Some Specialties of the Solutions of the Differential Equations in Banach Space

Abstract

In this paper we investigate the existence and uniqueness of solution of differential equation in Banach space under condition (1.2). The theorems which we proved had been investigated at first in the papers [Canada, Math. Bull. 2(1) (1959); Canada, Math. Bull. 1(1) (1958); Y.D. Mamedov, The Convergence of Iterations for Differential Equations in Banach Spaces, in: Convergent Methods of Ordinary Differential Equations, Naukova Dumka, Kiev, 1964 (Russian)] by other methods for special case. (C) 2003 Elsevier Inc. All rights reserved.