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The fractional Hénon-Lane-Emden conjecture and some critical nonexistence phenomena
Abstract
We refine the proof method for the Hénon-Lane-Emden system and extend it to fractional orders 0<s<1, proving subcritical nonexistence of positive classical solutions. And we find examples with 0<s<1/2 and fixed nonzero weights for which existence and nonexistence occur at different points of the same critical hyperbola.
Related
- Sharp Adams inequality for Critical Biharmonic Equations with Hardy--Hénon Weights in ℝ4
- The Hénon equation beyond the critical Sobolev exponent
- The polyharmonic Hénon--Lane--Emden conjecture
- Nonradial entire solutions of the critical Hénon equation for every α>2
- Unique continuation, nonexistence and bubbling for the critical p-Laplace equation in the plane
BibTeX
@misc{li2026fractional,
title = {{The fractional Hénon-Lane-Emden conjecture and some critical nonexistence phenomena}},
author = {Kui Li and Haoyang Lu and Zhitao Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22802},
eprint = {2610.22802},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22802},
}
RIS
TY - UNPB
TI - The fractional Hénon-Lane-Emden conjecture and some critical nonexistence phenomena
AU - Kui Li
AU - Haoyang Lu
AU - Zhitao Zhang
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.22802
UR - https://arxiv.org/abs/2610.22802
AB - We refine the proof method for the Hénon-Lane-Emden system and extend it to fractional orders 0<s<1, proving subcritical nonexistence of positive classical solutions. And we find examples with 0<s<1/2 and fixed nonzero weights for which existence and nonexistence occur at different points of the same critical hyperbola.
ER -