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

Abstract EN

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.