Positive vortex solutions and phase separation for coupled Schrodinger system with singular potential
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Date
2020-10-30
Authors
Deng, Jin
Xia, Aliang
Yang, Jianfu
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We consider the existence of rotating solitary waves (vortices) for a coupled Schrödinger equations by finding solutions to the singular system
-Δu + λ1u + u/|x|2 = μ1u3 + βuv2, x ∈ ℝ2,
-Δv + λ2v + v/|x|2 = μ2v3 + βu2v, x ∈ ℝ2,
u, v ≥ 0, x ∈ ℝ2,
where λ1, λ2, μ1, μ2 are positive parameters, β ≠ 0. We show that this system has a positive least energy solutions for the cases when either β is negative or β is positive and small or large. Moreover, if λ1 = λ2, then the solution is unique. We also study the limiting behavior of the least energy solutions in the repulsive case for β → -∞, and phase separation.
Description
Keywords
Schrödinger equation, Singular potential, Nehari manifold
Citation
Deng, J., Xia, A., & Yang, J. (2020). Positive vortex solutions and phase separation for coupled Schrodinger system with singular potential. <i>Electronic Journal of Differential Equations, 2020</i>(108), pp. 1-20.
Rights
Attribution 4.0 International