arXiv:2203.06702 Abstract | arXiv Analytics

arXiv:2203.06702 [math.AP]Abstract References Reviews Resources

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

Riccardo Adami, Filippo Boni, Raffaele Carlone, Lorenzo Tentarelli

Published 2022-03-13Version 1

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.

Comments: 18 pages. Contribution for the special issue of the "XX International Congress on Mathematical Physics". Keywords:standing waves, nonlinear Schr\"odinger, ground states, delta interaction, radially symmetric solutions, rearrangements

Categories: math.AP, math-ph, math.MP

Subjects: 35Q40, 35Q55, 35B07, 35B09, 35R99, 49J40, 49N15

Keywords: ground states, point defect, point interaction, robustness, radial direction

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