The Lipschitz K(t) – Function for the Initial Value Problem (i.v.p) of an Ordinary Differential Equation (o.d.e) in One Dimension

Abstract

An elaborate but brief proof of the existence and uniqueness of the solution of an i.v.p for an o.d.e. is given. Because in both proofs the same initial condition is used, a considerable simplification of the K(t) Lipschitz function takes place. If the solution of the o.d.e. is known then the maximum interval of existence of the o.d.e. can be found again.