2023
DOI: 10.58997/ejde.2023.24
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Blow-up criteria and instability of standing waves for the fractional Schrodinger Poisson equation

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.

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