椭圆方程奇异非线性问题与奇异边值问题正解的存在性

重庆交通大学学报（自然科学版） ›› 1999, Vol. 18 ›› Issue (3): 129-134.

椭圆方程奇异非线性问题与奇异边值问题正解的存在性

李建章

重庆交通学院管理系, 重庆 400074

收稿日期:1998-11-02 出版日期:1999-06-22 发布日期:2016-10-31
作者简介:李建章(1964-),男,重庆铜梁人,重庆交通学院讲师,从事偏微分方程理论与应用及交通运输系统工程研究.

The Existence of Postitive Solutions for Elliptic Equation with Singular Nonlinearity and Singular Boundary Value Problem

LI Jian-zhang

Department of Manegement, Chongqing Jiaotong Institute, Chongqing 400074, China

Received:1998-11-02 Online:1999-06-22 Published:2016-10-31

摘要/Abstract

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

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

中图分类号:

O175.29

李建章. 椭圆方程奇异非线性问题与奇异边值问题正解的存在性[J]. 重庆交通大学学报（自然科学版）, 1999, 18(3): 129-134.

LI Jian-zhang. The Existence of Postitive Solutions for Elliptic Equation with Singular Nonlinearity and Singular Boundary Value Problem[J]. Journal of Chongqing Jiaotong University(Natural Science), 1999, 18(3): 129-134.