Oscillation And Forced Oscillation Behavior For Some Kinds Of Solutions For Dynamic Equations With Positive And Negative Coefficients On Time Scales

With the development of modern science and technology, people have proposed a great many problems about differential and difference equations in natural science and social science, and some results are gained. The theory of time scales can unify continuous and discrete cases, which pioneers a new mathematical area. This theory not only unifies differential and difference equations, reveals the essence of continuous and discrete cases, avoids repeat study, but also contains many other cases. The prominent peculiarity of time scales is unification and generalization, so the study of time scales has important significance in theory and application. In addition, theory of dynamic equations on time scales has been and are being proved to be of great importance and potential application as to embranchment of applied mathematic. In application, dynamic equations has a wide base in nature, for instance, epidemic models, neuronal network model and insectile numbers models. Except these applications in biology, the mathematical tool has been used to prove calculational mode about stock market.This paper focuses on the research of oscillation and forced oscillation behavior for first order, second order and high order neutral dynamic equations with positive and negative coefficients on time scales.Firstly, oscillation and forced oscillation behavior for first order neutral dynamic equations with positive and negative coefficients on time scales are studied respectively in this paper. Some sufficient conditions to satisfy oscillations of all solutions of these equations are gained. These results are illustrated by examples.Secondly, this paper considers oscillations of solutions of second neutral dynamic equations with positive and negative coefficients. By employing Riccati technique, some sufficient conditions for oscillations of all solutions and bounded solutions of these equations are established. These results are explained by examples.Finally, discuss oscillation and forced oscillation behavior for high order neutral dynamic equations with positive and negative coefficients on time scales, some sufficient conditions to satisfy oscillation of all bounded solutions of these equations are derived.