Liouville theorems for supersolutions of semilinear elliptic equations with drift terms in exterior domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:449

Article

Hara, Takanobu¹ 

[1] Tokyo Metropolitan Univ, Dept Math & Informat Sci, Minami Ohsawa 1-1, Hachioji, Tokyo 1920897, Japan

关键词: Lionville theorem;    Drift terms;    Semilinear equations;    Potential theory;    Fundamental solution;   

DOI  :  10.1016/j.jmaa.2016.10.053

来源: Elsevier

【 摘 要 】

In this paper, we prove nonexistence of positive supersolutions of a semilinear equation -div (A(x)del u) + b(x) center dot del u = f(u) in exterior domains in R-n (n >= 3), where A(x) is bounded and uniformly elliptic, b(x) = O(vertical bar x vertical bar(-1)), div b = 0 and f is a continuous and positive function in (0, infinity) satisfying f(u) similar to u(q) as u -> 0 with q <= n/(n - 2). Furthermore, we investigate general conditions on b and f for nonexistence of positive supersolutions. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free