Asymptomatic Behavior For A Class Of High Order Functional Differential Equations

Differential equations have a wide range of applications in physics,mechanics,biology,engineering,economics and many other fields.the oscillation of differential equations is a very important branch in differential equation stability theory.In recent years,many scholars do the research and exploration in the oscillation of differential equations,improvement and existing some conclusions,What they have done there is an important meaning in theory,also have practical value.In this dissertation,we employ Philos integral average technique,a generalized Ric-cati transformation,Algebraic inequality to investigate the oscillation problems for two classes of higher-order nonlinear differential equations.We obtain some meaningfully new results.In chapter 1,we mainly introduce the background and development for the oscil-lation theory of differential equations.In chapter 2,we introduce the definition of the oscillation of functional differential equations,and the important theorems and inequalities.In chapter 3,we mainly discuss the n-order nonlinear neutral functional differential equationsthe oscillation criteria will be given in case of ??1,(?),we obtained three oscillation criteria,and further promote the conclusions in existing literature.In chapter 4,we mainly elaborate the n-order neutral functional differential equa-tionssome new oscillation theorems will be given in the case of ?=1,(?),we obtained four oscillation criteria,and improves the result in existing literature.