Liouville-type theorems for a quasilinear elliptic equation of the Hénon-type
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- 作者：Quoc Hung Phan ; Anh Tuan Duong
- 关键词：Primary 35B53 ; 35J62 ; Secondary 35K57 ; 35B33 ; Quasilinear ; Liouville ; type theorem ; Hénon ; typeequation
- 刊名：NoDEA : Nonlinear Differential Equations and Applications
- 出版年：2015
- 出版时间：December 2015
- 年：2015
- 卷：22
- 期：6
- 页码：1817-1829
- 全文大小：533 KB
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29.Tolksdorf P.: Re - 作者单位：Quoc Hung Phan (1)
Anh Tuan Duong (2)
1. Institute of Research and Development, Duy Tan University, Da Nang, Vietnam
2. Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Street, Cau Giay District, Hanoi, Vietnam - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Analysis - 出版者：Birkh盲user Basel
- ISSN：1420-9004
文摘
We consider the Hénon-type quasilinear elliptic equation \({-\Delta_m u=|x|^a u^p}\) where \({\Delta_m u={\rm div}(|\nabla u|^{m-2} \nabla u)}\), m > 1, p > m ?1 and \({a\geq 0}\). We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space \({{\mathbb R}^N}\). We prove the optimal Liouville-type theorem for dimension N < m + 1 and give partial results for higher dimensions. Keywords Quasilinear Liouville-type theorem Hénon-typeequation