| 一类非线性椭圆方程的Nehari流形 |
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| 引用本文： | 黄娟,陈丹.一类非线性椭圆方程的Nehari流形[J].成都大学学报(自然科学版),2013,32(4):343-351. |
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| 作者姓名： | 黄娟 陈丹 |
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| 作者单位： | 四川师范大学数学与软件科学学院,四川成都,610066;成都大学信息科学与技术学院,四川成都,610106 |
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| 基金项目： | 四川省教育厅青年科研基金（10ZB003）资助项目. |
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| 摘 要： | 研究了一类非线性椭圆方程的Nehari流形，并运用加权Sobolev空间的嵌入定理和齐次特征值问题的性质，分析了Nehari流形与fibrering映射的关系，进而讨论了Nehari流形的性质，运用这些性质还可得到该非线性椭圆方程正解的情况．
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| 关 键 词： | Nehari流形 变分方法 加权Sobolev空间 |
Nehari Manifold of Nonlinear Elliptic Equation |
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| HUANG Juan,CHEN Dan.Nehari Manifold of Nonlinear Elliptic Equation[J].Journal of Chengdu University (Natural Science),2013,32(4):343-351. |
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| Authors: | HUANG Juan CHEN Dan |
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| Institution: | 1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China; 2.School of Information Science and Technology, Chengdu University, Chengdu 610106, China) |
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| Abstract: | In this paper, we study the Nehari manifold of a nonlinear elliptic equation.By investigating the compact imbedding theorem and the properties of homogeneous eigenvalue problem in weighted Sobolev space and exploiting the relationship between the Nehari manifold and fibrering maps, we discuss the prop- erties of the Nehari manifold. Using these properties, we also derive out the existence and non-existence re- suits for positive solutions of the equations. |
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| Keywords: | Nehari manifold variational methods weighted Sobolev space |
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