Harnack's inequality and Green functions on locally finite graphs

Published 31 Oct 2013 in math.DG, cs.IT, math.AP, math.CA, math.IT, and math.MG | (1310.8390v1)

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.