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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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  • [1] D. Hinton and R. T. Lewis, Oscillation theory for generalized second-order differential equations, Rcky Mountain J. Math. 10 (1980), 751-766. MR 595103 (82c:34039)
  • [2] M. K. Kwong and H. G. Kaper, Oscillation of two-dimensional linear second-order differential systems, J. Differential Equations 56 (1985). MR 774162 (86j:34032)
  • [3] M. K. Kwong, H. G. Kaper, K. Akiyama and A. B. Mingarelli, Oscillation of linear second-order differential systems, Proc. Amer. Math. Soc. 91 (1984), 85-91. MR 735570 (85g:34027)
  • [4] P. Lancaster, Theory of matrices, Academic Press, New York, 1969. MR 0245579 (39:6885)
  • [5] A. B. Mingarelli, On a conjecture for oscillation of second-order ordinary differential systems, Proc. Amer. Math. Soc. 82 (1981), 593-598. MR 614884 (82j:34028)
  • [6] -, An oscillation criterion for second-order selfadjoint differential systems, C. R. Math. Rep. Acad. Sci. Canada 2 (1980), 287-290. MR 600563 (82b:34042)
  • [7] W. T. Reid, Sturmian theory for ordinary differential equations, Springer-Verlag, New York, 1980. MR 606199 (82f:34002)

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

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