Almost Periodic Type Solutions Of Functional Differential Equations

In this dissertation, we investigate three classes of almost periodic type solutions of differential equations:1. Besicovitch almost periodic solutions for a class of second order differential equations involving reflection of the argument; 2. Weighted pseudo almost periodic solutions of differential equations with piecewise constant argument; 3. The separation condition and almost periodic type solutions of hybrid differential equations with piecewise constant arguments.The first chapter is the introduction, which overviews some background of almost periodic type function theory, the research status at home and abroad and then we state some preliminary notes and notions.In the second chapter, we are concerned with the existence and uniqueness of Besicovitch almost periodic solutions for the second order differential equations.Firstly we obtain the corresponding linear unique almost periodic solutions by using construction method, generalized Fourier series expansion and coefficients method. Then prove the existence and uniqueness of almost periodic solution for the nonlinear equation by fixed point method.In the third chapter, we study the existence and uniqueness of weighted pseudo almost periodic solutions of differential equations with piecewise constant argument.Through introducing the new concepts of weighted pseudo almost periodic vector sequence, combined with pseudo almost periodic functions uniqueness of decomposition, corresponding linear equations to the weighted pseudo almost solution can be first obtained. Then prove the existence and uniqueness of weighted pseudo almost periodic solution for the nonlinear equation by fixed point method.In the fourth chapter, we investigate the existence and module containment of almost periodic solutions of differential equations with piecewise constant arguments under the separation condition.We study the influence of separation condition to the existence and module containment of almost periodic solution of relevant difference equations, and use the result to prove the existence and module containment of almost periodic solutions of hybrid differential equations with piecewise constant arguments. We also discuss the existence and module containment of almost automorphic solutions without Favard condition.