Abstract: In this paper, by the method of subsolutions and supersolutions, for smooth boundary domain Ω of Rⁿ, the existence of positive solutions for singular nonlinear elliptic boundary value problem Δu+f(x, u, Du)=0, u|∂Ω=0, has been obtained.By the transformation u=v^-p(p>2/(q-1)), the existence of positive solutions for Δv=Cv^q(C>0, q>1), v|∂Ω=+∞, has also been obtained.

Key words: elliptic equation, singular nonlinearity, singular boundary value, existence of positive solution

摘要： 用上下解方法得到了Rⁿ中光滑有界区域上f(x,u,Du)在u=0处具奇性的椭圆方程Δu+f(x,u,Du)=0零边值问题正解的存在性并由此直接获得了"超布朗运动"中所需的椭圆方程奇异边值问题正确的存在性.

关键词: 椭圆方程, 奇异非线性, 奇异边值问题, 正解的存在性