Ground states of nonlinear Schrödinger systems

Chang, Jinyong; Liu, Zhaoli

doi:10.1090/S0002-9939-09-10090-4

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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
Posted: 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

, $\lambda_j>0$ and $\mu_j>0$ for

, and $\beta>0$ . A result from Sirakov, Comm. Math. Phys. 271 (2007), 199-221, is improved.

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