Multisummability of formal power series solutions of nonlinear meromorphic differential equations
Annales de l'Institut Fourier, Volume 42 (1992) no. 3, pp. 517-540.

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.

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.

@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},
pages = {517--540},
publisher = {Institut Fourier},
volume = {42},
number = {3},
year = {1992},
doi = {10.5802/aif.1301},
zbl = {0759.34003},
mrnumber = {93j:34006},
language = {en},
url = {http://www.numdam.org/articles/10.5802/aif.1301/}
}
TY  - JOUR
AU  - Braaksma, Boele L. J.
TI  - Multisummability of formal power series solutions of nonlinear meromorphic differential equations
JO  - Annales de l'Institut Fourier
PY  - 1992
DA  - 1992///
SP  - 517
EP  - 540
VL  - 42
IS  - 3
PB  - Institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1301/
UR  - https://zbmath.org/?q=an%3A0759.34003
UR  - https://www.ams.org/mathscinet-getitem?mr=93j:34006
UR  - https://doi.org/10.5802/aif.1301
DO  - 10.5802/aif.1301
LA  - en
ID  - AIF_1992__42_3_517_0
ER  - 
%0 Journal Article
%A Braaksma, Boele L. J.
%T Multisummability of formal power series solutions of nonlinear meromorphic differential equations
%J Annales de l'Institut Fourier
%D 1992
%P 517-540
%V 42
%N 3
%I Institut Fourier
%U https://doi.org/10.5802/aif.1301
%R 10.5802/aif.1301
%G en
%F 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, Volume 42 (1992) no. 3, pp. 517-540. doi : 10.5802/aif.1301. http://www.numdam.org/articles/10.5802/aif.1301/

[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

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

[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 | Zbl

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

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

[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 | Zbl

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

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

[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 | Zbl

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

Cited by Sources: