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An Oscillation Criterion for Linear Second-Order Differential Systems
F. V. Atkinson, Hans G. Kaper and Man Kam Kwong
Proceedings of the American Mathematical Society
Vol. 94, No. 1 (May, 1985), pp. 91-96
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2044958
Page Count: 6
You can always find the topics here!Topics: Eigenvalues, Matrices, Infinity, Differentials, Riccati equation, Mathematical functions, Differential equations
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This article is concerned with the oscillatory behavior at infinity of the solution y: [ a, ∞) → Rn of a system of n second-order differential equations, y"(t) + Q(t) y(t) = 0, t ∈ [ a, ∞); Q is a continuous matrix-valued function on [ a, ∞) 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 ∫t aQ(t) dt tend to infinity as t → ∞.
Proceedings of the American Mathematical Society © 1985 American Mathematical Society