Newton polygons and formal Gevrey indices in the Cauchy-Goursat-Fuchs type equations

Masatake MIYAKE

doi:10.2969/jmsj/04320305

Masatake MIYAKE

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 2 Pages 305-330

DOI https://doi.org/10.2969/jmsj/04320305

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Published: 1991 Received: March 19, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) M.S. Baouendi and C. Goulaouic, Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26 (1973), 455-475.
2) G. Bengel and R. Gérard, Formal and convergent solutions of singular partial differential equations, Manuscripta Math., 38 (1982), 343-373.
3) Y. Hasegawa, On the initial value problems with data on a double characteristic, J. Math. Kyoto Univ., 11 (1971), 357-372.
4) Y. Hasegawa, On the initial-value problems with data on a characteristic hypersurface, J. Math. Kyoto Univ., 13 (1973), 579-593.
5) K. Igari, On the Cauchy-Kowalevski theorem for characteristic initial surface, Proc. Japan Acad., 63 (1987), 7-9.
6) K. Igari, The characteristic Cauchy problem at a point where the multiplicity varies, Japan J. Math., 16 (1990), 119-146.
7) K. Kitagawa and T. Sadamatsu, A remark on a necessary condition of the Cauchy-Kowalevski theorem, Publ. Res. Inst. Math. Sci., 11 (1976), 523-534.
8) M. Miyake, A remark on Cauchy-Kowalevski's theorem, Publ. Res. Inst. Sci., 10 (1974), 243-255.
9) M. Miyake, Global and local Goursat problems in a class of holomorphic or partially holomorphic functions, J. Differential Equations, 39 (1981), 445-463.
10) S. Mizohata, On the Cauchy-Kowalevski theorem, Math. Analysis and Appl., Advances in Math., Suppl. Studies, 7B (1981), 617-652.
11) S. Ouchi, Characteristic Cauchy problems and solutions of formal power series, Ann. Inst. Fourier, 33 (1983), 131-176.
12) J.P. Ramis, Théorèmes d'indices Gevrey pour les équations différentielles ordinaires, Mem. Amer. Math. Soc., 48, No. 296, 1984.
13) H. Tahara, Fundamental systems of analytic solutions of Fuchsian type partial differential equations, Funkcial. Ekvac., 24 (1981), 135-140.
14) A. Yonemura, Newton polygons and formal Gevrey classes, Publ. Res. Inst. Math. Sci., 26 (1990), 197-204.
15) M. Yoshino, Convergence of formal solutions for Fuchs-Goursat equations, J. Differential Equations, 74 (1988), 266-284.
16) C. Wagschal, Une généralization du problème de Goursat pour des systèmes d'équations intégro-différentielles holomorphes ou partiellement holomorphes, J. Math. Pures Appl., 53 (1974), 99-132.

Right : [1] M. S. Baouendi and C. Goulaouic, Cauchy problems with characteristic initial hypersurface, Comm. Pure Appl. Math., 26 (1973), 455-475.
[2] G. Bengel and R. Gérard, Formal and convergent solutions of singular partial differential equations, Manuscripta Math., 38 (1982), 343-373.
[3] Y. Hasegawa, On the initial value problems with data on a double characteristic, J. Math. Kyoto Univ., 11 (1971), 357-372.
[4] Y. Hasegawa, On the initial-value problems with data on a characteristic hypersurface, J. Math. Kyoto Univ., 13 (1973), 579-593.
[5] K. Igari, On the Cauchy-Kowalevski theorem for characteristic initial surface, Proc. Japan Acad., 63 (1987), 7-9.
[6] K. Igari, The characteristic Cauchy problem at a point where the multiplicity varies, Japan J. Math., 16 (1990), 119-146.
[7] K. Kitagawa and T. Sadamatsu, A remark on a necessary condition of the Cauchy-Kowalevski theorem, Publ. Res. Inst. Math. Sci., 11 (1976), 523-534.
[8] M. Miyake, A remark on Cauchy-Kowalevski's theorem, Publ. Res. Inst. Sci., 10 (1974), 243-255.
[9] M. Miyake, Global and local Goursat problems in a class of holomorphic or partially holomorphic functions, J. Differential Equations, 39 (1981), 445-463.
[10] S. Mizohata, On the Cauchy-Kowalevski theorem, Math. Analysis and Appl., Advances in Math., Suppl. Studies, 7B (1981), 617-652.
[11] S. Ouchi, Characteristic Cauchy problems and solutions of formal power series, Ann. Inst. Fourier, 33 (1983), 131-176.
[12] J. P. Ramis, Théorèmes d'indices Gevrey pour les équations différentielles ordinaires, Mem. Amer. Math. Soc., 48, No. 296, 1984.
[13] H. Tahara, Fundamental systems of analytic solutions of Fuchsian type partial differential equations, Funkcial. Ekvac., 24 (1981), 135-140.
[14] A. Yonemura, Newton polygons and formal Gevrey classes, Publ. Res. Inst. Math. Sci., 26 (1990), 197-204.
[15] M. Yoshino, Convergence of formal solutions for Fuchs-Goursat equations, J. Differential Equations, 74 (1988), 266-284.
[16] C. Wagschal, Une généralization du problème de Goursat pour des systèmes d'équations intégro-différentielles holomorphes ou partiellement holomorphes, J. Math. Pures Appl., 53 (1974), 99-132.

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