Nonuniqueness Criteria for Ordinary Differential Equations

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Nonuniqueness Criteria for Ordinary Differential Equations

Show simple item record Samimi, Mansour en 2010-06-09T15:17:08Z en 2010-06-09T15:17:08Z en 1981-10 en
dc.identifier.uri en
dc.description.abstract We consider an initial value problem (1.1) [see pdf for notation] where [see pdf for notation]. Several uniqueness results weaker than a Lipschitz condition are known, see [1,4]. However, results concerning with nonuniqueness criteria are rare. For the case n = 1, a nonuniqueness result was given in [5,6], see also [4]. Very recently the general case was also investigated in [3]. In this paper, we consider nonuniqueness problem from a very general point of view. Our first nonuniqueness result deals with the scalar case which extends the results of [5,6]. It also shows that when the conditions of general uniqueness theorem are violated there results nonuniqueness. We then investigate the general case which demands somewhat different methods, since the techniques employed in the scalar case are not extendable to cover the general situation. Furthermore, our results deal with the case when f is singular at t = 0. That is, f(t,x) blows up in some sense as t -> 0+ and f(0,x) is not defined, see [3]. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;169 en
dc.subject Initial value problem en
dc.subject Nonuniqueness problem en
dc.subject Differential equations en
dc.subject Scalar case en
dc.subject.lcsh Mathematics Research en
dc.title Nonuniqueness Criteria for Ordinary Differential Equations en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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