The spectrum theory of the discrete Schrödinger operator and its application

Guoping Zhang

doi:10.26637/mjm11S/009

Abstract

This paper introduces the spectrum theory of discrete Schrödinger operators with different kinds of potentials, including bounded, unbounded, periodic, or complex potentials. The paper also provides exponential estimates of the Green's function and eigenfunctions of the discrete Schrödinger operators. As an application, I review some of our results on standing wave solutions of discrete Schrödinger equations.

Keywords:

spectrum, bounded/unbounded potential, complex potential, periodic potential, Green's function, standing waves, discrete Schrödinger operator

Mathematics Subject Classification:

35Q55, 35Q51, 37L60, 39A12, 39A70, 47J30, 78A40

Authors Imprint References Funding Related Articles Downloads

Guoping Zhang Department of Mathematics, Morgan State University, 1700 E Cold Spring Ln, Baltimore, MD 21251, USA. https://orcid.org/0009-0004-0692-4359

Pages: 125-148
Date Published: 01-10-2023
Vol. 11 No. S (2023): Malaya Journal of Matematik (MJM): Special Issue Dedicated to Professor Gaston M. N'Guérékata’s 70th Birthday

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