Research On The Positive Solutions Of BVP And Anti-periodic Solutions For Functional Differential Equations

The functional differential equation is a mathematical model which is extracted from the reality in order to describe the delay phenomenon. It is widely applied to biology, physics, control theory, engineering, and so on. Therefore, it is significant to study the boundary value problem and anti-periodic solutions for functional differential equation. Furthermore, as a new study interesting, the boundary value problem for fractional differential equation has a wide application in many fields as the ones of functional differential equation. Hence, it becomes of great importance to discuss the existence of boundary value problem for fractional differential equation in theory and practice.The main aim of this paper is to study the existence of solutions for the boundary value problem of nonlinear functional differential equation and singular fractional differential equation and anti-periodic problem for high order neutral functional differential equation. Main contents are as follows:In chapter one, we introduce a survey to the development of boundary value problem and anti-periodic problem for nonlinear functional differential equation and fractional differential equation. Main results in this dissertation are summarized.Chapter two is about a boundary value problem for third-order functional differential equation with p - Laplacian. By virtue of Avery-Peterson fixed point theorem and some analysis techniques, we obtain some sufficient conditions for the existence of multiple solutions.In chapter three, by using of a result of coincident degree theory and some analysis techniques, we exam the existence and uniqueness for a class of high-order neutral functional differential equation with distributed delay. In this problem, the neutral term c(t) depends on t which had not been studied in previous works. In addition, the results is concise and easy to be verified.In chapter four, we study the three point boundary value problem of fractional differential equation and obtain some sufficient conditions for the existence of one and multiple solutions of this problem in the case of the nonlinear term is singular.