Types Of Differential Equations With Impulses Study

The thesis is composed of two parts.The first part is summarize,in which the background of subjects and development ofstudies are summed up simply.We introduce the development of oscillation of impulse dif-ferential equations brieffy.Furthermore,we simply mention the problems that we will discussin the thesis.The second part is the main body of the article.It is divided into four chapters,whichstudy the oscillations of several differential equations with impulses.The chapter two,by using the the oscillatory of linear impulse neutral delay differentialequations is equivalent to that of a kind of nonimpulse neutral differential equation,somesuffcient conditions of the oscillatory of linear impulse neutral delay differential equationsare obtained.In chapter three,by using reduction to absurdity and the impulse differential inequal-ity,we obtain some suffcient conditions for the oscillation of the equation which we discuss.In chapter four,we consider the oscillation of higher order linear ordinary differentialequation with impulses.By establishing some lemmas,we obtain some suffcient conditionsfor the equation.The chapter five,on base of chapter four ,we obtain some suffcient conditions for theequation by using similar means.