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Maximal and Minimal Solutions and Comparison Results for Differential Equations in Abstract Cones

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Maximal and Minimal Solutions and Comparison Results for Differential Equations in Abstract Cones

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dc.contributor.author Lakshmikantham, V. en
dc.contributor.author Mitchell, Roger W. en
dc.contributor.author Mitchell, A. Richard en
dc.date.accessioned 2010-05-26T15:53:26Z en
dc.date.available 2010-05-26T15:53:26Z en
dc.date.issued 1974-04 en
dc.identifier.uri http://hdl.handle.net/10106/2177 en
dc.description.abstract As is well known, an important technique in the theory of differential equations is concerned with estimating a function satisfying a differential inequality by means of the extremal solutions of the corresponding differential equation. This comparison principle has been widely employed in studying the qualitative theory of differential equations (see [3]). If we desire to develop a similar comparison result in abstract spaces we must consider cones. These results could be of great value in applications to the theory of differential equations in abstract spaces. First, we must consider existence results for maximal and minimal solutions in cones which can then be utilized to prove comparison results. This approach would unify various comparison theorems for scalar, finite, and infinite systems of differential equations. Naturally the notion of quasimonotone functions must be introduced for abstract spaces. In this paper, employing the properties of abstract cones and the Kuratowski measure of non-compactness of a set, we prove existence of extremal solutions, discuss comparison theorems and, as an application of the comparison technique, consider a general uniqueness theorem. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;10 en
dc.subject Differential equations en
dc.subject Differential inequality en
dc.subject Abstract spaces en
dc.subject Quasimonotone functions en
dc.subject.lcsh Mathematics Research en
dc.title Maximal and Minimal Solutions and Comparison Results for Differential Equations in Abstract Cones en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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