Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables
Volume 67 / 1997
Annales Polonici Mathematici 67 (1997), 31-41
DOI: 10.4064/ap-67-1-31-41
Abstract
We consider a nonlinear Laplace equation Δu = f(x,u) in two variables. Following the methods of B. Braaksma [Br] and J. Ecalle used for some nonlinear ordinary differential equations we construct first a formal power series solution and then we prove the convergence of the series in the same class as the function f in x.
