Calculus of Variations and Geometric Measure Theory

L. Tentarelli

A general review on the NLS equation with point-concentrated nonlinearity

created by tentarelli on 19 Apr 2023
modified on 16 Oct 2023


Published Paper

Inserted: 19 apr 2023
Last Updated: 16 oct 2023

Journal: Commun. Appl. Ind. Math.
Volume: 14
Number: 1
Pages: 62-84
Year: 2023
Doi: 10.2478/caim-2023-0004

ArXiv: 2304.09086 PDF


The paper presents a complete (to the best of the author's knowledge) overview on the existing literature concerning the NLS equation with point-concentrated nonlinearity. Precisely, it mainly covers the following topics: definition of the model, weak and strong local well-posedness, global well-posedness, classification and stability (orbital and asymptotic) of the standing waves, blow-up analysis and derivation from the standard NLS equation with shrinking potentials. Also some related problem is mentioned.