Multisummability of formal power series solutions of nonlinear meromorphic differential equations
Braaksma, Boele L. J.
Annales de l'Institut Fourier, Tome 42 (1992), p. 517-540 / Harvested from Numdam

Dans cet article on donne une démonstration d’un théorème de J. Écalle sur la multisommabilité des solutions formelles des équations différentielles méromorphes non-linéaires.

In this paper a proof is given of a theorem of J. Écalle that formal power series solutions of nonlinear meromorphic differential equations are multisummable.

@article{AIF_1992__42_3_517_0,
     author = {Braaksma, Boele L. J.},
     title = {Multisummability of formal power series solutions of nonlinear meromorphic differential equations},
     journal = {Annales de l'Institut Fourier},
     volume = {42},
     year = {1992},
     pages = {517-540},
     doi = {10.5802/aif.1301},
     mrnumber = {93j:34006},
     zbl = {0759.34003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1992__42_3_517_0}
}
Braaksma, Boele L. J. Multisummability of formal power series solutions of nonlinear meromorphic differential equations. Annales de l'Institut Fourier, Tome 42 (1992) pp. 517-540. doi : 10.5802/aif.1301. http://gdmltest.u-ga.fr/item/AIF_1992__42_3_517_0/

[1] W. Balser, A different characterization of multisummable power series, preprint Universität Ulm, (1990).

[2] W. Balser, Summation of formal power series through iterated Laplace integrals, preprint Universität Ulm, (1990). | Zbl 0769.34004

[3] W. Balser, B. L. J. Braaksma, J.-P. Ramis and Y. Sibuya, Multisummability of formal power series solutions of linear ordinary differential equations, Asymptotic Analysis, 5 (1991), 27-45. | MR 93f:34011 | Zbl 0754.34057

[4] B. L. J. Braaksma, Laplace integrals in singular differential and difference equations, in Proc. Conf. Ordinary and Partial Differential Equations Dundee, 1978, Lecture Notes in Mathematics, Vol. 827, Springer Verlag, (1980), 25-53. | MR 82f:34064 | Zbl 0449.34005

[5] B. L. J. Braaksma, Multisummability and Stokes multipliers of linear meromorphic differential equations, J. Differential Equations, 92 (1991), 45-75. | MR 93c:34010 | Zbl 0729.34005

[6] J. Ecalle, Les Fonctions Résurgentes, Tome I, II, Publ. Math. d'Orsay (1981), Tome III, Idem (1985). | Zbl 0499.30034

[7] J. Ecalle, L'accélération des fonctions résurgentes, manuscrit, 1987.

[8] J. Ecalle, Calcul accélératoire et applications, book submitted to "Travaux en Cours" Hermann, Paris, (1990). (See also The acceleration operators and their applications, invited address ICM Kyoto (1990)).

[9] M. Hukuhara, Sur les points singuliers des équations différentielles linéaires II, J. Fac. Sci. Hokkaido Univ., 5 (1937), 123-166. | JFM 64.1144.01 | Zbl 0016.30502

[10] W. B. Jurkat, Summability of asymptotic series, preprint Universität Ulm (1990).

[11] B. Malgrange, Sur les points singuliers des équations différentielles linéaires, Enseign. Math., 20 (1974), 147-176. | MR 51 #4316 | Zbl 0299.34011

[12] B. Malgrange and J.-P. Ramis, Fonctions multisommables, Ann. Inst. Fourier, Grenoble, 42-1 & 2 (1992), 353-368. | Numdam | MR 93e:40007 | Zbl 0759.34007

[13] J. Martinet and J.-P. Ramis, Elementary acceleration and multisummability, Ann. Inst. H. Poincaré, Physique Théorique, 54-1 (1991), 1-71. | Numdam | MR 93a:32036 | Zbl 0748.12005

[14] J.-P. Ramis, Conjectures, manuscrit, 1989.

[15] J.-P. Ramis, Multisummability, preprint, 1990.

[16] J.-P. Ramis and Y. Sibuya, Hukuhara domains and fundamental existence and uniqueness theorems for asymptotic solutions of Gevrey type, Asymp. Analysis, 2 (1989), 39-94. | MR 90k:58209 | Zbl 0699.34058

[17] Y. Sibuya, Linear differential equations in the complex domain : Problems of analytic continuation, Transl. Math. Monographs, 82, AMS, (1990). | Zbl 00048899

[18] Y. Sibuya, Gevrey asymptotics and Stokes multipliers, in Differential Equations and Computer Algebra, Academic Press, 1991, 131-147. | MR 92j:34012 | Zbl 0731.34002

[19] H. L. Turrittin, Convergent solutions of ordinary homogeneous differential equations in the neighborhood of a singular point, Acta Math., 93 (1955), 27-66. | MR 16,925a | Zbl 0064.33603

[20] W. Wasow, Asymptotic Expansions of Ordinary Differential Equations, Dover, 1976.