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Let (x, y, z) ∈ C. 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) ∈ Ox,y,z, where P = y∂x − z∂y : Ox,y,z → Ox,y,z. For this equation, our aim is to characterize the solvability on Ox,y,z by using the Im P , Coker P and Ker P , and we give the exact forms of these sets.

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