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三维点缺陷NLSE基态的存在性、结构和鲁棒性

Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect

Riccardo Adami, Filippo Boni, Raffaele Carlone, Lorenzo Tentarelli

备注：
17 pages. Keywords: standing waves, nonlinear Schrödinger, ground states, delta interaction, radially symmetric solutions, rearrangements. Accepted for publication in the Special Collection on the Proceedings of ICMP XX and in a regular issue of Journal of Mathematical Physics. arXiv admin note: text overlap with arXiv:2109.09482
发表信息：
J. Math. Phys. 63 (2022), no. 7, article number 071501, 16pp
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摘要：

研究了三维空间中具有聚焦非线性和点相互作用的薛定谔方程的基态。我们建立的基态存在的质量的每一个值，而且他们是积极的，径向对称，沿径向方向减少，并显示在点相互作用的位置库仑奇点。值得注意的是，基态的存在与点相互作用的吸引或排斥性质无关。

英文摘要：

We study the ground states for the Schrödinger equation with a focusing nonlinearity and a point interaction in dimension three. We establish that ground states exist for every value of the mass; moreover they are positive, radially symmetric, decreasing along the radial direction, and show a Coulombian singularity at the location of the point interaction. Remarkably, the existence of the ground states is independent of the attractive or repulsive character of the point interaction.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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