In this paper, we are interested in sufficient conditions on partial differential operators with several Fuchsian variables. We give a result of existence and uniqueness of global solutions of the associated Goursat problem, in holomorphic function spaces. Our techniques are those of C. Wagschal  based on formal norms of Leray-Waelbroeck .
"Holomorphic global solutions of the Goursat-Fuchs problem." Differential Integral Equations 19 (12) 1413 - 1436, 2006.