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

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Nonlinear oscillations of second order differential equations of Euler type
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by Jitsuro Sugie and Tadayuki Hara PDF
Proc. Amer. Math. Soc. 124 (1996), 3173-3181 Request permission

Abstract:

We consider the nonlinear equation $t^{2}x'' + g(x) = 0$, where $g(x)$ satisfies $xg(x) > 0$ for $x \ne 0$, but is not assumed to be sublinear or superlinear. We discuss whether all nontrivial solutions of the equation are oscillatory or nonoscillatory. Our results can be applied even to the case $\frac {g(x)}{x} \to \frac {1}{4} \; \text {as} \; |x| \to \infty$, which is most difficult.
References
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Additional Information
  • Jitsuro Sugie
  • Affiliation: Department of Mathematics, Faculty of Science, Shinshu University, Matsumoto 390, Japan
  • Address at time of publication: Department of Mathematics and Computer Science, Shimane University, Matsue 690, Japan
  • MR Author ID: 168705
  • Email: jsugie@botan.shimane-u.ac.jp
  • Tadayuki Hara
  • Affiliation: Department of Mathematical Sciences, University of Osaka Prefecture, Sakai 593, Japan
  • Email: hara@ms.osakafu-u.ac.jp
  • Received by editor(s): April 6, 1995
  • Additional Notes: The first author was supported in part by Grant-in-Aid for Scientific Research 06804008.

    • Dedicated: Dedicated to Professor Junji Kato on the occasion of his 60th birthday
  • Communicated by: Hal L. Smith
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 3173-3181
  • MSC (1991): Primary 34C10, 34C15; Secondary 34A12, 70K05
  • DOI: https://doi.org/10.1090/S0002-9939-96-03601-5
  • MathSciNet review: 1350965