.34073

Yang, Qigui; Cheng, Sui Sun

Proc. Edinb. Math. Soc., II. Ser. 46, No. 3, 609-625 (2003).

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.

Reviewer: Robert Mařík (Brno)

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

Citations:

Zbl 0661.34030