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Existence results of solitons in discrete non-linear Schrödinger equations†

Published online by Cambridge University Press:  15 February 2016

HAIPING SHI  and
YUANBIAO ZHANG
HAIPING SHI
Affiliation:
Modern Business and Management Department, Guangdong Construction Polytechnic, Guangzhou 510440, China email: shp7971@163.com
YUANBIAO ZHANG
Affiliation:
Packaging Engineering Institute, Jinan University, Zhuhai 519070, China email: abiaoa@163.com
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Abstract

The discrete non-linear Schrödinger equation is one of the most important inherently discrete models, having a crucial role in the modelling of a great variety of phenomena, ranging from solid-state and condensed-matter physics to biology. In this paper, a class of discrete non-linear Schrödinger equations are considered. Using critical point theory in combination with periodic approximations, we establish some new sufficient conditions on the existence results for solitons of the equation. The classical Ambrosetti–Rabinowitz superlinear condition is improved.

Keywords

existencesolitonsdiscrete non-linear Schrödinger equationscritical point theory
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 5 , October 2016 , pp. 726 - 737
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

†

This project is supported by the National Natural Science Foundation of China (No. 11401121) and Natural Science Foundation of Guangdong Province (No. S2013010014460).

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