Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (2): 357-368.doi: 10.1007/s10473-019-0202-x

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LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS

Phuong LE1, Vu HO2   

  1. 1. Department of Mathematical Economics, Banking University of Ho Chi Minh City, Vietnam;
    2. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam;Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
  • Received:2018-05-30 Revised:2018-11-03 Online:2019-04-25 Published:2019-05-06
  • Contact: Vu HO E-mail:hovu@tdtu.edu.vn
  • Supported by:
    This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.02-2017.307.

Abstract: This paper is devoted to the quasilinear equation

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

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