Academic Editor: V. Shakhmurov
Copyright © 2010 Ping Yan. 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.
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.