Document Type


Source Publication Title

Technical Report 10


As is well known, an important technique in the theory of differential equations is concerned with estimating a function satisfying a differential inequality by means of the extremal solutions of the corresponding differential equation. This comparison principle has been widely employed in studying the qualitative theory of differential equations (see [3]). If we desire to develop a similar comparison result in abstract spaces we must consider cones. These results could be of great value in applications to the theory of differential equations in abstract spaces. First, we must consider existence results for maximal and minimal solutions in cones which can then be utilized to prove comparison results. This approach would unify various comparison theorems for scalar, finite, and infinite systems of differential equations. Naturally the notion of quasimonotone functions must be introduced for abstract spaces. In this paper, employing the properties of abstract cones and the Kuratowski measure of non-compactness of a set, we prove existence of extremal solutions, discuss comparison theorems and, as an application of the comparison technique, consider a general uniqueness theorem.


Mathematics | Physical Sciences and Mathematics

Publication Date




Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.