Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 24, pp. 1-23.

Title: Blow-up criteria and instability of standing waves for the fractional Schrodinger Poisson equation
       
Authors: Yichun Mo (Northwest Normal Univ., Lanzhou, China)
         Min Zhu (Nanjing Forestry Univ., Nanjing, Jiangsu, China)
         Binhua Feng (Northwest Normal Univ., Lanzhou, China)

Abstract:
In this article, we consider blow-up criteria and instability of standing
waves for the fractional Schrodinger-Poisson equation.
By using the localized virial estimates, we establish the blow-up
criteria for non-radial solutions in both mass-critical and mass-supercritical cases.
Based on these blow-up criteria and three variational characterizations of the
ground state, we prove that the standing waves are strongly unstable.
These obtained results extend the corresponding ones presented in the literature. 

Submitted October 28, 2022. Published March 06, 2023.
Math Subject Classifications: 35J60, 35Q55, 35J20.
Key Words: Schrodinger-Poisson equation; blow-up criteria; strong instability;
    standing waves; well-posedness.