本文選題：p-laplacian + 偽單調(diào)算子�。� 參考：《大連理工大學(xué)》2016年碩士論文

【摘要】：本文討論下列奇異p-laplacian問(wèn)題的解的存在性及正則性。本文通過(guò)逼近方法得到了逼近解及解的先驗(yàn)估計(jì),然后利用弱收斂方法得到了問(wèn)題(P1)的解。本文共分為四章。第一章緒論,主要介紹了論文的研究背景、已有的工作以及本文研究的主要問(wèn)題及結(jié)果。第二章預(yù)備知識(shí),給出了證明過(guò)程中需要用到的定義、引理及記號(hào)。第三章和第四章為本文的主要結(jié)果及證明。第三章給出了當(dāng)0μCN,p時(shí)問(wèn)題(P1)的解的存在性及正則性。第四章給出了當(dāng)μ0時(shí)問(wèn)題(P1)的解的存在性及正則性。
[Abstract]:In this paper, we discuss the existence and regularity of solutions for the following singular p-laplacian problems. In this paper, a priori estimate of the approximate solution and solution is obtained by means of the approximation method, and then the solution of the problem / P _ 1 is obtained by using the weak convergence method. This paper is divided into four chapters. The first chapter is introduction, mainly introduces the research background, the existing work and the main problems and results of this paper. In the second chapter, the definitions, Lemma and notation are given. The third and fourth chapters are the main results and proofs of this paper. In chapter 3, we give the existence and regularity of the solution of the problem P _ (1) when 0 渭 CNP. In chapter 4, we give the existence and regularity of the solution of the problem P _ 1 when 渭 _ 0.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：O175

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 魏利;段麗凌;Ravi P.Agarwal;;含有廣義p-Laplace算子具混合邊值條件的積分微分方程解的存在唯一性(英文)[J];數(shù)學(xué)雜志;2013年06期

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本文編號(hào)：1789172