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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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