Advanced Mathematical Physics ProblemsNonlinear Partial Differential EquationsStability and Controllability of Differential Equations
Yupeng Li, Binhua Feng, Zhiqiang He
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 the $ L^2 $-subcritical case. Subsequently, we prove the existence and strong instability of normalized ground state standing waves in the $ L^2 $-supercritical case.
Citation format
LI, Yupeng; FENG, Binhua; HE, Zhiqiang. Stability and instability of standing waves for the schrödinger-choquard equation with mixed fractional laplacians. Communications in Analysis and Mechanics, 2026, 18(1): 117–141.