References

NONLINEAR SYSTEM OF SINGULAR PARTIAL DIFFERENTIAL EQUATIONS


[1] M. S. Baouendi and C. Goulaouic, Singular nonlinear Cauchy problems, J. Diff. Equ. 22 (1976), 268-291.

[2] W. A. Harris Jun, Y. Sibuya and L. Weinberg, Holomorphic solutions of linear differential systems at singular points, Arch. Ration. Mech. Anal. 35 (1969), 245-248.

[3] Y. Hasegawa, On the initial-value problems with data on a double characteristic, J. Math. Kyoto-Univ. 11(2) (1971), 357-372.

[4] N. A. Lednev, A new method for solving partial differential equations, Mat. Sbornik 22(64) (1948), 205-264.

[5] T. Mandai, Existence and non-existence of null-solutions for some non-Fuchsian partial differential operators with t-dependent coefficients, Nagoya Math. J. 122 (1991), 115-137.

[6] M. Miyake and Y. Hashimoto, Newton polygons and Gevrey indices for linear partial differential operators, Nagoya Math. J. 128 (1992), 15-47.

[7] M. Miyake, Newton polygon and Gevrey hierarchy in the index formulas for a singular system of ordinary differential equations, Funkcialaj Ekvacioj 55 (2012), 169-237.

[8] S. Ouchi, Genuine solutions and formal solutions with Gevrey type estimates of nonlinear partial differential equations, J. Math. Sci., Tokyo 2(2) (1995), 375-417.

[9] J. Persson, Singular holomorphic solutions of linear partial differential equations with holomorphic coefficients and nonanalytic solutions of equations with analytic coefficients, Astérisque, Soc. Math. France, 89(90) (1981), 223-247.

[10] P. Pongérard, Sur une classe d’équations de Fuchs non linéaires, J. Math. Sci. Univ. Tokyo 7 (2000), 423-448.

[11] P. Pongérard, Solutions ramifiées à croissance lente de certaines équations de Fuchs quasi-linéaires, Osaka Journal of Mathematics 47 (2010), 157-176.

[12] J. P. Ramis, Théorèmes d’indices Gevrey pour les équations différentielles ordinaires, Mem. Amer. Math. Soc. 48 (1984), 296.

[13] Y. Sibuya, Convergence of formal power series solutions of a system of nonlinear differential equations at an irregular singular point, Geometrical approaches to differential equations, Proc. 4th Scheveningen Conf., 1979, Lect. Notes Math. 810 (1980), 135-142.

[14] H. Tahara, Uniqueness of the solution of non-linear singular partial differential equations, J. Math. Soc. Japan 48 (1996), 729-744.

[15] C. Wagschal, Le problème de Goursat non linéaire, J. Math. Pures Appl. 58 (1979), 309-337.