| 某些半线性椭圆方程在环域上的正对径解的存在性 |
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| 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. |
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| 作者姓名： | 姚庆六 马勤生 |
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| 作者单位： | 1.南京经济学院应用数学系, 南京 210003; |
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| 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。
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| 关 键 词： | 二阶椭圆方程 环域 正对径解 |
| 文章编号： | 1000-0887(2002)12-1296-05 |
| 收稿时间： | 2000-04-21 |
| 修稿时间： | 2000年4月21日 |
Existence of Positive Radial Solutions for Some Semilinear Elliptic Equations in Annulus |
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| 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. |
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| Authors: | YAO Qing_liu MA Qin_sheng |
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| Institution: | 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 |
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| 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. |
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| Keywords: | second_order elliptic equation annular domain positve radial solution |
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