一类多调和方程边值问题的可解性研究  

Solvability of Boundary Value Problems of a Kind of Polyharmonic Equation

作　　者：古杨[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246133

出　　处：《安庆师范学院学报（自然科学版）》2011年第1期4-7,共4页Journal of Anqing Teachers College(Natural Science Edition)

基　　金：安徽省高校省级自然科学重点项目(KJ2010A224)资助

摘　　要：多调和方程边值问题的研究是椭圆型偏微分方程边值问题研究的热点之一,本文通过引入新变量将多调和方程边值问题转换为椭圆型方程组问题,再利用Leray-Schauder不动点定理,证明了多调和方程边值问题解的存在性,同时,证明了一定条件下正解的唯一性,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 polyharmonic equation boundary value problem is transformed into the one of the system of elliptic equations by introducing new variables,and the existence of the solution to the boundary value of the polyharmonic equation is proved by using the Levay-Schauder.Under certain condition,the uniqueness of the positive solution to the problem is also proved.At the same time,the nonexistence of the positive solution is discussed.

关 键 词：多调和方程 椭圆方程组 LERAY-SCHAUDER不动点定理 

分 类 号：O175[理学—数学]