某些半线性椭圆方程在环域上的正对径解的存在性  

Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus

作　　者：姚庆六[1] 马勤生[2] 

机构地区：[1]南京经济学院应用数学系,南京210003 [2]西北师范大学数学与信息科学学院,兰州730070

出　　处：《应用数学和力学》2002年第12期1296-1300,共5页Applied Mathematics and Mechanics

摘　　要：利用锥拉伸与锥压缩型的Krasnosel’skii不动点定理讨论了某些二阶非线性椭圆方程在环域上关于Dirichlet边界条件的正对径解的存在性·　通过考察非线性项在有界闭区间上的性质建立了若干正对径解的存在性结论·　主要结论不涉及非线性项的超线性增长和次线性增长·　当非线性项存在极值并满足适当条件时 。Applying Krasnosel′ skii fixed point theorem of cone expansion_compression type, the existence of positive radial solutions for some second_order nonlinear elliptic equations in annular domains, subject to Dirichlet boundary conditions, is investigated. By considering the properties of nonlinear term on boundary closed intervals, several existence results of positive radial solutions are established. The main results are independent of superlinear growth and sublinear growth of nonlinear term. If nonlinear term has extreme values and satisfies suitable conditions, the main results are very effective.

关 键 词：半线性椭圆方程 环域 正对径解 存在性 

分 类 号：O175.25[理学—数学] O175[理学—基础数学]