Oscillation Of Several Kinds Of Neutral Differential Equations

Differential equations and difference equations are powerful tools that describe the law of nature, but it is difficult to find their general solutions. Therefore, there has been an increasing interest in the study of the nature of solutions of differential equations and difference equations in theory. This dissertation focuses on two sides: one is the oscillation of differential equations, the other is the oscillation of difference equations. The paper is made up of four chapters. Main contents are as follows:In chapter one, we briefly address the main work of this paper and the back-ground.In the second passage the oscillation of the second order neutral differential equations and are studied. Sufficient conditions for the bounded oscillatory solution are given out, improving and promoting some corresponding results.In the third passage the oscillation for two kinds of the second order nonlin-ear neutral difference equations with several variable delay arguments and variable coefficients and are studied. Oscillation criterions are given out for the equations and the difference operatorâ–³.By introducing some new methods and techniques, in Chapter 4 we get some new oscillation criterions formulated directly in terms of the delay and coefficients for the first order delay difference equation, which intends to improve the existing results of the previous studies.