We show the solvability and nonsolvability of a singular nonlinear system of partial diﬀerential equations with resonance in a class of functions holomorphic in some neighborhood of the origin. These results are applied to the normal form theory of a singular vector ﬁeld.
Cite this article
Masafumi Yoshino, Convergent and Divergent Solutions of Singular Partial Differential Equations with Resonance or Small Denominators. Publ. Res. Inst. Math. Sci. 43 (2007), no. 4, pp. 923–943