A monotonicity theorem and its applications to weighted elliptic equations
文献类型：期刊论文
| 作者 | Li, Kui1; Zhang, Zhitao2,3 |
| 刊名 | SCIENCE CHINA-MATHEMATICS
 |
| 出版日期 | 2019-10-01 |
| 卷号 | 62期号:10页码:1925-1934 |
| 关键词 | monotonicity theorem nonlinear elliptic weighted equation Liouville-type theorem |
| ISSN号 | 1674-7283 |
| DOI | 10.1007/s11425-018-9414-8 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000498674000003 |
| 出版者 | SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50399]  |
| 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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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