Kato's inequality and Liouville theorems on locally finite graphs

TL;DR

This paper explores Kato's inequality on locally finite graphs and applies it to Ginzburg-Landau and Schrödinger equations, deriving properties and Liouville theorems relevant to mathematical physics.

Contribution

It introduces the application of Kato's inequality to graph-based PDEs and establishes new Liouville theorems for these discrete structures.

Findings

Kato's inequality is established for locally finite graphs.

Applications to Ginzburg-Landau equations are demonstrated.

Liouville type theorems are derived for Schrödinger equations on graphs.

Abstract

In this paper we study the Kato' inequality on locally finite graph. We also study the application of Kato inequality to Ginzburg-Landau equations on such graphs. Interesting properties of Schrodinger equation and a Liouville type theorem are also derived.