POHOZAEV MINIMIZERS FOR FRACTIONAL CHOQUARD EQUATIONS WITH MASS-SUPERCRITICAL NONLINEARITY

  • Liju WU1 ,
  • Jiankang XIA2 ,
  • 3 ,
  • *
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  • 1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, China;
    2. Shenzhen Research Institute of Northwestern Polytechnical University, Shenzhen 518057, China;
    3. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, China
Liju Wu, E-mail: 15035381897@163.com

Received date: 2024-09-02

  Revised date: 2025-03-11

  Online published: 2026-05-22

Supported by

Guangdong Basic and Applied Basic Research Foundation (2022A1515012138) and the NSFC (12271436, 12371119). J. Xia was supported by the Natural Science Basic Research Program of Shaanxi (2022JC-04).

Abstract

We investigate the constrained fractional Choquard equation
$\begin{align*} \begin{cases} (-\Delta)^s u=(I_{\alpha}*F(u))F'(u)-\mu u,\; \text{ in } \, \mathbb R^N,\\ u\in H^s(\mathbb R^N),\\ \displaystyle \int_{\mathbb R^N}|u|^2\mathrm{d} x=m, \end{cases} \end{align*}$
where $m>0$, $N> 2s $ with $s\in(0,1)$ being the order of the fractional Laplacian operator and $I_\alpha$ for $\alpha\in(0,N)$ denotes the Riesz potential. The parameter $\mu\in\mathbb R$ appears as a Lagrange multiplier. By imposing general mass-supercritical conditions on \(F\), we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold. Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity, a challenge that remains unsolved for this doubly nonlocal equation.

Cite this article

Liju WU1 , Jiankang XIA2 , 3 , * . POHOZAEV MINIMIZERS FOR FRACTIONAL CHOQUARD EQUATIONS WITH MASS-SUPERCRITICAL NONLINEARITY[J]. Acta mathematica scientia, Series B, 2026 , 46(1) : 164 -188 . DOI: 10.1007/s10473-026-0111-8

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