奇异椭圆边值问题和非局部椭圆边值问题的研究

发布时间：2019-03-05 19:50

【摘要】：随着科学技术的发展,奇异椭圆边值问题和非局部椭圆边值问题具有越来越广泛的应用背景和深刻的数学意义,它们已经成为数学工作者和其他科学工作者关心的重要问题.本文对给定的奇异椭圆边值问题和非局部椭圆边值问题给出研究,全文共分为三章.第一章,在引言中介绍主要的研究背景和研究结果,并且给出本篇文章讨论时所需的预备知识.第二章考虑奇异椭圆边值问题其中Ω为RN,N ≥ 2中带有C2,β边界(?)Ω的有界区域,γ 0,β∈(0,1)以及λ 0为实参数.f满足如下条件:(f1) f:R+ → R为连续函数;(f2) s-1f(s)关于s 0严格单调递增;(f3)f:R+→R严格单调递增.在第二章中,首先,利用上下解方法得出(1)至少存在一个正解,并且当0 γ 1时,证明出正解唯一.其次,对于0 7 1时(1)的正解的边界行为给出讨论.最后,在f(u) =up+1 0的假设下考虑(1)的正解的渐近行为,其中f(u)满足(f1)-(f3).第三章考虑非局部椭圆边值问题其中Ω为RN,N ≥ 2中带有C2,β边界(?)Ω的有界区域, ∈R,p 0, β ∈ (0, 1)以及λ 0为实参数.在第三章中,首先,利用分歧理论得出(2)的正解的分歧结果.其次,通过一些运算讨论出b 0时(2)的正解的先验界和不存在性结果.最后,利用上下解方法得出(2)至少存在一个正解,并且当≤0时,证明出正解唯一.
[Abstract]:With the development of science and technology, singular elliptic boundary value problems and nonlocal elliptic boundary value problems have more and more extensive application background and profound mathematical significance. They have become an important issue of concern to mathematics workers and other scientists. In this paper, the given singular elliptic boundary value problems and nonlocal elliptic boundary value problems are studied. The thesis is divided into three chapters. In the first chapter, the main research background and results are introduced in the introduction, and the preparatory knowledge required in this paper is given. In chapter 2, we consider singular elliptic boundary value problems where 惟 is a bounded domain with C 2, 尾 boundary 惟 in RN,N 鈮，

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