Stability and instability of standing waves for a generalized Choquard equation with potential

Abstract

We are going to study the standing waves for a generalized Choquard equation with potential: $$-i{\partial }_{t}u-\Delta u+V(x)u=(|x{|}^{-\mu }\ast |u{|}^p)|u{|}^{p-2}u,in\mathbb{R}\times {\mathbb{R}}^3,$$ where $V(x)$ is a real function, $0<\mu <3$, $2-\mu /3<p<6-\mu$ and $\ast$ stands for convolution. Under suitable assumptions on the potential and appropriate frequency $\omega$ , the stability and instability of the standing waves $u=e^{i\omega t}\phi (x)$ are investigated .

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Cited by in corpus (2)

• On the classification of the spectrally stable standing waves of the Hartree problem
• Schrödinger-Newton-Hooke system in higher dimensions. Part I: Stationary states