| Nonlinear functional analysis is an important branch of mathematics, and it canexplain several kinds of natural phenomena. The boundary value problems (BVPs)for nonlinear differential equations arise in a variety of areas of applied mathematics,physics and variational problems of control theory, it is at present one of the mostactive fields in analysis mathematics. Among them, multi-point BVPs come froma lot of branches of applied mathematics and physics, and it is very meaningful inboth practical and theoretical aspects. The present paper employs the cone theory,fixed point theory, topological degree theory and so on, to investigate the existenceof positive solutions to multi-point BVPs of some kinds of nonlinear differentialequations. The results obtained are either new or essentially generalize and improvethe previous relevant ones under weaker conditions.The thesis is divided into three chapters according to contents.In chapter 1, using the Schauder's fixed point and the theory of topological, weconsider the existence of positive solutions for second order three-point nonhomoge-neous BVPHere 0 < t12…< tm< 1 a:(0,1)→[0,∞) is continuous and can be singularat t = 0 or t = 1. Under the situations of impulsion and singularity, this paperwhich without the limitation of sublinear and superlinear is more wide-ranging than[2] and we get two positive solutions of the problem by the theory of fixed index.In Chapter 2, by using the Schauder's fixed point theorem, we study the exis-tence of positive solutions for a class of second order n-point differential nonhomo- geneous BVPHere(A2) a(t)∈C([0,1], [0,∞)), f(t)∈C([0,1], [0,∞)), a(t) (?) 0.It is more widely than (2.1.1) or (2.1.2), and what more, we obtain new results.In Chapter 3, by the theory of fixed point index, we study the existence ofpositive solutions for Strum-Liouville differential BVP with impulseWe obtain two positive solutions at least under some conditions. The thesis popu-larize the result of [22].
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