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Indefinite Eigenvalue Problems for -Laplacian Operators with Potential Terms on Networks

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  • Jea-Hyun Park
  • Soon-Yeong Chung

Abstract

We address some forward and inverse problems involving indefinite eigenvalues for discrete -Laplacian operators with potential terms. These indefinite eigenvalues are the discrete analogues of -Laplacians on Riemannian manifolds with potential terms. We first define and discuss some fundamental properties of the indefinite eigenvalue problems for discrete -Laplacian operators with potential terms with respect to some given weight functions. We then discuss resonance problems, anti-minimum principles, and inverse conductivity problems for the discrete -Laplacian operators with potential terms involving the smallest indefinite eigenvalues.

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  • Jea-Hyun Park & Soon-Yeong Chung, 2014. "Indefinite Eigenvalue Problems for -Laplacian Operators with Potential Terms on Networks," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-10, March.
    • Handle: RePEc:hin:jnlaaa:539603
    DOI: 10.1155/2014/539603
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