About this article
Published Online: Oct 13, 2023
Page range: 62 - 84
Received: Apr 18, 2023
Accepted: Jul 28, 2023
DOI: https://doi.org/10.2478/caim-2023-0004
Keywords
© 2023 Lorenzo Tentarelli, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
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.