## Document Type

Report

## Source Publication Title

Technical Report 7

## Abstract

A differential system [see pdf for notation] where [see pdf for notation] has asymptotic equilibrium if 1) for any initial condition [see pdf for notation] the system has a solution [see pdf for notation] existing on and such that [see pdf for notation] exists and is finite, and 2) for any v e B there exists [see pdf for notation] and a solution x(t) of (1)-(2) with [see pdf for notation] Several papers have appeared dealing with asymptotic equilibrium of (1)-(2) when [see pdf for notation], and f is majorized by a scalar function g(t,u) which is monotone in u for each t, [1,3]. However, when B is an arbitrary Banach space additional restrictions must be placed on f, (see [p.161,4; 5]). In [7] a set of sufficient conditions for local existence of solutions of (1)-(2) in an arbitrary Banach space is given. These conditions include the use of the Kuratowski measure of non-compactness of bounded sets, denoted throughout this paper by a (see [2,7]). Since our goal will be to give sufficient conditions for asymptotic equilibrium of (1)-(2) using [see pdf for notation], the first lemma incorporates some known properties of [see pdf for notation] (see [7]).

## Disciplines

Mathematics | Physical Sciences and Mathematics

## Publication Date

3-1-1974

## Language

English

## License

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

## Recommended Citation

Mitchell, Roger W. and Mitchell, A. Richard, "Asymptotic Equilibrium of Ordinary Differential Systems in a Banach Space" (1974). *Mathematics Technical Papers*. 28.

https://mavmatrix.uta.edu/math_technicalpapers/28