Study On Periodic Solution Of Nonlinear Differential Equations

Many questions of differential equation are induced in science and technology fields, such as physics, biology, automatic control, even is put forward in the realm of social sciences. Usually, in fact, we set a mathematical model according to practical problems, i. e. getting a differential equation from the reality, and then we make the best solutions to solve this equation. At last, we use the result to explain the phenomena, so as to attain our purpose to create and improve the world. The nonlinear differential equation, especially the second-order one is paid closed attention, because they relate to wide fields. The existence and uniqueness of the periodic solution of these problems are always one of the central issue of the research. Recently, in the course of research, authors find and work out many solutions. For instance, more high order differential equations are imperfect yet. At present, some authors start to seek methods to the periodic solution of high order equations. In this paper, we use upper-and-lower solution to discuss a class of second order equation of the existence and uniqueness about periodical solution, then we use most times and places to discuss the periodic solution to several classes of high order differential equations, where we adopt several kinds of ways, such as the fixed point theory, Leray-Schauder degree, and homeomorphism.