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arXiv 2203.06702math.APmath-phmath.MP
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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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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.

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