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On Existence of Extremal Solutions of Differential Equations in Banach Spaces

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On Existence of Extremal Solutions of Differential Equations in Banach Spaces

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dc.contributor.author Lakshmikantham, V. en
dc.contributor.author Deimling, K. en
dc.date.accessioned 2010-06-04T14:34:21Z en
dc.date.available 2010-06-04T14:34:21Z en
dc.date.issued 1978-06 en
dc.identifier.uri http://hdl.handle.net/10106/2367 en
dc.description.abstract Let X be a real Banach space, [see pdf for notation] a cone, [see pdf for notation] and [see pdf for notation] continuous. We look for conditions on X, K and f such that the IVP (1) [see pdf for notation] has a maximal solution [see pdf for notation] and a minimal solution u with respect to the partial ordering induced by K. Contrary to known results, [5,6], we shall not assume that K has interior points, since the standard cones of many infinite dimensional spaces have empty interior. The second essential new feature is that f is supposed to be defined only on K and this demands that the extra conditions on f are required only with respect to points in K, and not on the whole space. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;86 en
dc.subject Existence of minimal solutions en
dc.subject Existence of maximal solutions en
dc.subject.lcsh Banach spaces en
dc.subject.lcsh Differential equations en
dc.subject.lcsh Mathematics Research en
dc.title On Existence of Extremal Solutions of Differential Equations in Banach Spaces en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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