Existence Of Positive Solutions Multi-Point Boundary Value Problems Of Two Class Of Differential Equations

Nonlinear functional analysis is an important branch of modern analysis mathematics,because it can explain kinds of natural phenomenal, more and more mathematicians aredevoting their time to it.Among them the multi-point boundary value problems arises indifferent fields of applicable mathematics and physics. Because multi-point boundary valueproblems have wide applied background, they have important value. It is at present one ofthe most active fields that is studied in mathematics.The present paper employs the cone theory, fixed point theory and Krasnosel'skii fixedpoint theorem and so on, to investigate the existence of solutions to boundary value problemsof several kinds of multi-point boundary value problems. The obtained results are either newor intrinsically generalize and improve the previous relevant ones under weaker conditions.The thesis is divided into three chapters according to contents. We mainly discuss theexistence of positive solutions for the following two kinds of multi-point boundary value byfixed point theorem.In the first chapter, we introduce the historical background of multi-point boundaryvalue problems, the current research and our work on this field.In the second chapter, by using Krasnosel'skii fixed point theorem, we discuss the ex-istence of positive solutions for a kind of singular multi-point boundary value problems.Thecore of this part is the calculative process of Green Function, the estimating process of up-per and lower bounds to Green Function is of necessity and full of techniques. At the sametime, the method in this paper can also be used to deal with the resonance case, the resultsobtained generalize and improve the corresponding results.At end of the chapter, examplesare presented to illustrate the validity of our results.In the last chapter, we consider triple positive solutions for multi-point boundary valueproblems on infinite intervals.In order to overcome the difficulties of noncompact, a specialBanach space and a cone are introduced so that we can establish some similar inequalities,which guarantee that the functions defined on infinite interval have better properties andthen we can proceed with the Avery-Peterson fixed point theorem.