【作者】 金翻霞；

【导师】 孙建平；

【作者基本信息】 兰州理工大学 ， 应用数学， 2011， 硕士

【摘要】 微分方程多点边值问题是非线性分析理论的一个重要分支,它起源于各种不同的应用数学和物理学领域,尤其是在弹性和稳定性理论中有着广泛的应用.特别地,常微分方程非齐次多点边值问题受到了人们的广泛关注,它是目前分析数学中研究最活跃的领域之一.因此,对微分方程非齐次多点边值问题的研究具有重要意义.本硕士论文开展了以下三个方面的研究工作:首先,简述了课题的研究背景及本文的主要工作,并给出了本文用到的预备知识.其次,通过给予非线性项一些限制条件,建立了一类非线性三阶m?点非齐次边值问题解与正解的存在性准则,所用主要工具是Schauder不动点定理.最后,针对一类三阶m?点非齐次边值问题,通过运用Guo-Krasnoselskii不动点定理,在f满足超(次)线性时,给参数适当的取值,得到边值问题单调正解的存在性与不存在性.更多还原

【Abstract】 Multi-point boundary value problems (BVPs for short) of di?erential equationsare an important branch in the theory of nonlinear analysis, which arise in di?erentfields of applied mathematics and physics and have wide applications on elasticityand stability theory. Especially, nonhomogeneous multi-point BVPs of di?erentialequations have received much attention from many authors. At present, it is oneof the most active fields that is studied in analytic mathematics. Therefore, it issignificant to study the nonhomogeneous multi-point BVPs of di?erential equations.This thesis carries out research work in the following three aspects: first, we in-troduce the studying background of this thesis and our main works, and we list somepreliminary knowledge needed in this paper. Second, we discuss a class of nonlinearthird-order m? point BVP. By imposing some conditions on the nonlinear term, weconstruct some existence criteria of solution and positive solution for the third-orderm? point nonhomogeneous BVP. The mail tool used is the Schauder fixed pointtheorem. Finally, aiming at a class of third-order m? point nonhomogeneous BVP,The existence and nonexistence of monotone positive solution are discussed for suit-able parameter when f is superlinear or sublinear by using Guo-Krasnoselskii fixedpoint theorem.更多还原