Calculus of Variations and Geometric Measure Theory

R. Adami - F. Boni - R. Carlone - L. Tentarelli

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

created by tentarelli on 07 Jul 2022
modified on 31 Aug 2022


Published Paper

Inserted: 7 jul 2022
Last Updated: 31 aug 2022

Journal: J. Math. Phys.
Volume: 63
Number: 7
Pages: art. 071501, 16pp
Year: 2022
Doi: 10.1063/5.0091334

ArXiv: 2203.06702 PDF


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.