【摘要】：隨著科學(xué)技術(shù)的發(fā)展,奇異橢圓邊值問題和非局部橢圓邊值問題具有越來越廣泛的應(yīng)用背景和深刻的數(shù)學(xué)意義,它們已經(jīng)成為數(shù)學(xué)工作者和其他科學(xué)工作者關(guān)心的重要問題.本文對給定的奇異橢圓邊值問題和非局部橢圓邊值問題給出研究,全文共分為三章.第一章,在引言中介紹主要的研究背景和研究結(jié)果,并且給出本篇文章討論時(shí)所需的預(yù)備知識.第二章考慮奇異橢圓邊值問題其中Ω為RN,N ≥ 2中帶有C2,β邊界(?)Ω的有界區(qū)域,γ 0,β∈(0,1)以及λ 0為實(shí)參數(shù).f滿足如下條件:(f1) f:R+ → R為連續(xù)函數(shù);(f2) s-1f(s)關(guān)于s 0嚴(yán)格單調(diào)遞增;(f3)f:R+→R嚴(yán)格單調(diào)遞增.在第二章中,首先,利用上下解方法得出(1)至少存在一個(gè)正解,并且當(dāng)0 γ 1時(shí),證明出正解唯一.其次,對于0 7 1時(shí)(1)的正解的邊界行為給出討論.最后,在f(u) =up+1 0的假設(shè)下考慮(1)的正解的漸近行為,其中f(u)滿足(f1)-(f3).第三章考慮非局部橢圓邊值問題其中Ω為RN,N ≥ 2中帶有C2,β邊界(?)Ω的有界區(qū)域, ∈R,p 0, β ∈ (0, 1)以及λ 0為實(shí)參數(shù).在第三章中,首先,利用分歧理論得出(2)的正解的分歧結(jié)果.其次,通過一些運(yùn)算討論出b 0時(shí)(2)的正解的先驗(yàn)界和不存在性結(jié)果.最后,利用上下解方法得出(2)至少存在一個(gè)正解,并且當(dāng)≤0時(shí),證明出正解唯一.
[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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