Journal of Optimization Theory and Applications

, Volume 156, Issue 2, pp 294–319 | Cite as

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 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.


Eigenvalue p-Laplacian Minimization problem Integrable potential Critical equation 



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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© 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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