New Oscillation Criteria for Second Order Linear Matrix Differential Equations with Damping

By using the positive linear functional and the monotone subhomogeneous functional,including the general means and Riccati technique,some new oscillation criteria are established for thesecond order linear matrix differential system(P(t)X’(t))’+R(t)X’(t)+Q(t)X(t)=0,t≥to>0,where P(t),R(t),Q(t)are n×n real continuous matrix functions,P(t)and R(t)are commutative.Theresults improve and generalize those given in some previous papers,which can be seen by the examplesgiven at the end of this paper.