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

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

Author(s) -

Akira Shirai

Publication year - 2003

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1145476104

Subject(s) - mathematics , type (biology) , nonlinear system , order (exchange) , mathematical analysis , ecology , physics , finance , quantum mechanics , economics , biology

We shall study the first order singular nonlinear partial differential equation of the form f(x, u(x), ∂xu(x)) = 0 with u(0) = 0, where x ∈ C 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. 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. §

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