The Study About The Almost Periodic Solution Of Differential Equations

In this paper, we investigate certain ordinary differential equations, some sufficient conditions for the existence and uniqueness of the almost periodic solution of these systems are obtained. The thesis is composed of two chapters.In Chapter 1, we consider the almost periodic perturbation systems of the form By using the roughness theory of exponential dichotomies and the contraction mapping principle, some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution and bounded solution of the above systems. Our results generalize those ones of [3,4,7,8,9].[1-4] considered the almost periodic perturbation systems of the form,,By using the contraction mapping principle, some sufficient conditions are obtained for the existence and uniqueness of almost periodic solution and bounded solution of these systems. But, if we generalize to, only using the contraction mapping principle can not guarantee the existence and uniqueness of almost periodic solution. In Chapter 2, the almost periodic Lotka-Volterra model with m-predators and n-preys is considered. By constructing suitable Lyapunov function, some sufficient conditions are obtained for the existence and global attractivity of a unique positive almost periodic solution of this model. Our results generalize those ones of [18,19,23－26]. Examples showthat our criteria are new, general, and easily verifiable.