Blow-up criteria and instability of standing waves for the fractional Schrodinger Poisson equation

[摘要] 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.

[学科分类] 数学（综合）

[关键词] Schrodinger-Poisson equation;blow-up criteria;strong instability;standing waves;well-posedness