New Kamenev type oscillation criteria for linear matrix Hamiltonian systems

Some new Kamenev type criteria have been obtained for the oscillation of the linear matrix Hamiltonian system X' = A(t)X + B(t)Y, Y' = C(t)X - A*(t)Y under the hypothesis: A(t), B(t) = B*(t) > 0 and C(t) = C*(t) are n x n real continuous matrix functions on the interval [t(0), infinity) (t(0) > -infinity). Our results are different from most known ones in the sense that they are given in the form of lim(t-->infinity) sup g[(.)] > const. rather than in the form of lim(t-->infinity) sup lambda(1) [(.)] = infinity, where g is a positive linear functional on the linear space of n x n matrices with real entries. Consequently, our results improve some previous results to some extent, which can be seen by the examples given at the end of this paper. (C) 2003 Elsevier Inc. All rights reserved.