On Existence and Uniqueness of Solutions for Ordinary Differential Equations in Locally Convex Topological Linear Spaces-Reference-Cited by-同舟云学术

On Existence and Uniqueness of Solutions for Ordinary Differential Equations in Locally Convex Topological Linear Spaces

Published:2023-06-01 Issue:3 Volume:73 Page:737-748
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Ito Manabu¹

Affiliation:

1. , #101, 1-10-20 Hiranokita, Hirano-ku , Osaka JAPAN

Abstract

ABSTRACT This article discusses differential equations in infinite-dimensional spaces. We introduce a general version of the Lipschitz-type continuity criterion without the notion of a distance and prove an existence and uniqueness result for ordinary differential equations in locally convex topological linear spaces. It is shown that remarkable techniques of classical analysis, such as the method of successive approximations, are still adaptable tools in the study of the abstract models.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2023-0054/pdf

Reference14 articles.

1. Arnold, V. I.: Ordinary Differential Equations, Translated from the Russian by Roger Cooke, Second printing of the 1992 edition, Universitext, Springer-Verlag, Berlin, 2006.

2. Coddington, E. A.: An Introduction to Ordinary Differential Equations, Prentice-Hall Mathematics Series Prentice-Hall, Inc., Englewood Cliffs, N.J., 1961.

3. Dibík, J.—Nowak, C.—Siegmund, S.: A general Lipschitz uniqueness criterion for scalar ordinary differential equations, Electron. J. Qual. Theory Differ. Equ. 2014 (2014), Art. No. 34.

4. Dutkiewicz, A.: On the existence of solutions of ordinary differential equations in Banach spaces, Math. Slovaca 65(3) (2015), 573–582.

5. Godunov, A. N.—Durkin, A. P.: Differential equations in linear topological spaces, Vestnik Moskov. Univ. Ser. I Mat. Meh. 24(4) (1969), 39–47 (in Russian).