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

Abstract

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.

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

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Cited by in corpus (3)

• Ground states for the planar NLSE with a point defect as minimizers of the constrained energy
• NLS ground states on the half-line with point interactions
• Well-posedness of the three-dimensional NLS equation with sphere-concentrated nonlinearity