JournalsprimsVol. 39, No. 2pp. 275–296

A Maillet Type Theorem for First Order Singular Nonlinear Partial Differential Equations

  • Akira Shirai

    Nagoya University, Nagoya, Chikusa-Ku, Japan
A Maillet Type Theorem for First Order Singular Nonlinear Partial Differential Equations cover
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Abstract

We shall study the first order singular nonlinear partial differential equation of the form f(x, u(x), ∂_x__u_(x)) = 0 with u(0) = 0, where x ∈ ℂ_n_ and f(x, u, ξ) is holomorphic in a neighborhood of the origin. This equation is said to be singular if f(0, 0, ξ) ≡ 0 for all ξ ∈ ℂ_n_. The purpose of this paper is to study the Maillet type theorem which means to determine the Gevrey order of a formal power series solution which may diverge.

Cite this article

Akira Shirai, A Maillet Type Theorem for First Order Singular Nonlinear Partial Differential Equations. Publ. Res. Inst. Math. Sci. 39 (2003), no. 2, pp. 275–296

DOI 10.2977/PRIMS/1145476104