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Perturbed Schrödinger lattice systems: existence of homoclinic solutions

Part of: Difference and functional equations Equations of mathematical physics and other areas of application Difference equations

Published online by Cambridge University Press:  27 December 2018

Guanwei Chen  and
Shiwang Ma
Guanwei Chen
Affiliation:
School of Mathematical Sciences, University of Jinan, Jinan 250022, Shandong Province, China (guanweic@163.com)
Shiwang Ma
Affiliation:
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China (shiwangm@163.net)
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Abstract

We study a class of Schrödinger lattice systems with sublinear nonlinearities and perturbed terms. We get an interesting result that the systems do not have nontrivial homoclinic solutions if the perturbed terms are removed, but the systems have ground state homoclinic solutions if the perturbed terms are added. Besides, we also study the continuity of the homoclinic solutions in the perturbation terms at zero. To the best of our knowledge, there is no published result focusing on the perturbed Schrödinger lattice systems.

Keywords

Schrödinger lattice systemsperturbed termssublinearhomoclinic solutions

MSC classification

Primary: 35Q51: Soliton-like equations
Secondary: 35Q55: NLS-like equations (nonlinear Schrödinger) 39A12: Discrete version of topics in analysis 39A70: Difference operators
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 4 , August 2019 , pp. 1083 - 1096
Copyright
Copyright © Royal Society of Edinburgh 2018 

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