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