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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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Title: On Existence of Extremal Solutions of Differential Equations in Banach Spaces
Author: Lakshmikantham, V.; Deimling, K.
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.
URI: http://hdl.handle.net/10106/2367
Date: 1978-06

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