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Existence of Extremal Solutions and Comparison Results for Delay Differential Equations in Abstract Cones

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Existence of Extremal Solutions and Comparison Results for Delay Differential Equations in Abstract Cones

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dc.contributor.author Laughn, R. L. en
dc.contributor.author Vatsala, A. S. en
dc.date.accessioned 2010-06-01T18:51:59Z en
dc.date.available 2010-06-01T18:51:59Z en
dc.date.issued 1979-10 en
dc.identifier.uri http://hdl.handle.net/10106/2206 en
dc.description.abstract The study of Cauchy problem for ordinary differential equations in a Banach space has been extensive [2,4,10]. It is of interest to look at the corresponding problem for delay differential equations since such equations occur in many physical problems. Existence of solutions of such equations are considered in [6,8,9] using monotonicity conditions and dissipative conditions.In this paper our objective is to prove the existence of extremal solutions for the delay differential equation [see pdf for notation] (1.1) relative to a cone k of the Banach space E. For this purpose, we begin by proving an existence result under a simple set of conditions without assuming uniform continuity on f we then develop needed theory of differential inequalities and utilize this to show the existence of extremal solutions for (1.1) Several useful comparison theorems are then proved including a flow invariance result. Our results generalize some of the recent results for equations without delay [5,7]. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;114 en
dc.subject Extremal solutions en
dc.subject Banach space E en
dc.subject Cone k en
dc.subject.lcsh Delay differential equations en
dc.subject.lcsh Mathematics Research en
dc.title Existence of Extremal Solutions and Comparison Results for Delay Differential Equations in Abstract Cones en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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