Almost Periodic Solutions And Periodic Solutions For Several Kinds Of Functional Differential Equations

In this dissertation, the existence of almost periodic solutions and periodic solutions for several kinds of functional differential equations are investigated. This dissertation is organized by four parts.In Chapter 1, we simply introduce the development of almost periodic solutions and periodic solutions and the motivation of this paper.In Chapter 2, By means of bounded and asymptotic almost periodicity, the existence of positive almost periodic solutions for the following functional-differential equations with a parameterx'(t) = x(t)[a(t)g(x(t)) - λf(t, x(t - Ï„₁(t)),x(t - Ï„₂(t)), ???,x(t- Ï„_n(t)))], (2.1.1)was investigated. Especially, the results obtained are also applied to population dynamics models, some sufficient conditions of the existence positive almost periodic solutions for the systems are obtained. We make the hypothesis that(h2.1) a(t) and Ï„_j(t)(1 ≤ i ≤n) are continuous real almost periodic functions on R, the derivative of Ï„_j(t)(1 ≤ i ≤ n) is boundary; f(t, u) is a non-negative continuous real almost periodic function in t uniformly on u; g(x) is a boundary continuous function; parameter λ > 0;is constant. The main results are thatTheorem 2.2.1 Suppose that (h2.1)-(h2.4) hold, A is a positive constant, then (2.1.1), (2.1.6) has a positive almost periodic solution at least.Theorem 2.2.2 Suppose that (h2.1)-(2.2),(h2.5)-(h2.8) hold, then (2.1.1), (2.1.6) has a positive almost periodic solution least.Theorem 2.2.3 Suppose that λ = 1, and (h2.1)-(2.2),(h2.9)-(h2.10) hold, then (2.1.1), (2.1.6) has a positive almost periodic solution at least.