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Linear transformation and oscillation criteria for Hamiltonian systems. (English) Zbl 1124.34021

The author studies the linear Hamiltonian system

x ' =A(t)x+B(t)u,u ' =C(t)x-A * (t)u,

where A(t), B(t), C(t) are real n×n matrix-valued functions, B and C are Hermitian, B is positive definite. Using a transformation which preserves oscillation properties of this system, the author derives new oscillation criteria from known oscillation criteria of other authors.

MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34C20Transformation and reduction of ODE and systems, normal forms
37J99Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems