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arXiv · 2512.00922

Normalized Solutions and Semiclassical Concentration for Upper-Critical Fractional Choquard Equations

Yergen Aikyn·Yongpeng Chen·Michael Ruzhansky·Zhipeng Yang
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Abstract

We study a fractional Choquard equation with an upper-critical Hartree term, an $L^2$-supercritical Hartree perturbation, and a semiclassical potential under a prescribed $L^2$-mass constraint. The potential is bounded and nonnegative, has a nonempty zero set, and has a positive lower limit at infinity. For every prescribed mass and all sufficiently small semiclassical parameters, we prove the existence of a pair of normalized solutions $\pm u_\varepsilon$ with a negative Lagrange multiplier. The proof combines a strict energy bound below the critical one-bubble level, compactness modulo translations for the autonomous ground-state set, a simultaneous cutoff of both Hartree terms, and a localized constrained mountain-pass argument. Moreover, suitable translates of $u_\varepsilon$ converge strongly in $H^s(\mathbb{R}^N)$ to a positive autonomous ground state, and the corresponding concentration points approach the zero set of the potential as $\varepsilon\to0$.

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Yergen Aikyn, Yongpeng Chen, Michael Ruzhansky, Zhipeng Yang. 2026-07-31. Normalized Solutions and Semiclassical Concentration for Upper-Critical Fractional Choquard Equations. https://arxiv.org/abs/2512.00922

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