Oscillatory And Asymptotic Behavior Of Solutions Of The General Third-order Differential Equations

The qualitative theory of the ordinary differential equations has always been a popular topic for the national and foreign scholars for quite a long time , and it is also an important behavior of differential equations. With the development of the technology and the study methods, the space of study the solutions oscillation and asymptotic behavior is also developing rapidly. Among all the researches, the second-order differential equations have been studied more deeply and widely, while the study of the third-order differential equations has reached a new height. Even though, not only from the type of the equations, but also from the way of study are all waiting for a further development.The paper first described the widely study of oscillatory and asymptotic behavior of solutions of third-order linear differential equations y '''+p(t )y '+q(t )y =0 . Then make the result oscillatory and asymptotic behavior of solutions of third-order general linear differential equations y '''+p(t )y '+q(t )y =0. and the general third-order differential equations y '''+p(t )y ''+q(t )y '+r(t )y =f(t , y ,y',y'')...