Multisummability of formal power series solutions of nonlinear meromorphic differential equations

Boele L. J. Braaksma

Annales de l'institut Fourier (1992)

  • Volume: 42, Issue: 3, page 517-540
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Braaksma, Boele L. J.. "Multisummability of formal power series solutions of nonlinear meromorphic differential equations." Annales de l'institut Fourier 42.3 (1992): 517-540. <http://eudml.org/doc/74965>.

@article{Braaksma1992,
abstract = {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.},
author = {Braaksma, Boele L. J.},
journal = {Annales de l'institut Fourier},
keywords = {multisummability; Laplace transform; Borel transform; acceleration; formal power series solutions; nonlinear meromorphic differential equations; multisummable},
language = {eng},
number = {3},
pages = {517-540},
publisher = {Association des Annales de l'Institut Fourier},
title = {Multisummability of formal power series solutions of nonlinear meromorphic differential equations},
url = {http://eudml.org/doc/74965},
volume = {42},
year = {1992},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 42
IS - 3
SP - 517
EP - 540
AB - 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.
LA - eng
KW - multisummability; Laplace transform; Borel transform; acceleration; formal power series solutions; nonlinear meromorphic differential equations; multisummable
UR - http://eudml.org/doc/74965
ER -

References

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  1. [1] W. BALSER, A different characterization of multisummable power series, preprint Universität Ulm, (1990). 
  2. [2] W. BALSER, Summation of formal power series through iterated Laplace integrals, preprint Universität Ulm, (1990). Zbl0769.34004
  3. [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. Zbl0754.34057MR93f:34011
  4. [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. Zbl0449.34005MR82f:34064
  5. [5] B. L. J. BRAAKSMA, Multisummability and Stokes multipliers of linear meromorphic differential equations, J. Differential Equations, 92 (1991), 45-75. Zbl0729.34005MR93c:34010
  6. [6] J. ECALLE, Les Fonctions Résurgentes, Tome I, II, Publ. Math. d'Orsay (1981), Tome III, Idem (1985). Zbl0499.30034
  7. [7] J. ECALLE, L'accélération des fonctions résurgentes, manuscrit, 1987. 
  8. [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. [9] M. HUKUHARA, Sur les points singuliers des équations différentielles linéaires II, J. Fac. Sci. Hokkaido Univ., 5 (1937), 123-166. Zbl0016.30502JFM64.1144.01
  10. [10] W. B. JURKAT, Summability of asymptotic series, preprint Universität Ulm (1990). 
  11. [11] B. MALGRANGE, Sur les points singuliers des équations différentielles linéaires, Enseign. Math., 20 (1974), 147-176. Zbl0299.34011MR51 #4316
  12. [12] B. MALGRANGE and J.-P. RAMIS, Fonctions multisommables, Ann. Inst. Fourier, Grenoble, 42-1 & 2 (1992), 353-368. Zbl0759.34007MR93e:40007
  13. [13] J. MARTINET and J.-P. RAMIS, Elementary acceleration and multisummability, Ann. Inst. H. Poincaré, Physique Théorique, 54-1 (1991), 1-71. Zbl0748.12005MR93a:32036
  14. [14] J.-P. RAMIS, Conjectures, manuscrit, 1989. 
  15. [15] J.-P. RAMIS, Multisummability, preprint, 1990. 
  16. [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. Zbl0699.34058MR90k:58209
  17. [17] Y. SIBUYA, Linear differential equations in the complex domain : Problems of analytic continuation, Transl. Math. Monographs, 82, AMS, (1990). Zbl1145.34378
  18. [18] Y. SIBUYA, Gevrey asymptotics and Stokes multipliers, in Differential Equations and Computer Algebra, Academic Press, 1991, 131-147. Zbl0731.34002MR92j:34012
  19. [19] H. L. TURRITTIN, Convergent solutions of ordinary homogeneous differential equations in the neighborhood of a singular point, Acta Math., 93 (1955), 27-66. Zbl0064.33603MR16,925a
  20. [20] W. WASOW, Asymptotic Expansions of Ordinary Differential Equations, Dover, 1976. Zbl0369.34023

Citations in EuDML Documents

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  1. Jean Ecalle, Bruno Vallet, The arborification-coarborification transform : analytic, combinatorial, and algebraic aspects
  2. Maria Ewa Pliś, Bogdan Ziemian, Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables
  3. Bernard Malgrange, Jean-Pierre Ramis, Fonctions multisommables
  4. Boele L. J. Braaksma, Bernard F. Faber, Multisummability for some classes of difference equations
  5. Jean-Pierre Ramis, Yasutaka Sibuya, A new proof of multisummability of formal solutions of non linear meromorphic differential equations
  6. Grzegorz Łysik, Laplace integrals in partial differential equations in papers of Bogdan Ziemian
  7. Zhuangchu Luo, Hua Chen, Changgui Zhang, Exponential-type Nagumo norms and summability of formal solutions of singular partial differential equations
  8. Geertrui Klara Immink, Accelero-summation of the formal solutions of nonlinear difference equations

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