Differential equations with positive evolutions and some applications (Q860140)

The authors present some basic properties of finite dimensional ordered vector spaces, introduce positive equations and provide some characterizations for their generators. The fourth section of the paper is concerned with exponential stability of positive solutions and to Lyapunov type theorems. After that, the authors obtain some characterizations for uniform observability and deduce a robustness theorem for positive evolutions with respect to positive perturbations of their generators. Finally, they apply their main results to the study of the qualitative properties of differential Riccati equations, arising in game theory.