## 留言板

 引用本文: 姚庆六, 马勤生. 某些半线性椭圆方程在环域上的正对径解的存在性[J]. 应用数学和力学, 2002, 23(12): 1296-1300.
YAO Qing-liu, MA Qin-sheng. Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1296-1300.
 Citation: YAO Qing-liu, MA Qin-sheng. Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1296-1300.

## 某些半线性椭圆方程在环域上的正对径解的存在性

###### 作者简介:姚庆六(1946- ),男,上海人,教授,硕士(E-mail:maqs@nwnu.edu.cn).
• 中图分类号: O175.25;O175.8

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

• 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,主要结论是非常有效的。
•  [1] NI Wei-ming,Nussbanm R D.Uniqueness and nonuniqueness for positive radial solutions of Δu+f(u,r)=0 [J].Comm Pure Appl Math,1985,38(1):67-108. [2] Bandle C,Coffman C V,Marcus M.Nonlinear elliptic problems in annular domains[J].J Differential Equations,1987,69(3):322-345. [3] LIN Song-sun.On the existence of positive radial solutions for nonlinear elliptic equations in annular domains[J].J Differential Equations,1989,81(2):221-233. [4] WANG Hai-yan.On the existence of positive solutions for semilinear elliptic equations in annulus[J].J Differential Equations,1994,109(1):1-7. [5] Erbe L H,HU Shou-chuan,WANG Hai-yan.Multiple positive solutions of some boundary value problems[J].J Math Anal Appl,1994,184(3):640-648. [6] Lions P L.On the existence of positive solutions of semilinear elliptic equations[J].SIAM Rev,1982,24(4):441-467. [7] 姚庆六,白占兵.u(4)(t)-λh(t)f(u(t))=0的边值问题的正解存在性[J].数学年刊(A),1999,20(5):575-578. [8] 姚庆六.方程Δu+g(|X|)f(u)=0的环上Dirichlet边值问题的正对径解的存在性[J].数学物理学报(A),2000,20(3):414-418. [9] 姚庆六,王景荣.方程Δu+g(|X|)f(u)=0的环上Dirichlet边值问题的多重正对径解[J].系统科学与数学,2000,20(4):487-492. [10] 姚庆六.广义Gelfand模型的正解[J].高校应用数学学报(A),2001,16(4):407-413. [11] 姚庆六.一类奇异次线性两点边值问题的正解[J].应用数学学报,2001,24(4):522-526. [12] 钟承奎,范先令,陈文源.非线性泛函分析引论[M].兰州:兰州大学出版社,1998,143-154.
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##### 出版历程
• 收稿日期:  2000-04-21
• 修回日期:  2002-06-11
• 刊出日期:  2002-12-15

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