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

In this paper, we show existence of continuums (closed and connected sets in R x C-0 ((Omega) over bar)) of positive solutions for non-local quasilinear problems with strongly-singular reaction term on a bounded domain in R-N with N >= 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-loc(1,p)(Omega)-sub and supersolutions to obtain qualitative properties of the epsilon-continuum limit. Moreover, this technique empowers us to study a strongly-singular and non-homogeneous Kirchhoff problem to get the existence of a continuum of positive solutions. (C) 2019 Elsevier Masson SAS. All rights reserved.