Electron. J. Differential Equations, Vol. 2020 (2020), No. 108, pp. 1-20.

Positive vortex solutions and phase separation for coupled Schrodinger system with singular potential

Jin Deng, Aliang Xia, Jianfu Yang

Abstract:
We consider the existence of rotating solitary waves (vortices) for a coupled Schrodinger equations by finding solutions to the singular system

where $\lambda_1,\lambda_2,\mu_1, \mu_2$ are positive parameters, $\beta\neq 0$. We show that this system has a positive least energy solution for the cases When either $\beta$ is negative or $\beta$ is positive and small or large. Moreover, if $\lambda_1=\lambda_2$, then the solution is unique. We also study the limiting behavior of the least energy solutions in the repulsive case for $\beta\to-\infty$, and phase separation.

Submitted March 5, 2020. Published October 30, 2020.
Math Subject Classifications: 35J20, 35B08, 35B40.
Key Words: Schodinger equation; singular potential; Nehari manifold.
DOI: 10.58997/ejde.2020.108

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  Jin Deng
School of Mathematics and Statistics
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: Dengjin@jxnu.edu.cn
Aliang Xia
School of Mathematics and Statistics
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: aliang_xia@jxnu.edu.cn
Jianfu Yang
School of Mathematics and Statistics
Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: jfyang_2000@yahoo.com

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