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Minimization of Eigenvalues of One-Dimensional p-Laplacian with Integrable Potentials

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Abstract

In this paper, we will use the variational method and limiting approach to solve the minimization problems of the Dirichlet/Neumann eigenvalues of the one-dimensional p-Laplacian when the L 1 norm of integrable potentials is given. Combining with the results for the corresponding maximization problems, we have obtained the explicit results for these eigenvalues.

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Acknowledgements

The second author is supported by the National Natural Science Foundation of China (Grant No. 10901089), and the third author is supported by the Doctoral Fund of Ministry of Education of China (Grant No. 20090002110079) and the 111 Project of China (2007).

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Authors and Affiliations

  1. School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing, 100080, China

    Gang Meng

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Ping Yan & Meirong Zhang

  3. Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, 100084, China

    Meirong Zhang

Authors
  1. Gang Meng
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  2. Ping Yan
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  3. Meirong Zhang
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Corresponding author

Correspondence to Gang Meng.

Additional information

Communicated by Michael Hinze.

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Meng, G., Yan, P. & Zhang, M. Minimization of Eigenvalues of One-Dimensional p-Laplacian with Integrable Potentials. J Optim Theory Appl 156, 294–319 (2013). https://doi.org/10.1007/s10957-012-0125-3

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  • DOI: https://doi.org/10.1007/s10957-012-0125-3

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