Calculus of Variations and Geometric Measure Theory

R. Carlone - D. Finco - L. Tentarelli

Nonlinear singular perturbations of the fractional Schrödinger equation in dimension one

created by tentarelli on 07 Jul 2022


Published Paper

Inserted: 7 jul 2022
Last Updated: 7 jul 2022

Journal: Nonlinearity
Volume: 32
Number: 8
Pages: 3112-3143
Year: 2019
Doi: 10.1088/1361-6544/ab1273

ArXiv: 1805.06952 PDF


The paper discusses nonlinear singular perturbations of delta type of the fractional Schr\"odinger equation $\imath\partial_t\psi=\left(-\triangle\right)^s\psi$, with $s\in(\frac{1}{2},1]$, in dimension one. Precisely, we investigate local and global well posedness (in a strong sense), conservations laws and existence of blow-up solutions and standing waves.