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 dydx =f(x, y), y(x0) = y0,where f is Lipschitz continuous function. So that to show the exist tenceand 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 appliedto prove the Picard’s Existence and Uniqueness Theorem.This theorem also provides aconstructive procedures(called iteration) by which to get a better approximation to thesolution of ODE.