Nonnegative solutions of a fractional sub-Laplacian differential inequality on Heisenberg group

被引：5

作者：

Liu, Y. ^{[1
]}

Wang, Y. ^{[2
]}

Xiao, J. ^{[3
]}

机构：

[1] Univ Sci & Technol Beijing, Sch Math & Phys, Beijing 100083, Peoples R China

[2] North China Elect Power Univ, Dept Math & Phys, Beijing 102206, Peoples R China

[3] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

来源：

DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 12卷 / 04期

基金：

加拿大自然科学与工程研究理事会; 中国国家自然科学基金; 北京市自然科学基金;

关键词：

LIOUVILLE THEOREMS; POSITIVE SOLUTIONS; NORM INEQUALITIES; EXTENSION PROBLEM; EQUATIONS; SPACES; NONEXISTENCE;

D O I：

10.4310/DPDE.2015.v12.n4.a4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study nonnegative solutions of (dagger) vertical bar g vertical bar(gamma)(Hn) u(p) <= (-Delta(Hn)) (alpha/2) u on H-n, where H-n is the Heisenberg group; vertical bar.vertical bar H-n is the homogeneous norm; Delta(Hn) is the sub-Laplacian; (p, alpha, gamma) is an element of (1, infinity) x (0,2) x [0, (p-1)Q); and Q = 2n + 2 is the homogeneous dimension of Ifin. In particular, we prove that any nonnegative solution of (dagger) is zero if and only if p <= Q+gamma/Q-alpha.

引用

页码：379 / 403

页数：25

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