A Functional Analytic Approach to the Power Series Solutions of an Nonlinear Differential Equations

A functional analytic method was developed by E.K.Ifantis in 1987 to prove that certain non-linear ordinary differential equation (ODEs) have a unique power series solution which converges absolutely in a specified disc of the complex plane. In this thesis, we extended this method to certain systems of two non-linear ordinary differential equations.We then applied the result to an nonlinear differential system and obtained the power series solutions.