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  • Research Article
  • Open Access

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

Boundary Value Problems20102010:690342

https://doi.org/10.1155/2010/690342

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

Abstract

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.

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
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Authors’ Affiliations

(1)
Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

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