Existence Of Solutions For Singular Boundary Value Problems

Singular boundary value problems (SBVP,for short)have resulted from nuclear physics,gas dynamics,Newtonian fluid machanics, the theorey of boundary layer,non-linear optics and so on.From 1980s such problems have received a great deal of attention by many researchers.Therefore they become a new study field,and there many excellent results.For example,see the results of reference [1-3,5-7,20,27,30].In recent years, many boundary value problems can describe the deformation of an elastic beam equilibrium state and have comprehensive application in elasticity mechanics and engineering physics.Because either the function or the variable itself, which is mathematical model resulted from some important actual problems,may be singular at endpoints,the study of SBVP becomes very active,for example,see[2,3,19,20-23,27-30].So the content that we studied has important theoretical and applicable value.This paper discusses the two-point and m-point singular boundary value problems more generally,and obtains some useful results on the basis of above discussions.There are four chapters in the dissertation.In the first chapter,we deal with positive solutions for m-point boundary-value problems with a one-dimensional P - Laplacian:In the cone ,we give sup-linear and sub-linear conditions,by using fixed-point index theorem,the existence of at least two positive solutions is guaranteed.In the second chapter,we investigates the fourth-order singular boundary value problemWhere f(t,u) maybe singular at t = 0, t = 1, u = 0.by constructing upper and lower solutions ,we not only get the existence of at least one positive solution whenλlarge enough,but also get the existence of at least one positivesolution whenλarbitrary value in (0, +∞) the study of differential equations containing parameters with upper and lower method , the result alway give the scope of the parameters , when the parameter is smaller than this range , solutions exist, at last, an example is worked out to indicate our conditions are reasonable.In the third chapter,we investigates the existence results for nonlinear boundary-value problems with integral boundary conditions in banach spaces:where f(t,u) maybe singular at t = 0, t = 1,u = 0.In this chapter,under certain conditions, by constructing a special cone and using cone compression and expansion fixed point theorem,we obtain an excellent result .Chapter four investigates the second-order impulsive differential equations :by using Schauder fixed-point theorem,we obtained the existence of solution.