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

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• 作者：Takanobu Hara ^{takanobuhara526@gmail.com}
• 关键词：Liouville theorem ; Drift terms ; Semilinear equations ; Potential theory ; Fundamental solution
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：601-618
• 全文大小：395 K
• 卷排序：449

文摘

In this paper, we prove nonexistence of positive supersolutions of a semilinear equation −div(A(x)∇u)+b(x)⋅∇u=f(u) in exterior domains in RnRn (n≥3n≥3), where A(x)A(x) is bounded and uniformly elliptic, b(x)=O(|x|−1)b(x)=O(|x|−1), divb=0 and f   is a continuous and positive function in (0,∞)(0,∞) satisfying f(u)∼uqf(u)∼uq as u→0u→0 with q≤n/(n−2)q≤n/(n−2). Furthermore, we investigate general conditions on b and f for nonexistence of positive supersolutions.