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An oscillation criterion for linear second-order differential systems

Authors: F. V. Atkinson, Hans G. Kaper and Man Kam Kwong
Journal: Proc. Amer. Math. Soc. 94 (1985), 91-96
MSC: Primary 34C10
MathSciNet review: 781063
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Abstract: This article is concerned with the oscillatory behavior at infinity of the solution $y:[a,\infty ) \to {{\mathbf {R}}^n}$ of a system of $n$ second-order differential equations, $y''(t)y(t) = 0,\;t \in [a,\infty );\;Q$ is a continuous matrix-valued function on $[a,\infty )$ whose values are real symmetric matrices of order $n$. It is shown that the solution is oscillatory at infinity if (at least) $n - 1$ eigenvalues of the matrix $\smallint _a^tQ(t)\;dt$ dt end to infinity as $t \to \infty$.

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Keywords: Matrix differential equation, oscillation theory, matrix Riccati equation, Riccati inequality
Article copyright: © Copyright 1985 American Mathematical Society