一类多调和方程的可解性研究  

Discussion on the solvability of a kind of polyharmonic equation

作　　者：陈定元[1] 钟金标[1] 

机构地区：[1]安庆师范学院数学与计算科学学院,安徽安庆246011

出　　处：《合肥工业大学学报（自然科学版）》2008年第7期1145-1148,共4页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省高校自然科学研究资助项目(2005kj214)

摘　　要：多调和方程问题的研究是椭圆形偏微分方程边值问题研究的热点之一,文章通过将多调和方程边值问题转换成椭圆形方程组问题,利用不动点原理以及上调和函数的极值原理,证明了多调和方程边值问题正解的存在性;同时,证明了一定条件下正解的惟一性,最后讨论了正解的不存在性。The polyharmonic equation problem is one of the popular issues in the study of the boundary value problem of elliptic partial differential equations. In this paper, the polyharrnonic equation boundary value problem is transformed into the problem of the system of elliptic equations, and the existence of the positive solution to the boundary value of the polyharrnonic equation is proved by means of the fixed point theorem and the extreme value principle of superharmonic functions. The uniqueness of the positive solution to the problem under certain conditions is also proved. The nonexistence of the positive solution is discussed.

关 键 词：多调和方程 椭圆方程组 POINCARE不等式 

分 类 号：O175[理学—数学]