New Kamenev type oscillation criteria for linear matrix Hamiltonian systems

摘要

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×n real continuous matrix functions on the interval [t0,∞) (t0>−∞). Our results are different from most known ones in the sense that they are given in the form of limt→∞supg[·]>const. rather than in the form of limt→∞supλ1[·]=∞, where g is a positive linear functional on the linear space of n×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.