Extremal Values of Half-Eigenvalues for p-Laplacian with Weights in L1 Balls
نویسنده
چکیده
For one-dimensional p-Laplacian with weights in Lγ : L 0, 1 ,R 1 ≤ γ ≤ ∞ balls, we are interested in the extremal values of the mth 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.
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Article history: Received 16 April 2008 Revised 17 March 2009 Available online 2 April 2009 MSC: primary 34L15 secondary 34L40, 47J30
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