| 半线性双调和方程奇异位势问题的非平凡解 |
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| 引用本文： | 熊辉,陈祖墀.半线性双调和方程奇异位势问题的非平凡解[J].中国科学技术大学学报,2005,35(6):777-782. |
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| 作者姓名： | 熊辉 陈祖墀 |
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| 作者单位： | 1. 中国科学技术大学数学系,安徽,合肥,230026;东莞理工学院数学系,广东,东莞,523106
2. 中国科学技术大学数学系,安徽,合肥,230026 |
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| 摘 要： | 研究了在四维空间R4中球域B内的半线性奇异双调和方程的Dirichlet边值问题.其中,奇异项中不但含有通常的奇位势,还含有对数权,使得该奇异项成为R4空间中的临界位势.文中首先建立了相应的Hardy不等式,然后通过山路引理得出了该问题非平凡解的存在性.
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| 关 键 词： | Hardy不等式 临界奇异位势 对数权 |
| 文章编号： | 0253-2778（2005）06-0777-06 |
| 收稿时间： | 2003-09-23 |
| 修稿时间： | 2004-07-02 |
Nontrivial Solutions to Semilinear Biharmonic Equation with Singular Critical Potential |
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| XIONG Hui,CHEN Zu-chi.Nontrivial Solutions to Semilinear Biharmonic Equation with Singular Critical Potential[J].Journal of University of Science and Technology of China,2005,35(6):777-782. |
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| Authors: | XIONG Hui CHEN Zu-chi |
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| Institution: | 1. Department of Mathematics, University of Science and Technology of China, He f ei 230026, China; 2. Department of Mathematics, Dongguan College of Science and Technology, Dongguan 523106, China |
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| Abstract: | A semilinear singular biharmonic equation with Dirichlet boundary condition is investigated in the ball B belong to R^4 . Not only is the common singular potential is contained in the singular item, but the logarithm weighted is involved so that the singular item becomes the critical potential in R^4. The relative Hardy inequality is established first, and then by Mountain Pass theorem the existence of nontrivial solutions is obtained. |
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| Keywords: | Hardy inequality critical singular potential logarithm weight |
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