KAMENEV TYPE THEOREMS FOR 2ND-ORDER MATRIX DIFFERENTIAL-SYSTEMS

We consider the second order matrix differential systems (1) (P(t)Y')' + Q(t)Y = 0 and (2) Y'' + Q(t)Y = 0 where Y, P, and Q are n x n real continuous matrix functions with P(t), Q(t) symmetric and P(t) positive definite for t is-an-element-of [t0, infinity) (P(t) > 0, t greater-than-or-equal-to t0). We establish sufficient conditions in order that all prepared solutions Y(t) of (1) and (2) are oscillatory. The results obtained can be regarded as generalizing well-known results of Kamenev in the scalar case.