| 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
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| Degree Grantor | 兰州大学
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| Place of Conferral | 兰州
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| Degree Name | 硕士
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| Keyword | 拟线性椭圆方程
上解
奇异非线性
正解
Picone 等式
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| 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
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| Language | 中文
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| Document Type | 学位论文
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| Identifier | https://ir.lzu.edu.cn/handle/262010/225661
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| Collection | 数学与统计学院
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Recommended Citation
GB/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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