<abstract xmlns="http://www.w3.org/1999/xhtml"><p> In this article, we describe the differential equations on functions from R into real Banach space. The descriptions are based on the article [20]. As preliminary to the proof of these theorems, we proved some properties of differentiable functions on real normed space. For the proof we referred to descriptions and theorems in the article [21] and the article [32]. And applying the theorems of Riemann integral introduced in the article [22], we proved the ordinary differential equations on real Banach space. We referred to the methods of proof in [30].</p></abstract>

In this article, we describe the differential equations on functions from R into real Banach space. The descriptions are based on the article [20]. As preliminary to the proof of these theorems, we proved some properties of differentiable functions on real normed space. For the proof we referred to descriptions and theorems in the article [21] and the article [32]. And applying the theorems of Riemann integral introduced in the article [22], we proved the ordinary differential equations on real Banach space. We referred to the methods of proof in [30].

Differential Equations on Functions from R into Real Banach Space

Gifu National College of Technology Gifu, Japan

Formalized Mathematics

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

{"article-title":"Differential Equations on Functions from R into Real Banach Space"}

In this article, we describe the differential equations on functions from R into real Banach space. The descriptions are based on the article [20]. As...

Differential Equations on Functions from R into Real Banach Space

Published Online: Dec 27, 2013

Page range: 261 - 272

Received: Dec 31, 2013

DOI: https://doi.org/10.2478/forma-2013-0028

Keywords
formalization of differential equations

© by Keiko Narita

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Differential Equations on Functions from R into Real Banach Space

Published Online: Dec 27, 2013

Page range: 261 - 272

Received: Dec 31, 2013

DOI: https://doi.org/10.2478/forma-2013-0028

Keywordsformalization of differential equations

© by Keiko Narita

This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0)

Keywords
formalization of differential equations