The Almost Periodic Solution And Bounded Solutions Of Differential Equations

This paper consists of two parts: We first study certain almost periodic perturbation systems.By using the exponential dichotomy, its roughness theory and the contraction mapping principle, under some suitable conditions some sufficient conditions for the existence and uniqueness of almost periodic solutions and bounded solutions of these systems are obtained. Our results generalize some known ones of [1-5].In the second part, we study the roughness of generalized exponential dichotomy of linear differential equation and establish two integral inequalities, and under the conditions similar to Coppel ones prove the roughness of generalized exponential dichotomy. Our results generalize Coppel ones. For application, we consider systemand prove the existence and uniqueness of bounded solutions of perturbation equation (4). This result generalizes known ones of [20-22].