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arXiv · 2203.06702

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

Riccardo Adami·Filippo Boni·Raffaele Carlone·Lorenzo Tentarelli
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Abstract

We study the ground states for the Schr\"odinger 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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Riccardo Adami, Filippo Boni, Raffaele Carlone, Lorenzo Tentarelli. 2022-03-13. Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect. https://doi.org/10.1063/5.0091334

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