Kamenev-type Oscillation Criteria For Neutral Differential Equation

The oscillation criteria for differential equations is an important part of qualitative theory of differential equations. And it originated in the equation x"(t)+q(t)x(t)=0Sturm proposed. After decades, the research of oscillation of differential equations has remarkably improved, and furthermore these results and theories are used in many fields such as physics, chemistry and biology. As a result, we should pay more attention to study the oscillation of differential equations. This paper mainly studies the Kamenev-typc oscillation criteria for neutral differential equations, it is organized as follows:Chapter1introduces the background and main method of the problem researching in this field.Chapter2mainly studies the Kamenev-type oscillation criteria for second order neutral differential equation:(r(t){x(t)+p(t)x(T(t))]’+f(t, x(t), x(σ(t)))=0.Chapter3, based on the chapter2, studies the Kamenev-type oscillation criteria for even order neutral differential equation:(r(t)[x(t)+P(t)x(τ(t))](n-1))1+f(t, x(t),x(σ(t)))=0.