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Monotone Iterative Technique for Differential Equations in a Banach Space

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Monotone Iterative Technique for Differential Equations in a Banach Space

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dc.contributor.author Lakshmikantham, V. en
dc.contributor.author Du, Sen-Wo en
dc.date.accessioned 2010-06-09T15:12:20Z en
dc.date.available 2010-06-09T15:12:20Z en
dc.date.issued 1981-02 en
dc.identifier.uri http://hdl.handle.net/10106/2427 en
dc.description.abstract Let E be a real Banach space with norm [see pdf for notation]. Consider the initial value problem (1.1) [see pdf for notation], where [see pdf for notation]. Generally speaking of approximate solutions of (1.1) consist of three steps, namely, (i) constructing a sequence of approximate solutions of some kinds for (1.1); (ii) showing the convergence of the constructed sequence; (iii) proving that the limit function is a solution. If f is continous, steps (i) and (iii) are standard and straight forward. It is a step (ii) that deserves attention. This in turn leads to three possibilities; namely to show that the sequence of approximate solutions is (a) a Cauchy sequence; (b) relatively compact so that one can appeal to Ascoli's theorem; and (c) a monotone sequence in a cone. The first two possibilities are well known and are discussed in [2,3]. This paper is devoted to the investigation of (c) which leads to the development of a monotone interative technique in an arbitrary cone. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;150 en
dc.subject Monotone iterative technique en
dc.subject Abstract cones en
dc.subject Banach spaces en
dc.subject Boundary value problems en
dc.subject Differential equations en
dc.subject.lcsh Mathematics Research en
dc.title Monotone Iterative Technique for Differential Equations in a Banach Space en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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