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Summary: KAMENEV-TYPE OSCILLATION CRITERIA FOR LINEAR
HAMILTONIAN SYSTEMS
DOUGLAS R. ANDERSON
Abstract. New oscillation criteria of Kamenev type are established for
linear Hamiltonian matrix systems using generalized Riccati and integral
averaging techniques. The results generalize some recent work on linear
Hamiltonian systems and the related self-adjoint second-order matrix
equation, without controllability or differentiability requirements on the
coefficient matrix functions.
1. Introduction
We are concerned with the linear Hamiltonian system
X = A(t)X + B(t)Y
Y = C(t)X - A(t)Y, t t0,
(1.1)
where A, B, and C are continuous n × n real-valued matrix functions such
that B and C are symmetric with B positive definite. Here A denotes
the transpose of A. For any two solutions (X1, Y1) and (X2, Y2) of (1.1),
the Wronskian X
1 (t)Y2(t) - Y
1 (t)X2(t) is a constant matrix. In particular,
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