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Poincaré theorem and nonlinear PDE's

100%

Pliś M.

Annales Polonici Mathematici

1998

tom 69

nr 2

99-105

A family of formal solutions of some type of nonlinear partial differential equations is found. Terms of such solutions are Laplace transforms of some Laplace distributions. The series of these distributions are locally finite.

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

100%

Pliś M. E., Ziemian B.

Annales Polonici Mathematici

1997

tom 67

nr 1

31-41

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.

Ograniczanie wyników

2 Annales Polonici Mathematici

1 Pliś M.

1 Pliś M. E.

1 Ziemian B.

1 1998

1 1997

Wyniki wyszukiwania

Poincaré theorem and nonlinear PDE's

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