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On the classification of standing wave solutions to a coupled Schrödinger system

Part of: Elliptic equations and systems Partial differential equations

Published online by Cambridge University Press:  17 January 2019

Zhi-You Chen ,
Yu-Jen Huang  and
Yong-Li Tang
Zhi-You Chen
Affiliation:
Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan ([email protected]; [email protected])
Yu-Jen Huang
Affiliation:
Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan ([email protected]; [email protected])
Yong-Li Tang
Affiliation:
Calculus Teaching Center, Feng Chia University, Taichung 40724, Taiwan ([email protected])
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Abstract

In this paper, we consider a nonlinear elliptic system which is an extension of the single equation derived by investigating the stationary states of the nonlinear Schrödinger equation. We establish the existence and uniqueness of solutions to the Dirichlet problem on the ball and entire space as the parameters within certain regions. In addition, a complete structure of different types of solutions for the radial case is also provided.

Keywords

Coupled Schrödinger systemstanding wave solutionsclassification of solutions

MSC classification

Primary: 35J47: Second-order elliptic systems 35J60: Nonlinear elliptic equations
Secondary: 35A02: Uniqueness problems
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 5 , October 2019 , pp. 1347 - 1370
Copyright
Copyright © Royal Society of Edinburgh 2019 

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