Journal of Optimization Theory and Applications

, Volume 156, Issue 2, pp 294–319

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



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.


Eigenvalue p-Laplacian Minimization problem Integrable potential Critical equation 

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Graduate UniversityChinese Academy of SciencesBeijingChina
  2. 2.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  3. 3.Zhou Pei-Yuan Center for Applied MathematicsTsinghua UniversityBeijingChina

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