Abstract and Applied Analysis

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

Jea-Hyun Park and Soon-Yeong Chung

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We address some forward and inverse problems involving indefinite eigenvalues for discrete p -Laplacian operators with potential terms. These indefinite eigenvalues are the discrete analogues of p -Laplacians on Riemannian manifolds with potential terms. We first define and discuss some fundamental properties of the indefinite eigenvalue problems for discrete p -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 p -Laplacian operators with potential terms involving the smallest indefinite eigenvalues.

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Abstr. Appl. Anal., Volume 2014 (2014), Article ID 539603, 10 pages.

First available in Project Euclid: 2 October 2014

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Park, Jea-Hyun; Chung, Soon-Yeong. Indefinite Eigenvalue Problems for $p$ -Laplacian Operators with Potential Terms on Networks. Abstr. Appl. Anal. 2014 (2014), Article ID 539603, 10 pages. doi:10.1155/2014/539603. https://projecteuclid.org/euclid.aaa/1412273216

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