Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents

Authors:	N Ghoussoub C Yuan

Institution:	Department of Mathematics, The University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada C. Yuan ; Department of Mathematics, The University of British Columbia, Vancouver, B.C. V6T 1Z2, Canada

Abstract:	We use variational methods to study the existence and multiplicity of solutions for the following quasi-linear partial differential equation: $\left\{ \begin{matrix} {-\triangle_{p} u = \lambda \vert u\vert^{r-2}u + \mu ... ... }, {}} {\hphantom{-} u\vert _{\partial \Omega} = 0, } \end{matrix}\right.$ where $\lambda$ and $\mu$ are two positive parameters and $\Omega$ is a smooth bounded domain in $\mathbf{R}^n$ containing in its interior. The variational approach requires that , $p\leq q\leq p^{}(s)\equiv \frac{n-s}{n-p}p$ and $p\leq r\leq p^\equiv p^(0)=\frac{np}{n-p}$ , which we assume throughout. However, the situations differ widely with and , and the interesting cases occur either at the critical Sobolev exponent () or in the Hardy-critical setting () or in the more general Hardy-Sobolev setting when $q=\frac{n-s}{n-p}p$ . In these cases some compactness can be restored by establishing Palais-Smale type conditions around appropriately chosen dual sets*. Many of the results are new even in the case , especially those corresponding to singularities (i.e., when $0<s\leq p)$ .

Keywords:

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文

设为首页 | 免责声明 | 关于勤云 | 加入收藏