Proceedings of the Japan Academy, Series A, Mathematical Sciences

Hypoellipticity and existence of periodic solutions on $\mathbf{T}^d$

Masafumi Yoshino

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Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 65, Number 4 (1989), 106-108.

Dates
First available in Project Euclid: 19 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195512946

Digital Object Identifier
doi:10.3792/pjaa.65.106

Mathematical Reviews number (MathSciNet)
MR1011844

Zentralblatt MATH identifier
0701.35057

Subjects
Primary: 35H05
Secondary: 58G15

Citation

Yoshino, Masafumi. Hypoellipticity and existence of periodic solutions on $\mathbf{T}^d$. Proc. Japan Acad. Ser. A Math. Sci. 65 (1989), no. 4, 106--108. doi:10.3792/pjaa.65.106. https://projecteuclid.org/euclid.pja/1195512946


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References

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  • [2] C. Siegel: Uber die Normalform analytischer Differentialgleichungen in der Nahe einer Gleichgewichtslosung. Nachr. Akad. Wiss. Gottingen, pp. 21-30 (1952).
  • [3] K. Taira: Le principe du maximum et I'hypoellipticite globale. Seminaire Bony-Sjostrand-Meyer 1984-1985, n° 1.
  • [4] K. Tanaka: Infinitely many periodic solutions for the equation. uu-uxx±\u\s 1u = f(x,t). Comm. in P.D.E., 10, 1317-1345 (1985).
  • [5] M. Yoshino: An application of generalized implicit function theorem to Goursat problems for nonlinear Leray-Volevich systems. J. Diff. Eqs., 57, 44-69 (1985).
  • [6] M. Yoshino: The diophantine nature for the convergence of formal solutions. Tohoku J. Math., 38, 625-641 (1986).