Indefinite eigenvalue problems for \(p\)-Laplacian operators with potential terms on networks (Q1724349)

Summary: 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.