Positive Operators and Maximum Principles for Ordinary Differential Equations

Paul W. Eloe

Positive Operators and Maximum Principles for Ordinary Differential Equations

Authors

Paul W. Eloe Department of Mathematics, University of Dayton Dayton, Ohio 45469-2316, USA.

Keywords:

Maximum principle, Positive operators, sign properties of Green‘s functions

Abstract

We show an equivalence between a classical maximum principle in differential equations and positive operators on Banach Spaces. Then we shall exhibit many types of boundary value problems for which the maximum principle is valid. Finally, we shall present extended applications of the maximum principle that have arisen with the continued study of the qualitative properties of Green‘s functions.