Research On Existence Of Almost Periodic Solutions For Several Kinds Of Systems With Delays And Impulses

As we all know, one of the most important problems in differential equation theory is the research on the properties of the solutions. In the natural sciences and social sciences, such as physics, astrophysics, economics, ecology, engineering and technology, which many problems can be attributed to differential equations of mathematical models. So, study of differential equations on the properties of the solutions has important practical significance. In recent years, the research of almost periodic solutions of differential equations with delays and impulses not only in theory but also in practice get a lot of progress. Many researchers applied their theories to the actual models, such as neural network models, ecological models, contribute to these properties of solutions of the actual models do in-depth understanding.This dissertation separately discuss several types of differential equations with delays and impulsive effects. By means of different research methods, several kinds of the sufficient conditions of the systems existing almost periodic solutions have been obtained, and some examples are explained the feasibility of each chapter. The full text structures are as follows:In Chapter1, we simply introduce the development and basic information of almost periodic solutions, delay differential equations, impulsive differential equations, and the dif-ferential equations which will be investigated in our dissertation, and give the necessary prior knowledge.In Chapter2, by using the contraction mapping fixed point theorem, we mainly discuss the existence of almost periodic solutions for some nonlinear equation with delays and im-pulses, some sufficient conditions are given to the almost periodic solutions of these equations for ensuring their existence under some assumptions.In Chapter3, by using the property of solutions of linear system and the contrac-tion mapping principle, we investigate the existence of almost periodic solutions for high-dimensional impulsive equation with delays, some sufficient conditions are obtained for ex-istence of almost periodic solutions.In Chapter4, we mainly study the existence of almost periodic solutions for forced perturbed differential equations admit an exponential dichotomy, some sufficient conditions are obtained to guarantee the existence of almost periodic solutions. In Chapter5, as this paper’s conclusion, we have carried on the subtotal to the paper and proposed several questions which were worth further studying.