Remarks on ordinary differential equations in ordered Banach spaces

This paper contains a unified simple approach to the main theorems on ordinary differential equations in ordered Banach spaces when the positive cone has a nonempty interior. The main features are (i) the inclusion of the case of absolutely continuous functions where the differential inequality holds only a.e.; (ii) the different situation corresponding to weak or strong inequalities in the initial conditions. An application to matrix differential equations yields generalizations of known theorems for matrix Riccati equations, among others.Dedicated to professor E. Hlawka on the occasion of his seventieth birthdayGuest professor at the Mathematisches Institut I, University of Karlsruhe, under auspices of the U.S. Special Program, Alexander von Humboldt-Stiftung.