Journal of Optimization Theory and Applications

, Volume 156, Issue 2, pp 294–319

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


    • School of Mathematical Sciences, Graduate UniversityChinese Academy of Sciences
  • Ping Yan
    • Department of Mathematical SciencesTsinghua University
  • Meirong Zhang
    • Department of Mathematical SciencesTsinghua University
    • Zhou Pei-Yuan Center for Applied MathematicsTsinghua University

DOI: 10.1007/s10957-012-0125-3

Cite this article as:
Meng, G., Yan, P. & Zhang, M. J Optim Theory Appl (2013) 156: 294. doi:10.1007/s10957-012-0125-3


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 L1 norm of integrable potentials is given. Combining with the results for the corresponding maximization problems, we have obtained the explicit results for these eigenvalues.


Eigenvaluep-LaplacianMinimization problemIntegrable potentialCritical equation

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© Springer Science+Business Media, LLC 2012