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A Sharp Mass Threshold for Fractional Choquard Equations with Lower Hardy-Littlewood-Sobolev and L2-Critical Terms

  • Yongpeng Chen
  • Zhipeng Yang
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Abstract

For 1/2≤ s<1, we study a fractional Choquard equation with prescribed mass and nonlinearities at the lower Hardy-Littlewood-Sobolev and L2-critical exponents. The sharp Hardy-Littlewood-Sobolev and Choquard Gagliardo-Nirenberg inequalities determine an explicit critical mass a*. For 0<a≤ a*, we compute the exact infimum of the constrained energy and prove that it is not attained and that no normalized solution exists. For a>a*, the energy is unbounded from below on the mass sphere, while the Pohozaev set is nonempty.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026sharp,
  title = {{A Sharp Mass Threshold for Fractional Choquard Equations with Lower Hardy-Littlewood-Sobolev and \(L^2\)-Critical Terms}},
  author = {Yongpeng Chen and Zhipeng Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11284},
  eprint = {2609.11284},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11284},
}
RIS
TY  - UNPB
TI  - A Sharp Mass Threshold for Fractional Choquard Equations with Lower Hardy-Littlewood-Sobolev and L^2-Critical Terms
AU  - Yongpeng Chen
AU  - Zhipeng Yang
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11284
UR  - https://arxiv.org/abs/2609.11284
AB  - For 1/2≤ s<1, we study a fractional Choquard equation with prescribed mass and nonlinearities at the lower Hardy-Littlewood-Sobolev and L^2-critical exponents. The sharp Hardy-Littlewood-Sobolev and Choquard Gagliardo-Nirenberg inequalities determine an explicit critical mass a_*. For 0<a≤ a_*, we compute the exact infimum of the constrained energy and prove that it is not attained and that no normalized solution exists. For a>a_*, the energy is unbounded from below on the mass sphere, while the Pohozaev set is nonempty.
ER  -