Kamenev type theorems for second-order matrix differential systems

Abstract

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 × n real continuous matrix functions with P(t), Q(t) symmetric and P(t) positive definite for t ∈ [t 0 , ∞) (P(t) > 0, t ≥ t 0 ). 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