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math.AP2025
Eigenvalues of the discrete p-Laplacian via graph surgery
Gregory Berkolaiko, Matthias Hofmann
We develop a Hellmann--Feynman type perturbation theory for the discrete signed -Laplacian and apply it to a parametrized perturbation by edge cuts. We show that the eigenvalues…
math.AP2025
On the existence of Nehari ground states for the Nonlinear Schrödinger Equation on Discrete Graphs
Setenay Akduman, Matthias Hofmann, Sedef Karakılıç
We study standing waves for the nonlinear Schrödinger equation on a discrete graph. We characterize for a self-adjoint realizations of Schrödinger operators conditions related with…