Solutions ramifiées à croissance lente de certaines équations de Fuchs quasi-linéaires

Abstract

We consider a class of quasilinear fuchsian operators $Q$ of order $m\geq 1$, holomorphic in a neighborhood of the origin in $\mathbf{C}_{t} \times \mathbf{C}_{x}^{n}$, and having a simple characteristic hypersurface transverse to $S$: $t=0$. Under an assumption on the linear part of $Q$, we construct solutions of the problem $Qu=v$ in spaces of ramified functions of slow growth. The result is an extension of [15] to the quasilinear case.