Document Type
Report
Source Publication Title
Technical Report 86
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.
Disciplines
Mathematics | Physical Sciences and Mathematics
Publication Date
6-1-1978
Language
English
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Lakshmikantham, V. and Deimling, K., "On Existence of Extremal Solutions of Differential Equations in Banach Spaces" (1978). Mathematics Technical Papers. 241.
https://mavmatrix.uta.edu/math_technicalpapers/241