Harnack's inequality and Green functions on locally finite graphs

2013/10/31 by Li Ma, Ma, Li
Mathematics · #53 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Limits and Structures in Graph Theory #Metric Geometry (math.MG) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1310.8390

openalex publication_date 2013/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the gradient estimate for positive solutions of Schrodinger equations on locally finite graph. Then we derive Harnack's inequality for positive solutions of the Schrodinger equations. We also set up some results about Green functions of the Laplacian equation on locally finite graph. Interesting properties of Schrodinger equation are derived.

Related

• Kato's inequality and Liouville theorems on locally finite graphs
• Characterization of Green's function of discrete Schrödinger operator on a finite graph by its spanning subgraphs
• Global gradient estimate on graph and its applications
• A gradient estimate for positive functions on graphs
• On a class of nonlinear Schrödinger equation on finite graphs