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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the location of zeros of second-order differential equations
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by Vadim Komkov
Proc. Amer. Math. Soc. 35 (1972), 217-222
DOI: https://doi.org/10.1090/S0002-9939-1972-0298128-5

Abstract:

The paper considers the location of zeros of the equation $(\alpha (t)x’)’ + \gamma (t)x = 0,t \in [{t_0},{t_1}]$. The following theorem is proved. Let $[a,a + T],T = na$ (n a positive integer), be a subset of $[{t_0},{t_1}]$. Denote $\omega = \pi /T$. Let the coefficient functions obey the inequality $\smallint _a^{a + T}\{ \gamma (t) - {\omega ^2}\alpha (t){\sin ^2}(\omega t)\} dt > {\omega ^2}\smallint _a^{a + T}\{ \alpha \cos 2\omega t\} dt$. Then every solution of this equation will have a zero on $[a,a + T]$. A more general form of this theorem is also proved.
References
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Bibliographic Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 35 (1972), 217-222
  • MSC: Primary 34C10
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0298128-5
  • MathSciNet review: 0298128