Oscillation Results for Linear Matrix Hamiltonian Systems
Yuan Gong Sun, Fanwei Meng · Rocky Mountain Journal of Mathematics · 2006
Some new criteria have been established for the oscillation of the linear matrix Hamiltonian system X 0 = A(t)X + B(t)Y; Y 0 = 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;1) (t0 > 1 ). Our results are dieren t from most known ones in the sense that they are given in the form lim supt!1 g( ) > const: rather than lim supt!1 1( ) = 1, where g is a positive linear functional on the linear space of n n matrices with real entries. Our results improve some previous ones. Two examples are worked out to illustrate the eectiv eness of our results. AMS (MOS) Subject Classication. 34A30, 34C10.