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Proceedings of the American Mathematical Society

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A second order differential equation of T. Otsuki


Author: W. R. Utz
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
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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 [Enhancements On Off] (What's this?)

  • [1] 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) Springer, Berlin, 1971, pp. 320–323. Lecture Notes in Math., Vol. 243. MR 0435516
  • [2] Tominosuke Ôtsuki, Minimal hypersurfaces in a Riemannian manifold of constant curvature., Amer. J. Math. 92 (1970), 145–173. MR 0264565, https://doi.org/10.2307/2373502
  • [3] Tominosuke Ôtsuki, On integral inequalities related with a certain nonlinear differential equation, Proc. Japan Acad. 48 (1972), 9–12. MR 0308521
  • [4] 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 0393674, https://doi.org/10.2969/jmsj/02620206
  • [5] 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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DOI: https://doi.org/10.1090/S0002-9939-1977-0466772-2
Article copyright: © Copyright 1977 American Mathematical Society