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

Yupeng Li; Binhua Feng; Zhiqian He; Yupeng Li; Binhua Feng; Zhiqian He

doi:10.3934/cam.2026005

Communications in Analysis and Mechanics

2026, Volume 18, Issue 1: 117-141. doi: 10.3934/cam.2026005

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Research article

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

1.
Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China
2.
School of Mathematics and Physics, Qinghai University, Xining, 810016, China

Received: 04 July 2025 Revised: 10 September 2025 Accepted: 15 December 2025 Published: 03 February 2026
35Q55, 35A15

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.
- standing waves,
- stability,
- instability,
- mixed fractional Laplacians,
- ground state
Citation: Yupeng Li, Binhua Feng, Zhiqian He. Stability and instability of standing waves for the Schrödinger-Choquard equation with mixed fractional Laplacians[J]. Communications in Analysis and Mechanics, 2026, 18(1): 117-141. doi: 10.3934/cam.2026005

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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.

References

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