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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.

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A second order differential equation of T. Otsuki
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by W. R. Utz PDF
Proc. Amer. Math. Soc. 64 (1977), 238-240 Request permission

Abstract:

It is shown that an ordinary differential equation arising in the study of minimal hypersurfaces in certain Riemannian manifolds and for which one family of periodic solutions is known has, in fact, a second family of periodic solutions.
References
  • Shigeru Furuya, On periods of periodic solutions of a certain nonlinear differential equation, Japan-United States Seminar on Ordinary Differential and Functional Equations (Kyoto, 1971) Lecture Notes in Math., Vol. 243, Springer, Berlin, 1971, pp. 320–323. MR 0435516
  • Tominosuke Ôtsuki, Minimal hypersurfaces in a Riemannian manifold of constant curvature, Amer. J. Math. 92 (1970), 145–173. MR 264565, DOI 10.2307/2373502
  • Tominosuke Ôtsuki, On integral inequalities related with a certain nonlinear differential equation, Proc. Japan Acad. 48 (1972), 9–12. MR 308521
  • Tominosuke Ôtsuki, On a bound for periods of solutions of a certain nonlinear differential equation. I, J. Math. Soc. Japan 26 (1974), 206–233. MR 393674, DOI 10.2969/jmsj/02620206
  • M. Urabe, Computations of periods of a certain nonlinear autonomous oscillation. Study of algorithms of numerical computations, Sûrikaiseki Kenkyûsho Kôkyû-roku 148 (1972), 111-129. (Japanese)
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 64 (1977), 238-240
  • MSC: Primary 34C25; Secondary 58E10
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0466772-2
  • MathSciNet review: 0466772