Journal of the Mathematical Society of Japan

The method of Frobenius to Fuchsian partial differential equations

Takeshi MANDAI

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Abstract

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

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

Dates
First available in Project Euclid: 10 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213107293

Digital Object Identifier
doi:10.2969/jmsj/05230645

Mathematical Reviews number (MathSciNet)
MR1760611

Zentralblatt MATH identifier
0993.35004

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

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

Citation

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. https://projecteuclid.org/euclid.jmsj/1213107293


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