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Research Article | Open Access

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

Yupeng Li1, Binhua Feng1( ), Zhiqian He2
Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China
School of Mathematics and Physics, Qinghai University, Xining, 810016, China
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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.

Keywords

standing wavesstabilityinstabilitymixed fractional Laplaciansground state
CLC number: 35Q55, 35A15

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Communications in Analysis and Mechanics
Volume 18 Issue 1,
March 2026
Pages 117-141
DOI: 10.3934/cam.2026005

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Cite this article:
Li Y, Feng B, He Z. 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. https://doi.org/10.3934/cam.2026005

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Received: 04 July 2025
Revised: 10 September 2025
Accepted: 15 December 2025
Published: 03 February 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)