Fixed-spinor radial solutions of a perturbed Euclidean spinorial Yamabe equation

We study the perturbed Euclidean spinorial Yamabe equation $$D_{g_{{\mathbb{R}}^n}}\psi =\frac{n}{2}(1+\epsilon K(x))\mathrm{\mid }\psi {\mathrm{\mid }}^{2^{\ast }-2}\psi \text{on }{\mathbb{R}}^n,n\ge 2,$$where $2^{\ast }:=2n\mathrm{/}(n-1)$, $\epsilon >0$ 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.