Basic Material

Abstract

In this chapter we collect some material which will play a part in the theory to be developed in the subsequent chapters. This background material consists of the existence and uniqueness theorem for initial value problems based on contraction and, associated with this, continuation results and growth estimates. Moreover we shall enumerate some theorems which arise if the system of differential equations has attraction properties. The general form of the equations which we shall study is

$$\dot x = f\left( {t,x; \in } \right)$$

where x and f are vectors, elements of R ⁿ. All quantities used will be real except if explicitly stated otherwise.