A nonlinear elliptic PDE with multiple Hardy-Sobolev critical exponents in RN
A nonlinear elliptic PDE with multiple Hardy-Sobolev critical exponents in RN
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DOI：
10.1016/j.jde.2021.05.027
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发表时间：
2021
影响因子：
2.4
通讯作者：
W. Zou
中科院分区：
文献类型：
--
作者：
X. Zhong;W. Zou
In this paper, we will study the following PDE in $\R^N$ involving multiple Hardy-Sobolev critical exponents:.$$\begin{cases}.\Delta u+\sum_{i=1}^{l}\lambda_i \frac{u^{2^*(s_i)-1}}{|x|^{s_i}}+u^{2^*-1}=0\;\hbox{in}\;\R^N,\\.u\in D_{0}^{1,2}(\R^N),.\end{cases}$$.where $0<s_1<s_2<\cdots<s_l<2, 2^\ast:=\frac{2N}{N-2}, \; 2^\ast(s):=\frac{2(N-s)}{N-2}$ and there exists some $k\in \{1,\cdots,l\}$ such that $\lambda_i>0$ for $1\leq i\leq k$; $\lambda_i<0$ for $k+1\leq i\leq l$. We develop an interesting way to study this class of equations involving mixed sign parameters. We prove the existence of the positive ground state solution. The regularity of the least-energy solution is also investigated.
