Continuums of positive solutions for classes of non-autonomous and non-local problems with strong singular term

In this paper, we show existence of $\mathit{\text{continuums}}$ of positive solutions for non-local quasilinear problems with strongly-singular reaction term on a bounded domain in ${\mathbb{R}}^N$ with $N\ge 2$. We approached non-autonomous and non-local equations by applying the Bifurcation Theory to the corresponding $ϵ$-perturbed problems and using a comparison principle for $W_{\mathrm{l}\mathrm{o}\mathrm{c}}^{1,p}(\mathrm{\Omega })$-sub and supersolutions to obtain qualitative properties of the $ϵ$-$\mathit{\text{continuum}}$ limit. Moreover, this technique empowers us to study a strongly-singular and non-homogeneous Kirchhoff problem to get the existence of a $\mathit{\text{continuum}}$ of positive solutions.