Nonoscillatory Study Of A Class Of Dynamical Equations On Time Scales

Time scales refer to non-empty closed subsets of the real number sets.Time scales combine continuous analysis and discrete analysis perfectly.It is a new branch of research in the field of nonlinear dynamic systems with broad application prospects.Time scales not only promote the development of mathematical theory but also work out related practical problems.The s-tudy of nonoscillation solutions of dynamic equations is an important aspect.Its research has extremely important value and significance not only in theory but also in practice.And its research will further enrich the theoretical system of dynamic equations.The paper mainly study the existence of nonoscilla-tion solutions for a class of dynamic equations and some related results are generalized.In chapter 1,it mainly introduces the dynamic equation on time scales as well as the research background and current situation.Some basic concepts,definitions,lemmas,theorems and conclusions for theory of time scales are introduced in chapter 2.In chapter 3,4 and 5,the existence of nonoscillatory solutions for the first-order,second-order and higher-order neutral dynamic equation on a time scale T are studied respectively.And some examples related to the theorem are given.