Well posedness of the nonlinear Schrödinger equation with isolated singularities

DOI10.1016/j.jde.2021.10.017zbMath1479.35263arXiv2012.12391OpenAlexW3209341291MaRDI QIDQ2242548

Domenico Finco, Claudio Cacciapuoti, Diego Noja

Publication date: 9 November 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2012.12391

zbMATH Keywords

nonlinear Schrödinger equationsingular solutionspoint interactions

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Schrödinger operator, Schrödinger equation (35J10) Singularity in context of PDEs (35A21)

Related Items (12)

On stability and instability of standing waves for 2d-nonlinear Schrödinger equations with point interaction ⋮ Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect ⋮ Ground states for the planar NLSE with a point defect as minimizers of the constrained energy ⋮ Doubly nonlinear Schrödinger ground states on metric graphs ⋮ NLS ground states on the half-line with point interactions ⋮ Failure of scattering for the NLSE with a point interaction in dimension two and three ⋮ A general review on the NLS equation with point-concentrated nonlinearity ⋮ Mini-workshop: Zero-range and point-like singular perturbations: for a spillover to analysis, PDE and differential geometry. Abstracts from the mini-workshop held October 2--8, 2022 ⋮ Blow-up and instability of standing waves for the NLS with a point interaction in dimension two ⋮ Well–posedness of the three–dimensional NLS equation with sphere–concentrated nonlinearity ⋮ Generalised solutions to linear and non-linear Schrödinger-type equations with point defect: Colombeau and non-Colombeau regimes ⋮ Singular solution of the Hartree equation with a delta potential

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