POHOZAEV MINIMIZERS FOR FRACTIONAL CHOQUARD EQUATIONS WITH MASS-SUPERCRITICAL NONLINEARITY

doi:10.1007/s10473-026-0111-8

Abstract

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.

Key words: nonlinear fractional Choquard equation, double nonlocality, super-critical mass, normalized solutions, Pohozaev minimizer

CLC Number:

35A01

Liju WU¹, Jiankang XIA^2,3,*. POHOZAEV MINIMIZERS FOR FRACTIONAL CHOQUARD EQUATIONS WITH MASS-SUPERCRITICAL NONLINEARITY[J].Acta mathematica scientia,Series B, 2026, 46(1): 164-188.

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