What question did this study set out to answer?

This research addresses the existence of solutions for a critical Choquard equation related to the Hardy–Littlewood–Sobolev inequality.

February 12, 2026Open Access

Nonlocal problems with Hardy–Littlewood–Sobolev critical exponent and Hardy potential

Key Points

This research addresses the existence of solutions for a critical Choquard equation related to the Hardy–Littlewood–Sobolev inequality.
Utilized variational methods
Explored existence results for critical equations
Investigated perturbation terms
Analyzed nonlocal minimization problems
Proved existence results for various perturbations
Derived significant estimates related to minimization problems
Extended findings to different perturbation scenarios

Abstract

Abstract We are concerned with a Brezis–Nirenberg-type problem for a critical Choquard equation, in the sense of Hardy–Littlewood–Sobolev inequality, and with the Hardy potential in a smooth bounded domain. By exploiting variational methods, we obtain existence results, which extend to different perturbation terms. Some estimates of independent interest about a nonlocal minimization problem are also derived.

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Gu et al. (Wed,) studied this question.

synapsesocial.com/papers/698d6f0d5be6419ac0d551f6 https://doi.org/https://doi.org/10.1007/s00033-026-02732-w

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