半线性椭圆方程奇异边值问题正解的存在性

The Existence of Positive Solutions for Semilinear Elliptic Equation with Singular Boundaiy Value

用上下解方法获得了“超布朗运动”研究中所需的半线性椭圆方程Δｕ＝ｃｕｑ（ｑ＞１，ｃ＞０）在球域内和一般光滑有界区域奇异边值问题（即）当ｘ→边界点时，ｕ（ｘ）→＋∞正解的存在性．

In this paper,by the method of subsolutions and superstutions,the existence of positive solutions for semilinear elliptic equation Δu=u q(q>0) in a ball and Lu=u q(q>0) in the bounded domain with smooth bundary,with singular boundary value (ie u(Ω)=+∞ ),has been obtained.