Several Kind Of Nonlocal Boundary Value Problems Is The Existence Of The Solution

Ordinary differential equation of modern mathematics is an important branch ofmodern math, it is the way of studying natural science and social science of something,the basic mathematical theory of studying object and phenomenon movement, evolutionand the change rule of the, society. It is produced in a variety of problems, and it can bewidely applied in geometry, mechanics, physics, electronic technology, automatic control,space, and life science and economic and other fields. Pushed by functional analysistheory and the practical problems, ordinary differential equations boundary value problemof research have been developing rapidly for half a century. As an important branch ofnonlinear differential equation theory, it has been deeply researched by many scholars,and obtained the systemic and profound results.There are abundant in the source of the mechanical and electrical about Ordinarydifferential equations. These practical problems often boils down to the local problems ofordinary differential equations. But because of its inherent difficulty, people have a laterstart on the local problems, especially for the existence of positive solutions of theresearch is to be further studied. Therefore, the study of the ordinary differential equationshas the profound theoretical significance and practical value.This thesis is mainly used the theory of cones, AveryPeterson fixed point theorem, aLeggettWilliams fixed point theorems and superposition theorem of coincidence degreetools,and it studied several boundary value problems for the existence of the solution. Thearticle is divided into four parts, main contents are as follows:Chapter1introduce the the historical background of the expounds differentialequations and the research present situation at home and abroad and the main content ofthis article.Chapter2the theory of application on cone Avery-Peterson fixed point theorem, givethe existence of a infinite interval on integral boundary value problem and applicationexamples are given.Chapter3, by constructing Green function and use stack of coincidence degree theory,given proper conditions to establish a kind of infinite interval f and on the second order msome resonance boundary value problems the existence and uniqueness of the solutioncriterion.Chapter4on condition of the certain growth of in nonlinear term, make use of Leggett-Williams continuation theorem to study the existence of p-Laplacian operatorwith a mixture of second order nonlinear singular boundary value problem.