| 一类奇异临界双调和椭圆方程的群不变解 |
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| 引用本文： | 邓志颖,黄毅生.一类奇异临界双调和椭圆方程的群不变解[J].应用数学,2012,25(3):608-615. |
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| 作者姓名： | 邓志颖 黄毅生 |
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| 作者单位： | 1. 重庆邮电大学数理学院,重庆400065;苏州大学数学科学学院,江苏苏州215006
2. 苏州大学数学科学学院,江苏苏州,215006 |
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| 基金项目： | 国家自然科学基金(11071180);重庆邮电大学博士启动基金(A2011-46) |
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| 摘 要： | 讨论一类含有Hardy-Sobolev临界指数项的奇异双调和椭圆方程,应用Lions集中紧性原理、Palais对称临界原理、Hardy-Rellich型不等式和变分方法,证明了方程在适当条件下群不变解的存在性和多重性.
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| 关 键 词： | 群不变解 Hardy-Sobolev临界指数 Hardy-Rellich型不等式 双调和椭圆方程 |
On Group-invariant Solutions of a Class of Singular Critical Biharmonic Elliptic Equations |
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| DENG Zhiying
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HUANG Yisheng.On Group-invariant Solutions of a Class of Singular Critical Biharmonic Elliptic Equations[J].Mathematica Applicata,2012,25(3):608-615. |
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| Authors: | DENG Zhiying HUANG Yisheng |
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| Institution: | 1 (1.School of Mathematics and Physics,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;2.School of Mathematical Sciences,Suzhou University,Suzhou 215006,China) |
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| Abstract: | In this paper,we discuss a class of singular biharmonic elliptic equations with critical Hardy-Sobolev exponent terms.By using the concentration-compactness principle of Lions together with the symmetric criticality principle of Palais,the Hardy-Rellich inequality and variational methods,we prove several existence and multiplicity results of group-invariant solutions under certain appropriate conditions. |
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| Keywords: | Group-invariant solution Critical Hardy-Sobolev exponent Hardy-Rellich inequality Biharmonic elliptic equation |
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