Electron. J. Differential Equations, Vol. 2026 (2026), No. 63, pp. 1-19.

Existence of ground state solutions for fractional Choquard systems

Hui Xu, Yulin Zhao

Abstract:
This article studies the existence of ground state solutions for nonlinear fractional Choquard systems. Under Berestycki-Lions type assumptions on the nonlinearity, we develop a variational framework in fractional Sobolev spaces to tackle the system. The main difficulties arising from the nonlocality of the fractional Laplacian and the associated loss of compactness are overcome by combining the concentration-compactness principle, the Pohozaev identity, and s-harmonic extension techniques. We establish the existence of ground state solutions of the fractional Choquard systems, and a numerical example is provided to verify the main result obtained in this paper.

Submitted May 31, 2026. Published August 19, 2026.
Math Subject Classifications: 35J50, 35J60, 35J61, 35A15.
Key Words: Fractional Choquard system; ground state solution; Pohozaev identity; concentration-compactness principle.
DOI: 10.58997/ejde.2026.63

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Hui Xu
School of Science
Hunan University of Technology
Zhuzhou, 412007 Hunan, China
email: 2771575875@qq.com
Yulin Zhao
School of Science
Hunan University of Technology
Zhuzhou, 412007 Hunan, China
email: zhaoylch@sina.com

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