Existence and Comparison Theorems for Differential Equations in Banach Spaces
dc.contributor.author | Lakshmikantham, V. | en |
dc.contributor.author | Deimling, K. | en |
dc.date.accessioned | 2010-06-04T13:31:34Z | en |
dc.date.available | 2010-06-04T13:31:34Z | en |
dc.date.issued | 1978-07 | en |
dc.identifier.uri | http://hdl.handle.net/10106/2356 | en |
dc.description.abstract | **Please note that the full text is embargoed** ABSTRACT: In our recent paper [3] we have studied the existence of maximal and minimal solutions to the IVP in a Banach space [see pdf for notation]. (1) [see pdf for notation] where [see pdf for notation] maps [see pdf for notation] into [see pdf for notation], with [see pdf for notation] and [see pdf for notation] a cone. The essential hypotheses have been that [see pdf for notation]f is quasimonotone with respect to [see pdf for notation] and that [see pdf for notation] and [see pdf for notation] have some natural properties. If such extremal solutions exist then it is trivial to prove the usual comparison theorems known from the finite-dimensional case. For example, if [see pdf for notation] is the minimal solution of (1) on some interval [see pdf for notation] and if [see pdf for notation] satisfies [see pdf for notation] and [see pdf for notation] then [see pdf for notation]. In the present paper we shall establish existence and comparison theorems for (1) without the hypothesis that [see pdf for notation] be quasimonotone, but under conditions which have been considered in case [see pdf for notation] in the classical paper of M. Muller [10] in 1926. This is not the first attempt to extend Muller's results to infinite dimensions, since recently P. Volkmann [12] tried to do this. We shall improve the existing results considerably. | en |
dc.language.iso | en_US | en |
dc.publisher | University of Texas at Arlington | en |
dc.relation.ispartofseries | Technical Report;88 | en |
dc.subject | Existence theorems | en |
dc.subject | Comparison theorems | en |
dc.subject | Differential equations | en |
dc.subject | Banach Spaces | en |
dc.subject | Müller | en |
dc.subject.lcsh | Mathematics Research | en |
dc.title | Existence and Comparison Theorems for Differential Equations in Banach Spaces | en |
dc.type | Technical Report | en |
dc.publisher.department | Department of Mathematics | en |