Almost periodic differential equations.

Abstract

In this thesis, we will study almost periodic differential equations. The motivation to study such a subject is mainly due to its wide applications. We will focus our attention on the topics of boundedness, almost periodicity, disconjugacy and the non-existence of periodic solutions for the n-body problem. Our main investigation in chapter 1 deals with Bohr almost periodic differential equations. In chapter 2, we will study Stepanov almost periodic differential equations, which is a wider class than Bohr's class and we will give a general Floquet theorem in some special cases. We devote our effort in the last chapter to the special n-body problem-if the configuration remains similar throughout the motion and show some applications of oscillation theory of differential equations to the n-body problem.