Liouville property of fractional Lane-Emden equation in general unbounded domain

被引：7

作者：

Wang, Ying ^{[1
]}

Wei, Yuanhong ^{[2
]}

机构：

[1] Jiangxi Normal Univ, Dept Math, Nanchang 330022, Jiangxi, Peoples R China

[2] Jilin Univ, Sch Math, Changchun 130012, Jilin, Peoples R China

来源：

ADVANCES IN NONLINEAR ANALYSIS | 2021年 / 10卷 / 01期

关键词：

Fractional Laplacian; Lane-Emden equation; Nonexistence; ELLIPTIC-EQUATIONS; CLASSIFICATION; LAPLACIAN; THEOREMS;

D O I：

10.1515/anona-2020-0147

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our purpose of this paper is to consider Liouville property for the fractional Lane-Emden equation (-Delta)(alpha)u = u(p) in Omega, u = 0 in R-N \ Omega, where alpha is an element of (0, 1), N >= 1, p > 0 and Omega subset of R-N-(1) x [0, +infinity) is an unbounded domain satisfying that Omega(t) := {x' is an element of RN-1 : (x', t) is an element of Omega} with t >= 0 has increasing monotonicity, that is, Omega(t) subset of Omega(t), for t' >= t. The shape of Omega(infinity):= lim(t ->infinity) Omega(t) in R-N-(1) plays an important role to obtain the nonexistence of positive solutions for the fractional Lane-Emden equation.

引用

页码：494 / 500

页数：7