某些半线性椭圆方程在环域上的正对径解的存在性

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

姚庆六¹,
马勤生²

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

详细信息

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
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- 被引次数: 0
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

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

YAO Qing-liu¹,
MA Qin-sheng²

1.
Department of Applied Mathematics, Nanjing University of Economics, Nanjing 210003, P R China;
2.
College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, P R China

摘要

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。
- 二阶椭圆方程 /
- 环域 /
- 正对径解
Abstract: Applying Krasnoselc 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.
- second-order elliptic equation /
- annular domain /
- positve radial solution

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参考文献(12)

[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.