| R2 中带不定权与临界位势的非线性椭圆问题 |
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| 引用本文： | 章国庆,刘三阳. R2 中带不定权与临界位势的非线性椭圆问题[J]. 数学物理学报(A辑), 2008, 28(5): 929-936 |
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| 作者姓名： | 章国庆 刘三阳 |
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| 作者单位： | [1]上海理工大学理学院,上海200093 [2]西安电子科技大学应用数学系,西安710071 |
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| 基金项目： | 中国博士后科学基金，上海市教委科研创新基金 |
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| 摘 要： | 该文讨论了R2中一类带不定权且含临界位势的二阶椭圆方程的特征值问题,然后,借此特征值问题的第一特征值性质,利用临界点理论及Trudinger-Moser不等式,证明了R2 中一类带不定权且含临界位势的二阶非线性椭圆方程非平凡解的存在性.
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| 关 键 词： | 特征值问题 不定权 临界点理论 |
| 收稿时间： | 2006-02-28 |
| 修稿时间： | 2008-01-26 |
On a Class of Elliptic Equation with Critical Potential and Indefinite Weights in R2 |
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| Zhang Guoqing,Liu Sanyang. On a Class of Elliptic Equation with Critical Potential and Indefinite Weights in R2[J]. Acta Mathematica Scientia, 2008, 28(5): 929-936 |
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| Authors: | Zhang Guoqing Liu Sanyang |
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| Affiliation: | (College of Science,University of Shanghai for Science and Technology, Shanghai 200093; Department of Applied Mathematics, Xidian University, Xi’an 710071) |
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| Abstract: | The eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is investigated. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, the authors prove the existence of nontrivial solutions for a class of nonlinear elliptic equations with critical potential and indefinite weights in R2. |
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| Keywords: | Eigenvalue problemzz Indefinite weightszz Critical point theoryzz |
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