LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS

doi:10.1007/s10473-019-0202-x

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 357-368.doi: 10.1007/s10473-019-0202-x

LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS

Phuong LE¹, Vu HO²

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

收稿日期:2018-05-30 修回日期:2018-11-03 出版日期:2019-04-25 发布日期:2019-05-06
通讯作者: Vu HO E-mail:hovu@tdtu.edu.vn
作者简介:Phuong LE,phuongl@buh.edu.vn
基金资助:
This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.02-2017.307.

LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS

Phuong LE¹, Vu HO²

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.

摘要/Abstract

摘要： This paper is devoted to the quasilinear equation

where p ≥ 2, Ω is a (bounded or unbounded) domain of R^N, 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.

关键词: quasilinear equations, stable solutions, nonexistence, Liouville theorems

Abstract: This paper is devoted to the quasilinear equation

where p ≥ 2, Ω is a (bounded or unbounded) domain of R^N, 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

Phuong LE, Vu HO. LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS[J]. 数学物理学报(英文版), 2019, 39(2): 357-368.

Phuong LE, Vu HO. LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS[J]. Acta mathematica scientia,Series B, 2019, 39(2): 357-368.

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LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS

LIOUVILLE RESULTS FOR STABLE SOLUTIONS OF QUASILINEAR EQUATIONS WITH WEIGHTS

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