Convergence of formal solutions of first order singular partial differential equations of nilpotent type

• Autorzy: Masatake Miyake , Akira Shirai
• Języki publikacji: EN

Abstrakty

EN

Let (x,y,z) ∈ ℂ³. In this paper we shall study the solvability of singular first order partial differential equations of nilpotent type by the following typical example:
$Pu(x,y,z): = (y∂_x - z∂_y)u(x,y,z) = f(x,y,z) ∈ 𝒪_{x,y,z}$,
where
$P = y∂_x - z∂_y: 𝒪_{x,y,z} → 𝒪_{x,y,z}$.
For this equation, our aim is to characterize the solvability on $𝒪_{x,y,z}$ by using the Im P, Coker P and Ker P, and we give the exact forms of these sets.

Kategorie tematyczne

• 34M03: Linear equations and systems
• 34M25: Formal solutions, transform techniques
• 35A20: Analytic methods, singularities

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2012
• Tom: 97
• Numer: 1
• Strony: 91-99

Daty

wydano

2012

Twórcy

autor

Masatake Miyake

• Graduate School of Mathematics, Nagoya University, Furo-cho, Chikusa, 464-8602 Nagoya, Japan

autor

Akira Shirai

• School of Education, Sugiyama Jogakuen University, Hoshigaoka Motomachi 17-3, Chikusa, 464-8662 Nagoya, Japan

Identyfikatory

DOI

10.4064/bc97-0-6