| 类p-Laplacian方程的特征值问题 |
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| 引用本文： | 陈祖墀,罗涛.类p-Laplacian方程的特征值问题[J].数学学报,2003,46(4):631-638. |
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| 作者姓名： | 陈祖墀 罗涛 |
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| 作者单位： | 中国科学技术大学数学系,合肥,230026 |
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| 基金项目： | 国家自然科学基金(10071080，10101024) |
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| 摘 要： | 本文考虑类p-Laplacian方程-div(a(|Du|~p)|Du|~(p-2)Du)=λf(x,u),x∈Ω,u=0,x∈Ω的特征值问题,其中ΩR~n(n≥2)是有界光滑区域.当λ>0充分小,本质上仅在凸函数的假设下,得到了性质完全不同的两个特征函数的存在性,作为定理的应用,文中给出了两个实例.
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| 关 键 词： | 类p-Laplacian方程 山路引理 极大极小原理 |
| 文章编号： | 0583-1431(2003)04-0631-08 |
| 修稿时间： | 2001年2月13日 |
The Eigenvalue Problem for p-Laplacian-Like Equations |
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| Zu Chi CHEN Tao LUO.The Eigenvalue Problem for p-Laplacian-Like Equations[J].Acta Mathematica Sinica,2003,46(4):631-638. |
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| Authors: | Zu Chi CHEN Tao LUO |
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| Institution: | Zu Chi CHEN Tao LUO
(Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China) |
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| Abstract: | In this paper, we consider the eigenvalue problem for the p-Laplacian-like equation -div(a(|Du|p)|Du| p-2Du) = λf(x,u), χ∈Ω, u = 0,χ∈(?)Ω, where Ω(?) Rn (n ≥ 2) is a bounded smooth domain. Essentially the only under convexity assumption, when A > 0 small enough, we obtain the existence of two eigenfunctions which have very different asymptotic behaviors. As applications of our theorems, two examples in physics are given. |
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| Keywords: | p-Laplacian-like equation Mountain pass lemma Minimax principle |
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