Spectrum of One-Dimensional p-Laplacian with an Indefinite Integrable Weight
Spectrum of One-Dimensional p-Laplacian with an Indefinite Integrable Weight
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DOI：
10.1007/s00009-010-0040-5
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发表时间：
2010-04
影响因子：
1.1
通讯作者：
Gang Meng;P. Yan;Meirong Zhang
中科院分区：
文献类型：
--
作者：
Gang Meng;P. Yan;Meirong Zhang
受加权狄利克雷或诺伊曼特征值极值问题的启发，我们将建立关于一维 p-拉普拉斯加权特征值对不定可积权重的依赖性的两个基本结果。一是勒贝格空间 Lγ 中权重特征值与通常范数的连续可导性。另一个是权重特征值相对于 Lγ 空间中弱拓扑的连续性。这里 1 ≤ γ ≤ ∞。在此过程中，我们将借助非线性分析中的几种典型技术（例如 Fréchet 导数和弱*收敛）对相应的谱问题给出更简单的解释。
Motivated by extremal problems of weighted Dirichlet or Neumann eigenvalues, we will establish two fundamental results on the dependence of weighted eigenvalues of the one-dimensionalp-Laplacian on indefinite integrable weights. One is the continuous differentiability of eigenvalues in weights in the Lebesgue spacesLγwith the usual norms. Another is the continuity of eigenvalues in weights with respect to the weak topologies inLγspaces. Here 1 ≤γ≤ ∞. In doing so, we will give a simpler explanation to the corresponding spectrum problems, with the help of several typical techniques in nonlinear analysis such as the Fréchet derivative and weak* convergence.