najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2018-9-2-187-195najo-691Research ArticleMATHEMATICSМАТЕМАТИКАAn introduction to the two-dimensional Schrodinger equation with nonlinear¨ point interactionsCarloneR.

via Cinthia, I-80126, Napoli

raffaele.carlone@unina.itCorreggiM.

P.le Aldo Moro, 5, 00185, Roma

michele.correggi@gmail.comTentarelliL.

P.le Aldo Moro, 5, 00185, Roma

tentarelli@mat.uniroma1.itUniversita “Federico II” di Napoli, Dipartimento di Matematica e Applicazioni “R. Caccioppoli”Italy“Sapienza” Universita di Roma, Dipartimento di Matematica P.le Aldo MoroItaly“Sapienza” Universita di Roma, Dipartimento di MatematicaItaly20181208202592187195Copyright © Carlone R., Correggi M., Tentarelli L., 20252025Carlone R., Correggi M., Tentarelli L.Carlone R., Correggi M., Tentarelli L.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/691

We present an introduction to the nonlinear Schrodinger equation (NLSE) with concentrated nonlinearities in¨   R2. Precisely, taking a cue from the linear problem, we sketch the main challenges and the typical difficulties that arise in the two-dimensional case, and mention some recent results obtained by the authors on local and global well-posedness.

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The authors declare that there are no conflicts of interest present.