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math.AP2022★ 1 cited
Uniqueness of Single Peak Solutions for Coupled Nonlinear Gross-Pitaevskii Equations with Potentials
Xiaoyu Zeng, Huan-Song Zhou
For a couple of singularly perturbed Gross-Pitaevskii equations, we first prove that the single peak solutions, if they concentrate on the same point, are unique provided that the…
math.AP2022★ 5 cited
A constrained minimization problem related to two coupled pseudo-relativistic Hartree equations
Wenqing Wang, Xiaoyu Zeng, Huan-Song Zhou
We are concerned with the following constrained minimization problem: $$e(a_{1},a_{2},β) := \inf\left\{E_{a_{1},a_{2},β}(u_{1},u_{2}): \|u_{1}\|_{L^{2}(\mathbb{R}^{3})} = \|u_{2}\|…