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2018 Uniqueness of positive solutions for a class of Schrodinger systems with saturable nonlinearity
Xiaofei Cao, Junxiang Xu, Jun Wang, Fubao Zhang
Rocky Mountain J. Math. 48(6): 1815-1828 (2018). DOI: 10.1216/RMJ-2018-48-6-1815

Abstract

This paper is devoted to the study of the nonexistence and the uniqueness of positive solutions for a class of the following nonlinear coupled Schrodinger systems with saturable nonlinearity \begin{equation} \begin{cases} -\Delta u_{1}+\lambda _{1}u_{1}=\dfrac {u_{1}(\mu _1 u_{1}^2+\beta u_{2}^2)}{1+s(\mu _1 u_{1}^2+\beta u_{2}^2)} &\mbox {in } \mathbb {R}^N, \\-\Delta u_{2}+\lambda _{2}u_{2}=\dfrac {u_{2}(\mu _2 u_{2}^2+\beta u_{1}^2)}{1+s(\mu _2 u_{2}^2+\beta u_{1}^2)} &\mbox {in } \mathbb {R}^N, \\ u_{1}, u_{2}\in H^1(\mathbb {R}^N),\ u_{1}>0,\ u_{2}>0 &\mbox {in } \mathbb {R}^N, \end{cases} \end{equation} where $\lambda _{j}, \mu _{j}, j=1, 2$, are positive constants, $s$ is a positive parameter and $\beta $ is a positive coupling parameter. Moreover, we will show that any positive solution is a priori bounded.

Citation

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Xiaofei Cao. Junxiang Xu. Jun Wang. Fubao Zhang. "Uniqueness of positive solutions for a class of Schrodinger systems with saturable nonlinearity." Rocky Mountain J. Math. 48 (6) 1815 - 1828, 2018. https://doi.org/10.1216/RMJ-2018-48-6-1815

Information

Published: 2018
First available in Project Euclid: 24 November 2018

zbMATH: 06987226
MathSciNet: MR3879303
Digital Object Identifier: 10.1216/RMJ-2018-48-6-1815

Subjects:
Primary: 35A01, 35J60

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 6 • 2018
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