Abstract

 In differential equations, one of the cornerstones of most theorems and their framework (hypotheses) is the existence and uniqueness theorem. We consider theorems that guarantee the existence and uniqueness of solutions of differential equations. We consider the Carathedory theorem, Peano existence theorem, PicardLinderlof existence and uniqueness theorem, Brower and Schauder fixed point theorems. Picard successive approximation method is applied to establish the existence and uniqueness of solution to some initial value problems. Moreover, the conditions for the continuation of solutions from a given interval to an extended interval are also derived for ordinary differential equations.