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  • Research Article
  • Open Access

Extremal Values of Half-Eigenvalues for -Laplacian with Weights in Balls

Boundary Value Problems20102010:690342

  • Received: 24 May 2010
  • Accepted: 21 October 2010
  • Published:


For one-dimensional -Laplacian with weights in balls, we are interested in the extremal values of the th positive half-eigenvalues associated with Dirichlet, Neumann, and generalized periodic boundary conditions, respectively. It will be shown that the extremal value problems for half-eigenvalues are equivalent to those for eigenvalues, and all these extremal values are given by some best Sobolev constants.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Full Article

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Authors’ Affiliations

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


© Ping Yan. 2010

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.