Acta Mathematica Scientia

, Volume 39, Issue 2, pp 357–368 | Cite as

Liouville Results for Stable Solutions of Quasilinear Equations with Weights

  • Phuong Le
  • Vu HoEmail author


This paper is devoted to the quasilinear equation
$$\left\{ \begin{gathered}- div\left( {w_1 \left| {\nabla u} \right|^{p - 2} \nabla u} \right) = w_2 f\left( u \right)in\Omega , \hfill \\u = 0on\partial \Omega , \hfill \\ \end{gathered} \right.$$
where p ≥ 2, Ω is a (bounded or unbounded) domain of ℝN, w1,w2 are nonnegative continuous functions and f is an increasing function. We establish a Liouville type theorem for nontrivial stable solutions of the equation under some mild assumptions on Ω, w1, w2 and f, which extends and unifies several results on this topic.

Key words

quasilinear equations stable solutions nonexistence Liouville theorems 

2010 MR Subject Classification

35J92 35J25 35B53 35B35 


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Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.Department of Mathematical EconomicsBanking University of Ho Chi Minh CityHo Chi Minh CityVietnam
  2. 2.Division of Computational Mathematics and Engineering, Institute for Computational ScienceTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Faculty of Mathematics and StatisticsTon Duc Thang UniversityHo Chi Minh CityVietnam

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