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Formal power series solutions of nonlinear first order partial differential equations. (English) Zbl 1142.35310
From the text: E. Maillet [Ann. de l’Éc. Norm. (3) 20, 487–518 (1903; JFM 34.0282.01)] proved that if an algebraic ordinary differential equation has a formal power series as a solution then this formal power series is in some formal Gevrey class. Later, an other proof was given by K. Mahler [Lectures on transcendental numbers. Edited and completed by B. Divis and W. J. LeVeque. Berlin-Heidelberg-New York: Springer-Verlag (1976; Zbl 0332.10019)] and the result was extended to general analytic ordinary differential equations by R. Gérard [Funkc. Ekvacioj, Ser. Int. 34, No. 1, 117–125 (1991; Zbl 0739.34009)] and B. Malgrange [Asymptotic Anal. 2, No. 1, 1–4 (1989; Zbl 0693.34004)].
In this paper we are trying to generalize this result to partial differential equations.

35A20 Analyticity in context of PDEs
35C10 Series solutions to PDEs
35F20 Nonlinear first-order PDEs