兰州大学机构库 >数学与统计学院
一类具有临界非线性项的Kirchhoff问题的可解性
Alternative TitleThe solvability of a class of Kirchhoff problem with critical nonlinearity
崔秀芳
Thesis Advisor赵培浩
2016-05-28
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
KeywordKirchhoff 问题 Sobolev 临界指数 集中紧性 山路引理
Abstract本文将在带有光滑边界的有界区域 Omega 中研究问题Kirchhoff 证明了当p=(n-2)/(n+2),λ充分大时,对于任意的包含 C 的凸集 H,存在函数,使得方程存在一个局部的正的能量极小解. 此外, 将上述的问题一般化为 其中,G 为g的原函数.我们证明了当f满足一定条件以及 λ充分大, 方程存在局部的正的极小能量解.
Other AbstractIn this paper, we study the following Kirchhoff problem In the smooth bounded domain . We prove that when p=(n-2)/(n+2) and λ is large enough, for each convex sets C which including H, there is a function such that the above problem has a positive local minimal energy solution. Besides, we extend the above theorem to more general case, we let For each convex sets C include H , then the same conclusion holds true for the following problem When the f satisfied the condition and also has the restrication , when λ is large enough.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224477
Collection数学与统计学院
Recommended Citation
GB/T 7714
崔秀芳. 一类具有临界非线性项的Kirchhoff问题的可解性[D]. 兰州. 兰州大学,2016.
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