The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity

DOI10.1016/S0294-1449(02)00022-7zbMath1028.35137OpenAlexW1985046969MaRDI QIDQ1810734

Gianfausto Dell'Antonio, Riccardo Adami, Rodolfo Figari, Alessandro Teta

Publication date: 9 June 2003

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2003__20_3_477_0

zbMATH Keywords

Cauchy problempoint interactions3D nonlinear Schrödinger equationexistence and uniqueness in energy spacenonlinear Dirac delta potentials

Mathematics Subject Classification ID

Related Items (28)

The point-like limit for a NLS equation with concentrated nonlinearity in dimension three ⋮ Existence, structure, and robustness of ground states of a NLSE in 3D with a point defect ⋮ Competing nonlinearities in NLS equations as source of threshold phenomena on star graphs ⋮ Global attractor for 3D Dirac equation with nonlinear point interaction ⋮ On global well-posedness for Klein-Gordon equation with concentrated nonlinearity ⋮ Bound states of the NLS equation on metric graphs with localized nonlinearities ⋮ Asymptotic stability for standing waves of a NLS equation with subcritical concentrated nonlinearity in dimension three: neutral modes ⋮ Ground states for the planar NLSE with a point defect as minimizers of the constrained energy ⋮ Stability of the standing waves of the concentrated NLSE in dimension two ⋮ Doubly nonlinear Schrödinger ground states on metric graphs ⋮ Spectral stability and instability of solitary waves of the Dirac equation with concentrated nonlinearity ⋮ A general review on the NLS equation with point-concentrated nonlinearity ⋮ On global attraction to solitary waves for the Klein–Gordon equation with concentrated nonlinearity ⋮ Well–posedness of the three–dimensional NLS equation with sphere–concentrated nonlinearity ⋮ Numerical approximation of the Schrödinger equation with concentrated potential ⋮ The NLS equation in dimension one with spatially concentrated nonlinearities: the pointlike limit ⋮ Scattering for the 𝐿² supercritical point NLS ⋮ Orbital and asymptotic stability for standing waves of a nonlinear Schrödinger equation with concentrated nonlinearity in dimension three ⋮ NLS ground states on metric graphs with localized nonlinearities ⋮ On the standing waves of the Schrödinger equation with concentrated nonlinearity ⋮ On global attraction to stationary states for wave equations with concentrated nonlinearities ⋮ The Schrödinger-Maxwell system with Dirac mass ⋮ Blow-up for the pointwise NLS in dimension two: absence of critical power ⋮ Prescribed mass ground states for a doubly nonlinear Schrödinger equation in dimension one ⋮ Well-posedness of the two-dimensional nonlinear Schrödinger equation with concentrated nonlinearity ⋮ Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one ⋮ The One-Dimensional Dirac Equation With Concentrated Nonlinearity ⋮ The action of Volterra integral operators with highly singular kernels on Hölder continuous, Lebesgue and Sobolev functions

Cites Work

• Nonlinear Schrödinger equations and sharp interpolation estimates
• The evolution operator for time-dependent potentials of zero radius
• Quadratic forms for singular perturbations of the Laplacian
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Invariance Results for Delay and Volterra Equations in Fractional Order Sobolev Spaces
• Almost-periodic behavior of solutions of a nonlinear Volterra system.
• A class of nonlinear Schrödinger equations with concentrated nonlinearity
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity