The Study Of Two Problems For Impulsive Differential Equations

The singular ordinary differential equations arise in the fields of gas dynamics, Newtonian fluid mechanics,nuclear physics,the theory of boundary layer,nonlinear optics and so on.Recently ten years the existence and uniqueness of positive solutions for singular differential equations have been widely studied.The 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.For a long time,the perturbing differential equations have very strong applied settings and so are widely paid attention to.The thesis is divided into two chapters.In the first chapter,we study the existence of positive solutions of Emden-Fowler impulsive singular differential equations.In the second chapter, we study the stability of perturbing differential equations with impulses at variable times.In the first chapter,we study the mixed boundary value problem of impulsive singular differential equationsIn the first chapter,we first give the method of lower and upper solutions for the existence of positive solutions to problem (1.1.1) by means of the fixed point theorem,then obtain a necessary and sufficient condition for the existence of positive solutions of Emden-Fowler impulsive singular boundary value problem by using the method of lower and upper solutions. The main results are:in this chapter,we first give the comparison result of stability of equation(2.2.1),and then obtain a series of stability results.