Abstract
We consider the second-order differential system, (1) ( R( t) Y′)′ + Q( t) Y = 0, where R, Q, Y are n × n matrices with R( t), Q( t) symmetric and R( t) positive definite for t ϵ [ a, + ∞) ( R( t) > 0, t ⩾ a). We establish sufficient conditions in order that all prepared solutions Y( t) of (1) are oscillatory; that is, det Y( t) vanishes infinitely often on [ a, + ∞). The conditions involve the smallest and largest eigen-values λ n ( R −1( t)) and λ 1(∝ a t Q( s) ds), respectively. The results obtained can be regarded as generalizing well-known results of Leighton and others in the scalar case.
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