Some Problems In The Theory Of Differential Equations With Fixed Impulsive On The Half-line

This thesis is divided into two chapters. In the first chapter , we study impulsive founctional differential system as followwhere LThe theory of impulsive differential equations is a new important branch of differential equations. The theory can also be applied to medicine and biology, optimal control models in economics, the dynamical system and other fields.Using the theory of Arzela-Ascoli , we firstly study the exsistence properties of a nonsingular boundary value problem. Then the exsistence properties of the singular boundary value problem is obtained by means of the monotone iterative technique. And an example is given to illustrate the application of the theorems.In the second chapter, we study neutral impulsive founctional differential system as followwhere A Suppose [J,R], and hi is strictly increasing, gju is increasing,The theory of functional differential equations describles the phenomena of things and reveals the objective laws govering the development of things more precisely than the corresponding the theory of differential equations with delay effects. These equations derive from biology, engineering, optimal control models in economics, economical mathematics and so on. The theory of functional differential equations has been widely studied for more than thirty years.By the Darbo theory in nonlinear analysis , the asymptotic properties of positive solutions of nonlinear neutral impulsive functional differential equations are classified in detail , some sufficient conditions of the existence of positive solutions of system (2.2.1) are given. At last we give two examples to illustrate the application of the theorems.