Asymptotic Analysis of Solutions of Higher Order Differential Equations and Higher Order Difference Equations

Abstract

The periodicity and vibration of the almost periodic solutions of difference equations and higher-order differential equations are also helpful to the establishment of today's ecological mathematical models, which have made important theoretical contributions to the analysis and discussion of the current severe environmental problems and achieved rich academic achievements. The boundedness of solutions of higher-order differential equations was first proposed in the study of biology, ecology, physiology, physics and neural networks, and it is a very important field in the study of differential equations. Difference equation is also called discrete dynamical system, and it is a powerful mathematical tool in the fields of science, technology and economy. It is one of the important means to study higher-order differential equations. Based on the relevant theoretical knowledge of difference equations and higher-order differential equations, under the premise of exponential dichotomy, using the definition and basic properties of asymptotic almost periodic sequence and the principle of contractive mapping, this paper proves the existence of asymptotic almost periodic solutions for a class of Quasilinear Difference Equations.