Stability and instability of standing waves for the Schrödinger-Choquard equation with mixed fractional Laplacians

Abstract

In this paper, we investigate the stability and instability of standing waves for the Schrödinger- Choquard equation with mixed fractional Laplacians. We first establish the existence and stability of normalized standing waves in theL²-subcritical case. Subsequently, we prove the existence and strong instability of normalized ground state standing waves in theL²-supercritical case.

Keywords

standing waves / stability / instability / mixed fractional Laplacians / ground state

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