The Integrating Factor Method in Banach Spaces

Abstract

The so called integrating factor method, used to find solutions of ordinary differential equations of a certain type, is well known. In this article, we extend it to equations with values in a Banach space. Besides being of interest in itself, this extension will give us the opportunity to touch on a few topics that are not usually found in the relevant literature. Our presentation includes various illustrations of our results.

Keywords

• Banach spaces
• Cauchy-Riemann integral
• Exponential function