Pseudo Almost Periodic Solutions Of Forced Pendulum Equation

This paper is concerned with the pseudo almost periodic solutions of the forced pendulum equation by the fundamental theory and quality of the pseudo almost periodic functions and Banach contraction mapping principle.Chapter 0 introduces the development and current situation of the almost periodic theory, and the background, the newest results of the forced pendulum equation.In Chapter 1 we study the pseudo almost periodic problems of the forced pendulum equation. First we introduce the fundamental theory and quality of almost periodic and pseudo almost periodic functions, then we study the existence and uniqueness of the pseudo almost periodic solutions of Duffing equation y + cy?λy=p(t).Last we apply the quality of the pseudo almost periodic functions and Banach contraction mapping principle in the pseudo almost periodic solutions of the forced pendulum equation y + cy+asin y=p(t), finding the existence and the uniqueness under the condition y -πL <π2∞.In Chapter 2 we discuss two existences of the pseudo almost periodic solutions. First we introduce some lemmas, then we find the existence and uniqueness in region of the equation (,)1x ( )nax()ftxjnjjn +∑==? , and finding the forced pendulum equation have a pseudo almost periodic solution respect in ????π2 ,π2??? and ???π2 ,32π???.In Chapter 3 we discuss a particular type of pseudo almost periodic equation xg(t )xup(t)dtdx = ?n +λ+. After introduce the fundamental theory of ergodicity, we find the existence of pseudo almost periodic solution of this equation by using Banach contraction mapping principle.