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.
"Indefinite Eigenvalue Problems for -Laplacian Operators with Potential Terms on Networks." Abstr. Appl. Anal. 2014 1 - 10, 2014. https://doi.org/10.1155/2014/539603