Oscillatory Behavior And Asymptotic Behavior Of Several Classes Of Functional Differential Equations

The focus of this thesis is to study the oscillation and asymptotic behavior of several classes of functional differential equations (FDEs). Some new results are derived by using the qualitative theory of FDEs, together with the essential relationship between solutions and coefficients and the derivation variables of the given equations. This thesis is organ iced as follows.In Chapter One. we briefly address the background and history of differential equations, and then summarize the main results of this thesis.In Chapter Two, we employ new methods and analytical techniques, to generalize some existing results to much more oftener FDEs. By means of the relationship between the delay and coefficients of the equation, we obtain some sufficient criteria ensuring the oscillation of FDEs.By virtue of analytical techniques and comparison theorem as well, Chapter Three is devoted to two issues: one is the oscillation of a class of FDE with variable coefficients, the other is the oscillation and asymptotic behavior of bounded solutions of linear delay differential equations with forced terms and variable coefficients.In Chapter Four, by employing Schauder’ fixed point theorem, we first linearize a class of nonlinear FDE with variable coefficients, then relate it to some relevant linear FDEs, and finally obtain some new oscillation criteria.Based on the qualitative theory of FDEs and Bananch’ Contraction mapping principle, combined with some analytical techniques, the subject of chapter Five is two-fold: one is the oscillation and asymptotic behavior of a first-order neutral FDE, the other is the existence of no oscillatory solutions of a high-order neutral FDE with variable coefficients, obtaining both sufficient conditions of the equations with nonconciliatory solution and three corollaries.