Oscillation And Asymptotic Behavior Of Solutions For Higher-Order Delay Dynamic Equations On A Measure Chain

The theory of measure chain was introduced by Stefan Hilger in his PhD thesis in 1998, it has been created in order to unify continuous and discrete analysis. Recently, the study of dynamic equations on measure chain has recieved a lot of attention, But few studies consider the oscillation of higher-order dynamic equations on measure chain. In this article, we mainly discuss the asymptotic behavior, existence for nonoscillatory solutions and comparison theorems for oscillation. This article is composed of four charpters. In chapter 1, we introduce the preliminaries of dynamic equations on measure chain. In chapter 2, we utilize the theory of dynamic system on measure chain and obtain a necessary and sufficient condition is given for the asymptotic behavior of solutions of higher-order nonlinear equations. In chapter 3, we get some sufficient conditions for the existence of a nonoscillatory solution of nonlinear neutral delay dynamic equations, furthermore, our results unify and improve some known results of neutral functional differential equations and delay difference equations in the references. In chapter 4, we establish three comparison theorems for the oscillation of higher-order neutral delay dynamic equations.