RN上奇异拟线性椭圆问题正解的存在性 Alternative Title Existence of positive solution to a singular quasilinear elliptic problem in RN 柴晓娟 Thesis Advisor 赵培浩 2009-06-03 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 硕士 Keyword 拟线性椭圆方程 上解 奇异非线性 正解 Picone 等式 Abstract 本文研究如下拟线性椭圆问题(1.1)解的存在性与不存在性. 这里g(t) 或f(t) 或二者都在t = 0 点是奇异的, 即当t 趋于0 时, g(t),f(t)趋于无穷. 我们采用区域逼近的方法, 在半径为R 的球内, 使用扰动的方法排除了奇异性, 找到扰动方程在球上的解. 同时我们又找到了原问题的一个有界的上解, 让R趋于无穷, 我们就证明了原问题弱解的存在性. 此外, 我们还通过Picone 等式证明了解的不存在性. 这篇论文的主要结果改进了参考文献[Dragos-Patru Covei, 在RN 中, 拟线性椭圆方程的正解的存在性与逼近行为, Nonlinear Anal. 69 (2008) 2615-2622; J.V.Goncalves, C.A.Santos, 奇异椭圆问题: 存 在性, 不存在性和边界行为, Nonlinear Anal. 66 (2007) 2078-2090] 的相应结果. Other Abstract This paper deals with the existence and nonexistence of entire positive solutions of the quasilinear elliptic equation (1.1). Here either g or f (or both of them) are singular at 0 in the sense that g(t), f(t) tend to infinity as t tend to 0. By using a perturbation method which eliminates the singularity on a ball with radius R and then let R tends to infinity,with the help of the bounded super-solution of the original problem, we obtain the existence of a weak solution of the problem. The main results of this paper improve the corresponding results of [Dragos-Patru Covei, the existence and asymptotic behavior of a positive solution to a quasilinear elliptic problem in RN, Nonlinear Anal. 69 (2008) 2615-2622; J.V.Goncalves, C.A.Santos, Singular elliptic problems: Existence, nonexistence and boundary behavior, Nonlinear Anal. 66 (2007) 2078-2090]. URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/225661 Collection 数学与统计学院 Recommended CitationGB/T 7714 柴晓娟. RN上奇异拟线性椭圆问题正解的存在性[D]. 兰州. 兰州大学,2009.
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