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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 539603, 10 pages
http://dx.doi.org/10.1155/2014/539603
Research Article

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

1Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
2Department of Mathematics and Program of Integrated Biotechnology, Sogang University, Seoul 121-742, Republic of Korea

Received 7 November 2013; Revised 27 January 2014; Accepted 28 January 2014; Published 4 March 2014

Academic Editor: Chun-Lei Tang

Copyright © 2014 Jea-Hyun Park and Soon-Yeong Chung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.