# Exact asymptotics of nonlinear difference equations with levels $1$ and ${1}^{+}$

G.K Immink^{[1]}

- [1] Faculty of Economics, University of Groningen, P.O. Box 800, 9700 AV Groningen

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

- Volume: 17, Issue: 2, page 309-356
- ISSN: 0240-2963

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topImmink, G.K. "Exact asymptotics of nonlinear difference equations with levels $1$ and $1^+$." Annales de la faculté des sciences de Toulouse Mathématiques 17.2 (2008): 309-356. <http://eudml.org/doc/10088>.

@article{Immink2008,

abstract = {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.},

affiliation = {Faculty of Economics, University of Groningen, P.O. Box 800, 9700 AV Groningen},

author = {Immink, G.K},

journal = {Annales de la faculté des sciences de Toulouse Mathématiques},

keywords = {Gevrey asymptotics; formal power series solutions; nonlinear difference equations; analytic solutions},

language = {eng},

month = {6},

number = {2},

pages = {309-356},

publisher = {Université Paul Sabatier, Toulouse},

title = {Exact asymptotics of nonlinear difference equations with levels $1$ and $1^+$},

url = {http://eudml.org/doc/10088},

volume = {17},

year = {2008},

}

TY - JOUR

AU - Immink, G.K

TI - Exact asymptotics of nonlinear difference equations with levels $1$ and $1^+$

JO - Annales de la faculté des sciences de Toulouse Mathématiques

DA - 2008/6//

PB - Université Paul Sabatier, Toulouse

VL - 17

IS - 2

SP - 309

EP - 356

AB - 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.

LA - eng

KW - Gevrey asymptotics; formal power series solutions; nonlinear difference equations; analytic solutions

UR - http://eudml.org/doc/10088

ER -

## References

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