Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Citation:
Mathematics and Education in Mathematics, 2021, 045p - 054p
Abstract:
We consider the fractional Schrödinger-Hartree type equations and focus our study
on one particular case: the half-wave equation with nonlocal Hartree type interaction terms. The results we present can be divided in the following main topics:
a) existence, asymptotic properties of ground states and their linear stability/instability;
b) existence or explosion phenomena of the evolution flow with large data below/above the ground state barrier for the corresponding Cauchy problem for the
half-wave equation;
c) uniqueness of the ground states for the Schrödinger–Hartree type equations;
d) blow-up for mass-critical nonlinear Schrödinger (NLS) equation with non-local
Hartree type interaction terms. 2020 Mathematics Subject Classification: 35A15, 35B44, 35C07.
