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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

An oscillation criterion for linear second-order differential systems
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by F. V. Atkinson, Hans G. Kaper and Man Kam Kwong PDF
Proc. Amer. Math. Soc. 94 (1985), 91-96 Request permission

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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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 94 (1985), 91-96
  • MSC: Primary 34C10
  • DOI: https://doi.org/10.1090/S0002-9939-1985-0781063-2
  • MathSciNet review: 781063