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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Oscillation criteria and growth of nonoscillatory solutions of even order ordinary and delay-differential equations
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by R. Grimmer
Trans. Amer. Math. Soc. 198 (1974), 215-228
DOI: https://doi.org/10.1090/S0002-9947-1974-0348227-0

Abstract:

A number of results are presented on oscillation and growth of nonoscillatory solutions of the differential equation ${x^{(n)}}(t) + f(t,x(t)) = 0$. It is shown that a nonoscillatory solution satisfies a first-order integral inequality while its $(n - 1)$st derivative satisfies a first-order differential inequality. By applying the comparison principle, results are obtained by analyzing the two associated first-order scalar differential equations. In the last section it is shown that these results can be easily extended to delay-differential equations.
References
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Bibliographic Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 198 (1974), 215-228
  • MSC: Primary 34K15; Secondary 34C10
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0348227-0
  • MathSciNet review: 0348227