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Existence and Asymptotic Behavior of Reaction-Diffusion Systems Via Coupled Quasi-Solutions

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Existence and Asymptotic Behavior of Reaction-Diffusion Systems Via Coupled Quasi-Solutions

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dc.contributor.author Ladde, G. S. en
dc.contributor.author Vatsala, A. S. en
dc.contributor.author Lakshmikantham, V. en
dc.date.accessioned 2010-06-02T20:37:26Z en
dc.date.available 2010-06-02T20:37:26Z en
dc.date.issued 1980-08 en
dc.identifier.uri http://hdl.handle.net/10106/2248 en
dc.description.abstract In the study of comparison theorems, existence of extremal solutions and monotone iterative techniques for differential systems a property called quasimonotone property is necessary [2,7,10]. However, there are several physical situations wherein such a property is not satisfied [1]. This difficulty has been overcome by introducing the notion of quasi-solutions [3,8,9]. In this paper we consider the reaction-diffusion system in which quasi-monotone property is not satisfied but a mixed quasimonotone property holds. By utilizing fruitfully the notion of quasi-solutions we prove the existence of coupled maximal and minimal solutions. For this purpose we exploit the monotone iterative technique. We then offer methods of constructing explicit coupled upper and lower solutions from which we deduce the asymptotic behaviour of solutions. Our results are in the spirit of similar results given in [1,5,10] and shed much light on the whole situation. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;138 en
dc.subject Comparison theorems en
dc.subject Quasi-solutions en
dc.subject Quasimonotone property en
dc.subject Monotone iterative technique en
dc.subject.lcsh Mathematics Research en
dc.title Existence and Asymptotic Behavior of Reaction-Diffusion Systems Via Coupled Quasi-Solutions en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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