一类非线性椭圆型方程正解的存在性与唯一性  

The existence and uniqueness of positive solutions to a class of nonlinear elliptic equations

作　　者：汪光辉[1] 

机构地区：[1]合肥工业大学理学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2001年第3期416-419,共4页Journal of Hefei University of Technology：Natural Science

摘　　要：近年来 ,在非线性数学物理、生物等学科中涌现出大量的非线性椭圆型方程 ,对这类方程解的存在性、唯一性或多解性以及解的性态的研究 ,引起了国内外许多数学工作者的关注。该文主要采用 Banack空间中的不动点定理 ,研究了一类半线性椭圆型方程正解的存在性与唯一性 ,并且获得这类椭圆型方程正解存在的一个必要条件。In recent years, a lot of nonlinear elliptic equations emerge in those subjects like mathematical physics,biology, etc,and the research on the existance,uniqueness or diversity and properties of the solutions to these equations is attracting much attention of many mathematical workers at home or abroad.In this paper, an existence and uniqueness theorem of positive solutions to a class of semilinear ellipic equations is proved by using the fixed point theorem in Banach space.Also a necessary condition for the existence of the positive solution is obtained.

关 键 词：非线性椭圆型方程 不动点定理 紧正算子 正解 

分 类 号：O175.25[理学—数学] O175.29[理学—基础数学]