Systems by the Method of Quasisolutions

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Systems by the Method of Quasisolutions

Show simple item record Vatsala, A. S. en Lakshmikantham, V. en 2010-06-09T14:20:15Z en 2010-06-09T14:20:15Z en 1981-01 en
dc.identifier.uri en
dc.description.abstract Recently [10] the method of lower and upper solutions has been extended to systems of reaction diffusion equations which has become very useful in dealing with applications. This extension depends crucially on a certain property known as quasimonotone nondecreasing property [8] without which the results fail under natural definition of lower and upper solutions. When the quasimonotone property does not hold but a certain mixed quasimonotone property is satisfied, which is the case in several applications [7], the method of quasisolutions is more suitable [2,4,6,9]. All these results utilize monotone iterative technique. When no monotone condition holds one can also get just existence results [5] assuming Müller's type of lower and upper solutions. However in this case monotone technique fails. In this paper, we discuss the asymptotic stability of the stationary solution of reaction-diffusion systems. We employ the method of quasisolutions and monotone technique. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;145 en
dc.subject Quasimonotone nondecreasing property en
dc.subject Lower and upper solutions en
dc.subject Method of quasisolutions en
dc.subject Monotone technique en
dc.subject Asymptotic stability en
dc.subject.lcsh Mathematics Research en
dc.title Systems by the Method of Quasisolutions en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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