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

G.K Immink — 2008

Annales de la faculté des sciences de Toulouse Mathématiques

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 , 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 of the formal power series.

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Exact asymptotics of nonlinear difference equations with levels 1 and 1 +

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