## 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