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}, pages = {517--540}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {42}, number = {3}, year = {1992}, doi = {10.5802/aif.1301}, zbl = {0759.34003}, mrnumber = {93j:34006}, language = {en}, url = {https://aif.centre-mersenne.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 SP - 517 EP - 540 VL - 42 IS - 3 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/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 %C Grenoble %U https://aif.centre-mersenne.org/articles/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, Tome 42 (1992) no. 3, pp. 517-540. doi : 10.5802/aif.1301. https://aif.centre-mersenne.org/articles/10.5802/aif.1301/
[1] A different characterization of multisummable power series, preprint Universität Ulm, (1990).
,[2] Summation of formal power series through iterated Laplace integrals, preprint Universität Ulm, (1990). | Zbl
,[3] Multisummability of formal power series solutions of linear ordinary differential equations, Asymptotic Analysis, 5 (1991), 27-45. | MR | Zbl
, , and ,[4] 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] Multisummability and Stokes multipliers of linear meromorphic differential equations, J. Differential Equations, 92 (1991), 45-75. | MR | Zbl
,[6] Les Fonctions Résurgentes, Tome I, II, Publ. Math. d'Orsay (1981), Tome III, Idem (1985). | Zbl
,[7] L'accélération des fonctions résurgentes, manuscrit, 1987.
,[8] 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] Sur les points singuliers des équations différentielles linéaires II, J. Fac. Sci. Hokkaido Univ., 5 (1937), 123-166. | JFM | Zbl
,[10] Summability of asymptotic series, preprint Universität Ulm (1990).
,[11] Sur les points singuliers des équations différentielles linéaires, Enseign. Math., 20 (1974), 147-176. | MR | Zbl
,[12] Fonctions multisommables, Ann. Inst. Fourier, Grenoble, 42-1 & 2 (1992), 353-368. | Numdam | MR | Zbl
and ,[13] Elementary acceleration and multisummability, Ann. Inst. H. Poincaré, Physique Théorique, 54-1 (1991), 1-71. | Numdam | MR | Zbl
and ,[14] Conjectures, manuscrit, 1989.
,[15] Multisummability, preprint, 1990.
,[16] Hukuhara domains and fundamental existence and uniqueness theorems for asymptotic solutions of Gevrey type, Asymp. Analysis, 2 (1989), 39-94. | MR | Zbl
and ,[17] Linear differential equations in the complex domain : Problems of analytic continuation, Transl. Math. Monographs, 82, AMS, (1990). | Zbl
,[18] Gevrey asymptotics and Stokes multipliers, in Differential Equations and Computer Algebra, Academic Press, 1991, 131-147. | MR | Zbl
,[19] Convergent solutions of ordinary homogeneous differential equations in the neighborhood of a singular point, Acta Math., 93 (1955), 27-66. | MR | Zbl
,[20] Asymptotic Expansions of Ordinary Differential Equations, Dover, 1976.
,Cité par Sources :