Liouville type theorem for a singular elliptic equation with finite Morse index

doi:10.1186/s13661-019-1173-5

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	Liouville type theorem for a singular elliptic equation with finite Morse index
	Xiu,Zonghu 1; Zhao,Jing 1; Chen,Jianyi 1; Yang,Hongwei 2
	2019-03-19
发表期刊	Boundary Value Problems
ISSN	1687-2770
卷号	2019 期号:1
摘要	AbstractThis paper considers the nonexistence of solutions for the following singular quasilinear elliptic problem: 0.1{?div(\|x\|?ap\|?u\|p?2?u)=f(\|x\|)\|u\|r?1u,x∈R+N,\|x\|?ap\|?u\|p?2?u?ν=g(\|x\|)\|u\|q?1u,on??R+N,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\begin{aligned} \textstyle\begin{cases} -\operatorname{div} ( \vert x \vert ^{-ap} \vert \nabla u \vert ^{p-2}\nabla u)= f( \vert x \vert ) \vert u \vert ^{r-1}u, \quad x\in {\mathbb {R}} ^{N}_{+}, \\ \vert x \vert ^{-ap} \vert \nabla u \vert ^{p-2}\frac{\partial u}{\partial \nu }=g( \vert x \vert ) \vert u \vert ^{q-1}u, \quad \text{on } \partial {\mathbb {R}} ^{N}_{+}, \end{cases}\displaystyle \end{aligned}$$ \end{document} where R+N={x=(x′,xN)\|x′∈RN?1,xN>0}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\mathbb {R}} ^{N}_{+}=\{x=(x',x_{N})\| x'\in {\mathbb {R}} ^{N-1}, x_{N}>0 \}$\end{document} and ?R+N={x=(x′,xN)\|x′∈RN?1,xN=0}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\partial {\mathbb {R}} ^{N}_{+}=\{x=(x',x_{N})\| x'\in {\mathbb {R}} ^{N-1}, x_{N}=0\}$\end{document}. When the weight functions satisfy some suitable assumptions, we prove that problem (0.1) has no nontrivial bounded solutions with finite Morse index.
关键词	Liouville theorem Morse index Singular elliptic equation
DOI	10.1186/s13661-019-1173-5
语种	英语
WOS记录号	BMC:10.1186/s13661-019-1173-5
出版者	Springer International Publishing
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32528
专题	中国科学院数学与系统科学研究院
通讯作者	Xiu,Zonghu
作者单位	1. 2.
推荐引用方式 GB/T 7714	Xiu,Zonghu,Zhao,Jing,Chen,Jianyi,et al. Liouville type theorem for a singular elliptic equation with finite Morse index[J]. Boundary Value Problems,2019,2019(1).
APA	Xiu,Zonghu,Zhao,Jing,Chen,Jianyi,&Yang,Hongwei.(2019).Liouville type theorem for a singular elliptic equation with finite Morse index.Boundary Value Problems,2019(1).
MLA	Xiu,Zonghu,et al."Liouville type theorem for a singular elliptic equation with finite Morse index".Boundary Value Problems 2019.1(2019).