Oscillation Criteria For Higher Order Dynamic Equations On Time Scales

Research for the theory of time scales is not only the needs of the development of mathematics itself but also the needs of the practical prob-lems. The theory of time scales not only combine the theory of differential equations and the theory of difference equations excellently but also is more practical. In this thesis, we mainly study oscillation criteria for sev-eral classes of higher order dynamic equations on time scales.In the first chapter of this thesis, we briefly introduce the historic background, the current situation and some known results of research for the dynamic equations on time scales.In Chapter2, Chapter3, Chapter4, we investigate oscillation for higher order dynamic equations and on time scale T, respectively, and obtain some oscillation criteria for above equations. Where are continuous functions; quotient of two odd positive integers;rk:[to,∞)Tâ†'(0,∞)(1≤k≤functions with to∈T.