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 | **Please note that the full text is embargoed** 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 |