Oscillation And Nonoscillation Of Delay Dynamic Equations On A Measure Chain

The theory of measure chains has been received a lot of attentions since Stefan Hilger introduced it in his Ph.D. in 1988. But studies on nonlinear equations and high order equations is quite fewer on measure chains. In this article, we mainly discuss the oscillation and nonoscillation of delay dynamic equations on measure chains.. The article is composed of four chapters .Chapter one,we give a brief introduction to the measure chains. Chapter two ,we consider the oscillation and nonoscillation of two first order dynamic equations on measure chains. Chapter three, we mainly consider the second order quasilinear dynamic on measure chains,and obtain some sufficient and sufficient and necessary conditions for nonoscillatory solutions existence.Chapter four,we mainly study the existence and their asymptotic behavior of nonoscillatory solution for four order quasi-linear dynamic equation.