Problème de Goursat non linéaire dans la classe Denjoy-Carleman

Abstract

This thesis aims to establish the existence and uniqueness of a solution to a nonlinear Goursat problem within the class of quasi-analytic functions of Denjoy-Carleman type, specifically within the set of continuous Denjoy-Carleman functions. The approach involves transforming the integro-differential problem into a fixed-point problem, applied to a closed ball in a Banach algebra defined by a formal series and a suitably chosen logarithmically convex