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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ground states of nonlinear Schrödinger systems


Authors: Jinyong Chang and Zhaoli Liu
Journal: Proc. Amer. Math. Soc. 138 (2010), 687-693
MSC (2000): Primary 35J10, 35J50, 58E05
Published electronically: October 2, 2009
MathSciNet review: 2557185
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Abstract: This paper concerns the existence of positive radial ground states of the time-independent Schrödinger system

$\displaystyle \left\{\begin{array}{ll} -\Delta{u_1}+\lambda_1u_1=\mu_1u_1^3+\be... ...1(x)\to0, \ u_2(x)\to0, \ &\text{as} \vert x\vert\to\infty, \end{array}\right. $

where $ n=1,2,3$, $ \lambda_j>0$ and $ \mu_j>0$ for $ j=1,2$, and $ \beta>0$. A result from Sirakov, Comm. Math. Phys. 271 (2007), 199-221, is improved.


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Additional Information

Jinyong Chang
Affiliation: (J. Chang and Z. Liu) School of Mathematical Sciences, Capital Normal University, Beijing 100048, People’s Republic of China; (J. Chang) Department of Mathematics, Changzhi University, Shanxi 046011, People’s Republic of China

Zhaoli Liu
Affiliation: (J. Chang and Z. Liu) School of Mathematical Sciences, Capital Normal University, Beijing 100048, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10090-4
PII: S 0002-9939(09)10090-4
Keywords: Schr\"odinger system, nontrivial ground state, Morse index.
Received by editor(s): March 24, 2009
Received by editor(s) in revised form: June 19, 2009
Published electronically: October 2, 2009
Additional Notes: This work was supported by NSFC (10825106)
Communicated by: Yingfei Yi
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.