A Superlinear Singular Second-Order Three-Point Boundary Value Problem

Singular boundary value problems for nonlinear ordinary differential equations, which arise in a variety of areas such as mechanics, boundary layer theory, diffusion and reaction equations, biology, ect, become an im-potant topic in ordinary equations fields.In this paper, existence theory for at least one positive solution is presented to singular three-point boundary value problemThe singularity may appear at u = 0, t = 0 and the function g may be su-perlinear at u＝∞and change sign. The existence of solutions is obtained via an upper and lower solutions method.The present work is a direct extension of some results in [4] for the singular problem, our technique of proof uses essentially the modified method of upper and lower solutions which we believe is well adapted to this type of problem. We extented the results of two-point boundary value condition to three-point boundary value condition using the modified method of upper and lower solutions in [4] .This thesis is composed of four parts. In the first part, we introduce the historical background of problems which will be investigated and the main promlem studied in this paper, namely superlinear singular second-order three-point boundary value problem. There is a brief summarize of results of this problem in other literatures, and introduction of some basic knowledge and propositions that needed in the proof of the theorem.In the second part, we present our result on upper and lower solutions. In this part, we will using contents and methods from [4] .The third part is our main results, we establish existence principles for superlinear singular second-order three-point boundary value problem. In this part, we will using contents and methods from [4] and [17] . The last part is example, some examples are given to explain the mainresults.