Journal of the Mathematical Society of Japan

The method of Frobenius to Fuchsian partial differential equations

Takeshi MANDAI

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To Fuchsian partial differential equations in the sense of M. S. Baouendi and C. Goulaouic, which is a natural extension of ordinary differential equations with regular singularity at a point, all the solutions in a complex domain are constructed along the same line as the method of Frobenius to ordinary differential equations, without any assumptions on the characteristic exponents. The same idea can be applied to Fuchsian hyperbolic equations considered by H. Tahara.

Article information

J. Math. Soc. Japan, Volume 52, Number 3 (2000), 645-672.

First available in Project Euclid: 10 June 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35A07
Secondary: 35C20: Asymptotic expansions 35B40: Asymptotic behavior of solutions

The method of Frobenius Fuchsian partial differential equation regular singularity characteristic exponent characteristic index


MANDAI, Takeshi. The method of Frobenius to Fuchsian partial differential equations. J. Math. Soc. Japan 52 (2000), no. 3, 645--672. doi:10.2969/jmsj/05230645.

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