Various Half-Eigenvalues of Scalar -Laplacian with Indefinite Integrable Weights

Wei Li and Ping Yan

Abstract and Applied Analysis, 2009, vol. 2009, 1-27

Abstract:

Consider the half-eigenvalue problem a.e. , where , , for , and and are indefinite integrable weights in the Lebesgue space . We characterize the spectra structure under periodic, antiperiodic, Dirichlet, and Neumann boundary conditions, respectively. Furthermore, all these half-eigenvalues are continuous in , where denotes the weak topology in space. The Dirichlet and the Neumann half-eigenvalues are continuously Fréchet differentiable in , where is the norm of .

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:109757

DOI: 10.1155/2009/109757

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