Extremal Values of Half-Eigenvalues for
-Laplacian with Weights in !()
Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
Boundary Value Problems 2010, 2010:690342 doi:10.1155/2010/690342Published: 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.