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Asymptotic Equilibrium of Ordinary Differential Systems in a Banach Space

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Asymptotic Equilibrium of Ordinary Differential Systems in a Banach Space

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dc.contributor.author Mitchell, Roger W. en
dc.contributor.author Mitchell, A. Richard en
dc.date.accessioned 2010-05-26T15:45:18Z en
dc.date.available 2010-05-26T15:45:18Z en
dc.date.issued 1974-03 en
dc.identifier.uri http://hdl.handle.net/10106/2174 en
dc.description.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]). en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;7 en
dc.subject Asymptotic equilibrium en
dc.subject Differential system en
dc.subject Banach spaces en
dc.subject Measure of non-compactness en
dc.subject.lcsh Mathematics Research en
dc.title Asymptotic Equilibrium of Ordinary Differential Systems in a Banach Space en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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