Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables

M. Pliś, B. Ziemian
1997 Annales Polonici Mathematici  
We consider a nonlinear Laplace equation ∆u = 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. 1991 Mathematics Subject Classification: 35C20, 44A10.
doi:10.4064/ap-67-1-31-41 fatcat:fspsxbo37rhivcn3a3helfnqae