Spectrum of One-Dimensional p-Laplacian with an Indefinite Integrable Weight

@inproceedings{Meng2010SpectrumOO,
  title={Spectrum of One-Dimensional p-Laplacian with an Indefinite Integrable Weight},
  author={Gang Meng and Ping Yan and Meirong Zhang},
  year={2010}
}
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-dimensional p-Laplacian on indefinite integrable weights. One is the continuous differentiability of eigenvalues in weights in the Lebesgue spaces L with the usual norms. Another is the continuity of eigenvalues in weights with respect to the weak topologies in L spaces. Here 1 ≤ γ ≤ ∞. In doing so, we will give a simpler… CONTINUE READING
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