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Kamenev Type Theorems for Second Order Matrix Differential Systems

Lynn H. Erbe, Qingkai Kong and Shigui Ruan
Proceedings of the American Mathematical Society
Vol. 117, No. 4 (Apr., 1993), pp. 957-962
DOI: 10.2307/2159522
Stable URL: http://www.jstor.org/stable/2159522
Page Count: 6
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Kamenev Type Theorems for Second Order Matrix Differential Systems
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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 $t \in \lbrack t_0, \infty) (P(t) > 0, t \geq t_0)$. 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.

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