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Partial Differential Equations and Spectral Theory pp 63–71Cite as

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Some New Results on the Nonlinear Singular Partial Differential Equations

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 126))

Abstract

In this paper, we calculate the formal Gevrey index of the formal solution of a class of nonlinear first order totally characteristic type partial differential equations with irregular singular in the space variable.

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References

  1. H. Chen and H. Tahara, On the holomorphic solution of non-linear totally characteristic equations, to appear in Mathematische Nachrichten, Germany.

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  2. H. Chen and H. Tahara, On totally characteristic type non-linear partial differential equations in the complex domain, Publ. RIMS, Kyoto Univ., 26:621–636, 1999.

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  3. H. Chen and Z. Luo, On the holomorphic solution of nonlinear totally charac-teristic equations with several space variables, Preprint.

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  4. R. Gérard and H. Tahara, Nonlinear singular first order partial differential equations of Briot-Bouquet typeProc. Japan Acad., 66:72–74, 1990.

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  5. R. Gérard and H. Tahara, Holomorphic and singular solution of nonlinear singular first order partial differential equations, Publ. RIMS, Kyoto Univ., 26:979–1000, 1990.

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  6. R. Gérard and H. Tahara, Singular nonlinear partial differential equations, Aspects of Mathematics, E 28, Vieweg, 1996.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Wuhan University, Wuhan, 430072, China

    Chen Hua & Luo Zhuangchu

  2. Department of Mathematics, Sophia University, Japan

    Tahara Hidetoshi

Authors
  1. Chen Hua
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  2. Luo Zhuangchu
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  3. Tahara Hidetoshi
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, TU Clausthal, Erzstr. 1, Clausthal-Zellerfeld, 38678, Germany

    Michael Demuth

  2. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, Potsdam, 14469, Germany

    Bert-Wolfgang Schulze

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© 2001 Springer Basel AG

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Hua, C., Zhuangchu, L., Hidetoshi, T. (2001). Some New Results on the Nonlinear Singular Partial Differential Equations. In: Demuth, M., Schulze, BW. (eds) Partial Differential Equations and Spectral Theory. Operator Theory: Advances and Applications, vol 126. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8231-6_8

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  • DOI: https://doi.org/10.1007/978-3-0348-8231-6_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9483-8

  • Online ISBN: 978-3-0348-8231-6

  • eBook Packages: Springer Book Archive

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