Weighted potential and Green systems with Dini coefficients and primitive growth
Abstract
We prove a nonexistence theorem for positive potential systems with continuous coefficients satisfying distributional Euler lower bounds and a uniform Dini modulus on normalized logarithmic dilations. The nonlinearities have positive lower logarithmic derivatives and positive primitive-to-endpoint ratios. The common radial kernel is comparable with a Riesz kernel. A localized transport identity, a primitive pressure estimate and implicit amplitude normalization give uniform local energy bounds and a dilation contradiction. And we treats the genuine Green kernel of −Δ+V for nonnegative potentials under annular and Newton composition budgets and a strict gap corrected by the relative Green dilation defect. Relative endpoint differences and an exact virtual-energy cancellation retain local nonlinear energy as the only initial energy hypothesis. Independent representation arguments give these consequences, including even integer orders without initial tails. A compact family of normalized responses also yields universal interior bounds without regular variation.
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BibTeX
@misc{hu2026weighted,
title = {{Weighted potential and Green systems with Dini coefficients and primitive growth}},
author = {Hongtao Hu and Zhouyu Long and Wenming Zou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26656},
eprint = {2610.26656},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26656},
}
RIS
TY - UNPB
TI - Weighted potential and Green systems with Dini coefficients and primitive growth
AU - Hongtao Hu
AU - Zhouyu Long
AU - Wenming Zou
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26656
UR - https://arxiv.org/abs/2610.26656
AB - We prove a nonexistence theorem for positive potential systems with continuous coefficients satisfying distributional Euler lower bounds and a uniform Dini modulus on normalized logarithmic dilations. The nonlinearities have positive lower logarithmic derivatives and positive primitive-to-endpoint ratios. The common radial kernel is comparable with a Riesz kernel. A localized transport identity, a primitive pressure estimate and implicit amplitude normalization give uniform local energy bounds and a dilation contradiction. And we treats the genuine Green kernel of −Δ+V for nonnegative potentials under annular and Newton composition budgets and a strict gap corrected by the relative Green dilation defect. Relative endpoint differences and an exact virtual-energy cancellation retain local nonlinear energy as the only initial energy hypothesis. Independent representation arguments give these consequences, including even integer orders without initial tails. A compact family of normalized responses also yields universal interior bounds without regular variation.
ER -