ON THE UNIQUENESS OF NONNEGATIVE SOLUTIONS OF DIFFERENTIAL INEQUALITIES WITH GRADIENT TERMS ON RIEMANNIAN MANIFOLDS

被引：2

作者：

Sun, Yuhua ^{[1
,2
]}

机构：

[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[2] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2015年 / 14卷 / 05期

关键词：

Riemannian manifolds; volume growth; differential inequalities; POSITIVE SOLUTIONS; LIOUVILLE THEOREMS; NONEXISTENCE;

D O I：

10.3934/cpaa.2015.14.1743

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the uniqueness of nonnegative solutions to the following differential inequality div(A(x)vertical bar del u vertical bar(m-2)del u) + V(x)u(sigma 1) vertical bar del vertical bar u(sigma 2) <= 0, (1) on a noncompact complete Riemannian manifold, where A, V are positive measurable functions, m > 1, and sigma(1), sigma(2) >= 0 are parameters such that sigma(1) + sigma(2) > m - 1 Our purpose is to establish the uniqueness of nonnegative solution to (1) via very natural geometric assumption on volume growth.

引用

页码：1743 / 1757

页数：15

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