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Liouville-type theorems for a quasilinear elliptic equation of the Hénon-type

  • Quoc Hung Phan
  • Anh Tuan Duong
Article

Abstract

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 

Mathematics Subject Classification

Primary 35B53 35J62 Secondary 35K57 35B33 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Institute of Research and DevelopmentDuy Tan UniversityDa NangVietnam
  2. 2.Department of MathematicsHanoi National University of EducationCau Giay DistrictVietnam

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