Study On Existence Of Nonoscillatory Solutions Of A Class Of Two-dimensional Systems On Time Scale

Time scale theory perfectly combines the continuous analysis and the discrete analysis,and has been widely used in real life.The study of time scales is helpful to enrich the theoretical content of nonlinear dynamic systems.The existence of nonoscillatory solutions to dynamic equations is an important study in time scales.It has certain theoretical value and practical significance.In this paper,we use some fixed point theorems to research the existence of nonoscillatory solutions of a class of two-dimensional systems of first-order dynamic equations on time scales,and use classification discussion,proof by contradiction and other methods to abtain the necessary and sufficient conditions for the nonoscillation solution of the two-dimensional dynamical systems on S~+and S~-.Meanwhile,we use minimum restrictive conditions to get the sufficient conditions for the nonexistence of nonoscillatory solutions.In chapter 1,we briefly introduce the relevant research background and application prospect of time scale systems.In chapter 2,we mainly introduces some basic concepts,definitions,symbols and related theorems on time scales.In chapter 3,we mainly study the existence of nonoscillatory solutions of a class of two-dimensional dynamical systems in the case of S~+and give some examples to verify the main results.In chapter 4,we mainly consider the existence of nonoscillatory solutions of a class of two-dimensional dynamical systems in the case of S~-and give some examples to verify the main results.In chapter 5,we study the nonexistence of nonoscillatory solutions of a class of two-dimensional dynamical systems.