Several Categories Of The Positive Solutions Of Nonlinear Differential Equation Boundary Value Problem

With the development of science and technology,various non-linear problem has aroused people’s widespread interest day by day,The nonlinear functional analysis is an important branch in nonlinear analysis,because it can explain well Various the natural phenomenon.The boundary value problems of nonlinear differential equations stem from the applied mathematics,the engineering,the biology,the physics,the cybernetics and each kind of application discipline. It is one of most active domains of functional analysis studies at present.In this paper,we use the cone theory and the fixed point theory to study the existence of positive solutions for several kinds of boundary value problems for nonlinear differential equation.The thesis is divided into three chapters according to contents.In Chapter1,we consider the existence of positive solutions for the following singular second-order impulsive differential equations: whereφ:R→R is an increasing homeomorphism and positive homomor-phism,andφ(0)=0,ξi∈(0,1)with0<ξ1<ξ2<…<ξm2<1and??[0,+∞),[0,+∞)),α∈C((0,1),[0,+∞)).tk(k=1,2,...,)are impulsive points with0<t1<f2<…<fk<…<1,and ξi≠tk,i=1,2,...,m-2,k=1,2,...,△u|t=tk denotes the jump of u(t)at t=tk,i.e. where??and??represent the right-hand limit and left-hand limit,respec-tively,of u(t)at t=tk.In Chapter2,we establish the existence of positive solution for systems of second-order singular differential equations:(2.1.1) where?? Riemann-Stieltjes integral with signed measures,????O are constants such that????may be singular at x=0,y=0,i=1,2.In Chapter3,by using a fixed point theorem in a cone,we are concerned with the existelice of positive solutioiis for the following2nth-order singular boundary value problem:(3.1.1) where a?? is Lebesgue integrable,???? is continuous in which?? if n is an odd number??0,and??(-∞，+∞).