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H. Brezis, E. Lieb. A relation between point convergence of functions and convergence of functionals. Proc. AMS, 1983, 88(3): 486-490.

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• 标题: 含变号权的p-Laplcean算子的特征值问题On the Eigenvalue Problem for p-Laplcean Operator with Indefinite Weights

  作者: 熊辉

  关键字: p-Laplace, 特征值问题, Fu ik谱, 变号权p-Laplcean; Eigenvalue Problem; Fu Ik Spectrum; Indefinite Weight

  期刊名称: 《Pure Mathematics》, Vol.1 No.2, 2011-07-20

  摘要: 本文研究含不定权的Hardy-Sobolev算子的特征值问题(不定权表示权函数 可以变号，并具有非平凡的正部)，讨论了第一特征值的单一性、非第一特征值的特征函数的变号性和特征值序列的无穷性。并证明了Fu ik谱中非平凡曲线的存在性。 In this paper we study the eigenvalue problem for the -Laplcean operator with indefinite weights. The simplicity, isolation of the first eigenvalue is studied here. Furthermore, the existence of a nontrivial curve is shown in the Fu ik spectrum.