Existence Of Solutions For Some Nonlinear Differtial Equations Boundary Value Problens

Nonlinear functional analysis is an important branch of modem mathematics,it is developed by people in the study of classical and modern physics,medicine,biology etc. Nonlinear functional analysis provides an effect theoretical tool for studying many nonlinear problems.In recent years,the nonlinear functional analysis has become an important tool in the research of nonlinear problems of mathematics,physical,aerospace technology and biological technology.Therefore,the research of nonlinear functional analysis theory has extremely important significance.Some domestic and foreign scholars have done massive work to the nonlinear analysis.L.E.J.Brouwer had established the conception of topological degree for finite dimensional space in 1912.J.Leray and J.Schauder had extended the conception to completely continuous field of Banach space in 1934.Afrer,E.Rothe,M.A.Krasnoselskii, P.H.Rabinowitz,H.Amann,V.Lakshmikantham,K.Deimling had carried on research on topological degree and cone theory.Same well known mathematicians,Zhang Gongqing, Chen Wenyuan,Guo Dajun,Ma Ruyun,Sun Jingxian etc,have great works in various fields of nonlinear functional analysis.This article studies some multi-point boundary value problems by topological degree theory and method of upper and lower solutions.In chapter 1,we introduce the development of nonlinear functional method and the advancement of present stage,give some related conceptions and theorems,finally,we introduce the main work of this master thesis.In chapter 2,via the method of upper and lower solution and the Leray-Schauder theory, we show the existence of triple positive solutions for a kind of second-order three point boundary value problem.In chapter 3,we discuss a kind of second-order four point boundary value problem,via the fixed-point theorem,we obtain the existence of at least three solutions of the four point boundary value problem in the presence of two upper and lower solutions,and estimate the existence regions of the solutions.In chapter 4,we use the maximum principle to discuss the existence of solutions for a kind of four-order singular boundary value problem.