| LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT |
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| 引用本文： | 耿堤. LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT[J]. 数学物理学报(B辑英文版), 2005, 25(2): 283-295. DOI: 10.1016/S0252-9602(17)30285-0 |
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| 作者姓名： | 耿堤 |
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| 作者单位： | DepartmentofMathematics,SouthChinaNormalUniversity,Guangzhou510631,China |
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| 基金项目： | The research work was supported by the National Natural Foundation of China (10371045)Guangdong Provincial Natural Science Foundation of China (000671). |
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| 摘 要： | In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin‘s function corresponding to the Green‘s function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex.
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| 关 键 词： | 双谐算子 Navier边界条件 渐近性 临界指数 格林函数 数学物理方程 |
| 收稿时间： | 2002-08-29 |
LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT |
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| GENG Di. LOCATION OF THE BLOW UP POINT FOR POSITIVE SOLUTIONS OF A BIHARMONIC EQUATION INVOLVING NEARLY CRITICAL EXPONENT[J]. Acta Mathematica Scientia, 2005, 25(2): 283-295. DOI: 10.1016/S0252-9602(17)30285-0 |
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| Authors: | GENG Di |
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| Affiliation: | 1. School of Science and Technology, University of New England, Armidale, NSW 2351, Australia;2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui, 230026, PR China;1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, PR China;2. School of Mathematics and Information, China West Normal University, Nanchong, 637002, PR China;1. Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany;2. Mathematics Department, Technion – I.I.T., Haifa 32000, Israel;1. Department of Mathematical and Systems Engineering, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 432-8561, Japan;2. Department of Mathematics, Faculty of Science, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-ku, Kyoto-City, 603-8555, Japan;1. Departamento de Matemática, Universidad Técnica Federico Santa María, 1680 Av. españa Valparaíso, Chile;2. UFRGS, Instituto de Matemática, Av. Bento Goncalves 9500, 91540-000 Porto Alegre-RS, Brazil |
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| Abstract: | In this paper a semilinear biharmonic problem involving nearly critical growth with Navier boundary condition is considered on an any bounded smooth domain. It is proved that positive solutions concentrate on a point in the domain, which is also a critical point of the Robin's function corresponding to the Green's function of biharmonic operator with the same boundary condition. Similar conclusion has been obtained in [6] under the condition that the domain is strictly convex. |
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| Keywords: | Biharmonic operator Navier boundary conditions asymptotic behavior critical exponents Green's function |
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