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.
@article{bwmeta1.element.bwnjournal-article-apmv67z1p31bwm,
author = {Maria Ewa Pli\'s and Bogdan Ziemian},
title = {Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables},
journal = {Annales Polonici Mathematici},
volume = {66},
year = {1997},
pages = {31-41},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z1p31bwm}
}
Maria Ewa Pliś; Bogdan Ziemian. Borel resummation of formal solutions to nonlinear Laplace equations in 2 variables. Annales Polonici Mathematici, Tome 66 (1997) pp. 31-41. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z1p31bwm/
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