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Existence and Comparison Theorems for Differential Equations in Banach Spaces

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Existence and Comparison Theorems for Differential Equations in Banach Spaces

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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 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

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