- Research Article
- Open Access
© Ping Yan. 2010
- Received: 24 May 2010
- Accepted: 21 October 2010
- Published: 2 November 2010
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
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