New oscillation criteria for linear matrix Hamiltonian systems

摘要

Some new 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×n real continuous matrix functions on the interval [t0,∞)(t0>−∞). Our results are independent of the main results obtained in our recent paper [Appl. Math. Comput. 131 (2002) 357] in the sense that they are given in terms of the positive linear functional on the linear space of n×n matrices with real entries. At the same time, our results improve some previous results to a great extent, which can be seen by the examples given at the end of this paper.