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Interval oscillation criteria for self-adjoint matrix Hamiltonian systems. (English) Zbl 1105.34018

By using monotone functionals, the function class of the form H(t,s)k(s) and a generalized matrix Riccati substitution, the authors establish some new and general interval oscillation criteria for the selfadjoint matrix Hamiltonian system

X ' (t)=A(t)X(t)+B(t)Y(t),Y ' (t)=C(t)X(t)-A T (t)Y(t)·

Several interesting examples are included to illustrate the versatility of the results obtained.

It is worth noting that the function class of the form H(t,s)k(s) introduced the referee [Arch. Math. 76, 385–390 (2001; Zbl 0989.34024) and its usage was explained in J. Math. Anal. Appl. 295, 40–54 (2004; Zbl 1058.34038)]. Also, an earlier related paper on interval criteria for oscillation of second-order matrix differential systems gave the referee [J. Math. Anal. Appl. 276, 373–395 (2002; Zbl 1022.34032)].

34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems