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

作　　者：LI Qiuyue REN Yanxia 

机构地区：[1]LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,China LMAM,School of Mathematical Sciences,Peking University,Beijing 100871,China

出　　处：《Science China Mathematics》2005年第12期1683-1695,共13页中国科学：数学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.10471003);Foundation for Authors Awarded Excellent Ph.D.Dissertation.

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

关 键 词：super-Brownian motion nonlinear differential equation minimal POSITIVE solutions maximal POSITIVE solutions S-polar sets. 

分 类 号：N[自然科学总论]