Existence theorems for differential equations on Banach spaces

Date

1968

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

In this paper the local existence and uniqueness of solutions to differential equations on Banach spaces are proved for vector fields satisfying Lipschitz conditions. Some applications to classical theorems are given. Continuation of solutions and uniqueness of solutions on larger domains is studied using techniques involving approximate solutions. The final theorem combines the other results to prove that differential equations corresponding to time-dependent vector fields of class C[raised p], p > 1, have local solutions which are locally C[raised p] functions of time and initial conditions.

Description

Keywords

Citation