Remarks on ordinary differential equations in ordered Banach spaces (Q1078745)

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.