一类具有临界非线性项的Kirchhoff问题的可解性

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	一类具有临界非线性项的Kirchhoff问题的可解性
Alternative Title	The 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
Keyword	Kirchhoff 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 Abstract	In 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
Identifier	https://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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