| Rn上带奇异性的非线性双调和方程的正整解 |
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| 引用本文： | 许兴业.Rn上带奇异性的非线性双调和方程的正整解[J].数学物理学报(A辑),2009,29(1):87-93. |
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| 作者姓名： | 许兴业 |
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| 作者单位： | 广东教育学院数学系,广州,510310
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| 基金项目： | 广东省高校自然科学基金 |
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| 摘 要： | 该文以Schauder-Tychonoff不动点定理为工具,建立了一类Rn上带奇异性的非线性双调和方程 Δ2u=f(|x|, u,| u|)u-β (x ∈ Rn, n ≥ 3, β > 0) 正的径向对称整体解的存在性定理,并给出了解的有关性质,所得的结果丰富和发展了文献1--5]的结果.
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| 关 键 词： | 双调和方程 正整解 Lebesgue控制收敛定理 等度连续 不动点定理. |
| 收稿时间： | 2006-03-19 |
| 修稿时间： | 2007-12-22 |
The Positive Entire Solutions for a Class of Nonlinear Biharmonic Equations with Singularity on Rn |
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| Xu Xingye.The Positive Entire Solutions for a Class of Nonlinear Biharmonic Equations with Singularity on Rn[J].Acta Mathematica Scientia,2009,29(1):87-93. |
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| Authors: | Xu Xingye |
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| Institution: | (Department of Mathematics of Guangdong Education College, Guangzhou 510310) |
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| Abstract: | In this paper, author’s aim is to establish the theorems of existence of positive radially symmetric entire solutions for a class of singular nonlinear biharmonic equation Δ2u=f(|x|, u,| u|)u-β (x ∈ Rn, n ≥ 3, β > 0) on Rn with the Schauder-tychonoff fixed point theorem as the principal tool, and presents the properties of the solutions. They enrich and develop the theory and application of papes 1--5]. |
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| Keywords: | Biharmonic equationzz Positive entire solutionzz Lebesgue dominated covergence theoremzz Equicontinuityzz Fixed point theorem zz |
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