非线性微差分系统特征值问题

发布时间：2018-04-15 01:08

  本文选题：微分系统 + 差分系统　； 参考：《中国地质大学(北京)》2017年硕士论文

【摘要】：本文研究了两类微分、差分系统的特征值问题,利用上下解方法和锥上不动点定理给出了这两类特征值问题正解的存在性结论,总结了多解性结论.第一章,首先介绍了本文的研究背景,然后用两小节分别介绍了微分方程和差分方程特征值问题的发展概况,最后交代了本文的研究内容并列出了文中需要用到的基本定义和定理.第二章,考虑了一类带φ-Laplace算子的非线性微分系统混合边值问题:其中,φ为单调增奇函数,φ(u'),φ(v')∈C1((0,1),R).特征值入,μ为非负实数且不全为0.hi(i = 1,2)∈ C([0,1],R+)且在[0,1]的任意非零测度上不恒为0.f,g是非负的,并且满足在无穷远处超线性.文中首先建立了此类边值问题的上下解定理,给出了正解的存在性结论,然后利用Guo-Krasnosel'skii不动点定理给出了两个正解的存在性,得到关于正解的个数与特征值的大小关系.第三章,研究了二阶差分系统Dirichlet边值问题:其中,T1为给定的正整数,△为向前差分算子,△u(k+1)=△u(k+1)-△u(k).特征值λ,μ非负且不全为0,hi:[1,T]Z →(0,+∞),f,g非负且为连续函数.本文证明了当λ和μ较小时,这类边值问题正解的存在性,并运用不动点指标理论证明了多个解的存在性.
[Abstract]:In this paper, we study the eigenvalue problems of two kinds of differential and difference systems. By using the upper and lower solution method and the fixed point theorem on the cone, we obtain the existence of positive solutions for these two kinds of eigenvalue problems, and summarize the conclusions of multiple solutions.In the first chapter, the background of this paper is introduced, and then the development of eigenvalue problems of differential equation and difference equation is introduced in two sections.In the end, the basic definitions and theorems that need to be used in this paper are given.In chapter 2, we consider a class of mixed boundary value problems for nonlinear differential systems with 蠁 -Laplace operator, where 蠁 is a monotone increasing odd function, and 蠁 is a monotone increasing odd function.The eigenvalue 渭 is a nonnegative real number and not all 0.hi(i = 1n ~ 2) 鈭，

本文编号：1751822