ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

Abstract

This project work is mainly concerned with the question of the existence and unique ness solution of the IVP in linear first order ODE’s in Banach space.That is dy dx = f(x, y), y(x0) = y0,where f is Lipschitz continuous function.So that to show the exis tence and uniqueness solution of IVP of ODE’s we will use Picard’s Theorem and iter ation method.Firstly, state and prove Banach-Cacciopoli theorem that has been applied to prove the Picard’s Existence and Uniqueness Theorem.This theorem also provides a constructive procedures(called iteration) by which to get a better approximation to the solution of ODE.