S-polar sets of super-brownian motions and solutions of nonlinear differential equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

S-polar sets of super-brownian motions and solutions of nonlinear differential equations

Authors:	Li?Qiuyue,Ren?Yanxia author-information" > author-information__contact u-icon-before" > mailto:yxren@math.pku.edu.cn" title=" yxren@math.pku.edu.cn" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author

Affiliation:	LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,China

Abstract:	This paper gives probabilistic expressions of the minimal and maximal positive solutions of the partial differential equation -1/2δv(x)+γ(x)v(x)^α=0 in D, where D is a regular domain in ℝ^d(d⩾ 3) such that its complement D ^c is compact, γ(x) is a positive bounded integrable function in D, and 1 2. As an application, some necessary and sufficient conditions for a compact set to be S-polar are presented.

Keywords:	super-Brownian motion nonlinear differential equation minimal positive solutions maximal positive solutions S-polar sets.
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