- Research Article
- Open Access
Extremal Values of Half-Eigenvalues for -Laplacian with Weights in Balls
© 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
- Full Article
To access the full article, please see PDF.
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.