本文選題：微分系統(tǒng) + 差分系統(tǒng)��； 參考：《中國地質(zhì)大學(xué)(北京)》2017年碩士論文

【摘要】：本文研究了兩類微分、差分系統(tǒng)的特征值問題,利用上下解方法和錐上不動點定理給出了這兩類特征值問題正解的存在性結(jié)論,總結(jié)了多解性結(jié)論.第一章,首先介紹了本文的研究背景,然后用兩小節(jié)分別介紹了微分方程和差分方程特征值問題的發(fā)展概況,最后交代了本文的研究內(nèi)容并列出了文中需要用到的基本定義和定理.第二章,考慮了一類帶φ-Laplace算子的非線性微分系統(tǒng)混合邊值問題:其中,φ為單調(diào)增奇函數(shù),φ(u'),φ(v')∈C1((0,1),R).特征值入,μ為非負實數(shù)且不全為0.hi(i = 1,2)∈ C([0,1],R+)且在[0,1]的任意非零測度上不恒為0.f,g是非負的,并且滿足在無窮遠處超線性.文中首先建立了此類邊值問題的上下解定理,給出了正解的存在性結(jié)論,然后利用Guo-Krasnosel'skii不動點定理給出了兩個正解的存在性,得到關(guān)于正解的個數(shù)與特征值的大小關(guān)系.第三章,研究了二階差分系統(tǒng)Dirichlet邊值問題:其中,T1為給定的正整數(shù),△為向前差分算子,△u(k+1)=△u(k+1)-△u(k).特征值λ,μ非負且不全為0,hi:[1,T]Z →(0,+∞),f,g非負且為連續(xù)函數(shù).本文證明了當λ和μ較小時,這類邊值問題正解的存在性,并運用不動點指標理論證明了多個解的存在性.
[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，

本文編號：1751822