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Exact asymptotics of nonlinear difference equations with levels 1 and 1 +
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 2, pp. 309-356.

We study a class of nonlinear difference equations admitting a 1-Gevrey formal power series solution which, in general, is not 1- (or Borel-) summable. Using right inverses of an associated difference operator on Banach spaces of so-called quasi-functions, we prove that this formal solution can be lifted to an analytic solution in a suitable domain of the complex plane and show that this analytic solution is an accelero-sum of the formal power series.

On étudie une classe d’équations aux différences finies, nonlinéaires, possédants une solution formelle en forme de série 1-Gevrey qui, en général, n’est pas Borel-sommable. En utilisant des inverses à droite d’un opérateur aux différences associé, définies sur des espaces Banach de quasi-fonctions, on démontre qu’à la solution formelle peut être associée, de façon unique, une solution analytique sur un domaine approprié, qui est une accéléro-somme de la solution formelle.

DOI: 10.5802/afst.1185
G.K Immink 1

1 Faculty of Economics, University of Groningen, P.O. Box 800, 9700 AV Groningen
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     title = {Exact asymptotics of nonlinear difference equations with levels $1$ and $1^+$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {309--356},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 17},
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G.K Immink. Exact asymptotics of nonlinear difference equations with levels $1$ and $1^+$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 17 (2008) no. 2, pp. 309-356. doi : 10.5802/afst.1185. https://afst.centre-mersenne.org/articles/10.5802/afst.1185/

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