Existence and uniqueness of nonlinear Goursat problem in the class of Denjoy–Carleman

Abstract

The problem of existence and uniqueness of nonlinear Goursat is studied by Claude Wagschal in different spaces: holomorphic spaces, partially holomorphic, continuous-Gevrey and Gevrey-holomorphic. In this paper, we replace the sequence (n!)d−1 in the case Gevery with suitable sequence (Mn) in the case Carleman. After that, we study the problem of existence and uniqueness of nonlinear Goursat problem in Denjoy–Carleman space.