A monotonicity theorem and its applications to weighted elliptic equations

doi:10.1007/s11425-018-9414-8

CSpace

	A monotonicity theorem and its applications to weighted elliptic equations
	Li, Kui 1; Zhang, Zhitao 2,3
	2019-10-01
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
卷号	62 期号:10 页码:1925-1934
摘要	We study the equation w(tt) + Delta(SN-1)w - mu w(t) - delta w + h(t; omega)w(p) = 0, (t; omega) is an element of R x SN-1, and under some conditions we prove a monotonicity theorem for its positive solutions. Applying this monotonicity theorem, we obtain a Liouville-type theorem for some nonlinear elliptic weighted singular equations. Moreover, we obtain the necessary and sufficient condition for -div(vertical bar x vertical bar(theta)del u) = vertical bar x vertical bar(l)u(p), x is an element of R-N\{0} having positive solutions which are bounded near 0, which is also a positive answer to Souplet's conjecture (see Phan and Souplet (2012)) on the weighted Lane-Emden equation -Delta u = vertical bar x vertical bar(a)u(p), x is an element of R-N.
关键词	monotonicity theorem nonlinear elliptic weighted equation Liouville-type theorem
DOI	10.1007/s11425-018-9414-8
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11771428] ; National Natural Science Foundation of China[11331010] ; National Natural Science Foundation of China[11688101] ; National Natural Science Foundation of China[11571339]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000498674000003
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50400
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Zhitao
作者单位	1.Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Li, Kui,Zhang, Zhitao. A monotonicity theorem and its applications to weighted elliptic equations[J]. SCIENCE CHINA-MATHEMATICS,2019,62(10):1925-1934.
APA	Li, Kui,&Zhang, Zhitao.(2019).A monotonicity theorem and its applications to weighted elliptic equations.SCIENCE CHINA-MATHEMATICS,62(10),1925-1934.
MLA	Li, Kui,et al."A monotonicity theorem and its applications to weighted elliptic equations".SCIENCE CHINA-MATHEMATICS 62.10(2019):1925-1934.