Exact asymptotics of nonlinear difference equations with levels and
We study a class of nonlinear difference equations admitting a -Gevrey formal power series solution which, in general, is not - (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.