PreprintarXiv licencearXiv
Fixed-spinor radial solutions of a perturbed Euclidean spinorial Yamabe equation
Abstract
We study the perturbed Euclidean spinorial Yamabe equation Dgℝnψ = n/2(1+ε K(x)) |ψ|2*−2ψ on ℝn, n≥2,where 2*:=2n/(n−1), ε>0 is a small parameter and K is a prescribed radial function. We establish a finite-dimensional reduction within a radial spinor space determined by a fixed unit spinor, reducing the problem to the analysis of a function of the dilation parameter. Under suitable assumptions on K, we obtain explicit existence criteria for solutions with this prescribed spinorial structure, together with a multiplicity criterion yielding solutions associated with distinct scales. These criteria are expressed in terms of the behavior of K at the origin and weighted integral quantities.
Related
- Existence of multi-peak solutions for singularly perturbed problems in the zero-mass case
- Singular solutions from simple Euclidean Jordan algebras
- Existence of positive solutions to anisotropic elliptic equations in the entire Euclidean space
- Local rigidity of conformally Euclidean metrics for the anisotropic Helmholtz equation at fixed energy
- Hypergeometric Solutions for Variants of the q-Hypergeometric Equation
BibTeX
@misc{li2026fixedspinor,
title = {{Fixed-spinor radial solutions of a perturbed Euclidean spinorial Yamabe equation}},
author = {Ting Li and Zhongwei Tang and Yuhang Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21471},
eprint = {2610.21471},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21471},
}
RIS
TY - UNPB
TI - Fixed-spinor radial solutions of a perturbed Euclidean spinorial Yamabe equation
AU - Ting Li
AU - Zhongwei Tang
AU - Yuhang Zhang
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21471
UR - https://arxiv.org/abs/2610.21471
AB - We study the perturbed Euclidean spinorial Yamabe equation D_g_ℝ^nψ = n/2(1+ε K(x)) |ψ|^2^*−2ψ on ℝ^n, n≥2,where 2^*:=2n/(n−1), ε>0 is a small parameter and K is a prescribed radial function. We establish a finite-dimensional reduction within a radial spinor space determined by a fixed unit spinor, reducing the problem to the analysis of a function of the dilation parameter. Under suitable assumptions on K, we obtain explicit existence criteria for solutions with this prescribed spinorial structure, together with a multiplicity criterion yielding solutions associated with distinct scales. These criteria are expressed in terms of the behavior of K at the origin and weighted integral quantities.
ER -