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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On linearly coupled Schrödinger systems


Authors: Zhijie Chen and Wenming Zou
Journal: Proc. Amer. Math. Soc. 142 (2014), 323-333
MSC (2010): Primary 35B40, 35B45
DOI: https://doi.org/10.1090/S0002-9939-2013-12000-9
Published electronically: October 8, 2013
MathSciNet review: 3119206
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Abstract | References | Similar Articles | Additional Information

Abstract: We study the following system of nonlinear Schrödinger equations:

$\displaystyle \begin {cases}-\Delta u +u = f(u)+\lambda v, & x\in \mathbb{R}^N,\\ -\Delta v +v =g(v)+\lambda u, & x\in \mathbb{R}^N.\end{cases}$

Under almost optimal assumptions on $ f$ and $ g$, for small $ \lambda >0$, we obtain positive radial solutions and study their asymptotic behaviors as $ \lambda \to 0$.

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Additional Information

Zhijie Chen
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
Email: chenzhijie1987@sina.com

Wenming Zou
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
Email: wzou@math.tsinghua.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2013-12000-9
Received by editor(s): March 13, 2012
Published electronically: October 8, 2013
Additional Notes: This work was supported by NSFC (11025106, 11271386, 10871109)
Communicated by: Chuu-Lian Terng
Article copyright: © Copyright 2013 American Mathematical Society