Asymptotically Almost Periodic Logistic Equation

In recent years, many scholars had studied the existence of the solution of Logistic equation, and this equation had been discussed when the two important indexes r and k are periodic, almost periodic or asymptotically almost periodic functions (Reference were searched in [1~7]).In this paper, we study the problems of the existence and the character of the asymptotically almost periodic solution of Logistic equation after the review of the basic concepts and main results on almost periodic function. The main work of the paper is summarized as follows.1.Based on the work of Wei Fengying, Wang ke and so on, we obtain the asymptotically almost periodic solution of the following Logistic equation Furthermore, we prove that this solution is uniform stability.2. Based on the work of K.Gopalsamy, we obtain the sufficient conditions of the asymptotically almost periodic solution of the following discrete Logistic equation and we prove that the almost periodic part of this solution is a global attractive almost periodic solution. Furthermore, we prove that this almost periodic solution is local asymptotically stability.