Boundedness Of Solutions For Several Classes Of Nonlinear Differential Equations

With the rapid development of science and technology,there appear a large number of problems related to nonlinear differential equations in the practical problems of the field of mathematics,physics,biology and other subjects.In recent decades,the problem of nonlinear differential equation had huge development,and its theories and methods are becoming more and more mature.And the boundedness problem of differential equations is a very important branch in the theory of ordinary differential equations,which was first put forward in the study of problems of biology,ecology,physics and neural network,and had profound physical background and mathematical models.Although we can't find out the exact solutions of most of the differential equations,we can make estimations of solutions of equations by taking advantage of appropriate integral inequalities and Liapunov functions,and then prove the existence and uniqueness of solutions,boundedness and stability and other qualitative properties.This theory has made rapid development and extensive attention.The thesis is divided into four chapters according to the contents.Chapter 1 Introduction,introducing the main problems and its background of this thesis.Chapter 2 The boundedness of solutions of a class of third order nonlinear differential equations.Chapter 3 In this part,the type of equations in the second part were generalized to norder,and then we got the boundedness of solutions of this type of norder nonlinear differential equations.Chapter 4 In this part,we will use a modified Liapunov function to study the boundedness and the uniform ultimate boundedness of a class of third order nonlinear differential equations.