2024/03/22 by Schmidt, Marcel, Zimmermann, Ian
#Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2403.15125
We study non-linear Schrödinger operators on graphs. We construct minimal nonnegative solutions to corresponding semi-linear elliptic equations and use them to introduce the notion of stochastic completeness at infinity in a non-linear setting. We provide characterizations for this property in terms of a semi-linear Liouville theorem. It is employed to establish a non-linear characterization for stochastic completeness, which is a graph version of a recent result on Riemannian manifolds.