Existence and bifurcation of positive solutions for fractional p$$ p $$-Kirchhoff problems

In this paper, we are interested in the existence and bifurcation of positive solutions for Kirchhoff-type eigenvalue problems involving the fractional p$$ p $$-Laplacian. First, we investigate the properties of the first eigenvalue for fractional p$$ p $$-Laplacian equations with weighted functions. Furthermore, by using fixed-point argument and modified global bifurcation theorem of Rabinowitz, together with topological degree theory, we obtain the existence of unbounded continuum of positive weak solutions to Kirchhoff-type equations with subcritical and critical nonlinearities, where the bifurcation emanates from (0,0)$$ \left(0,0\right) $$. It is worth mentioning that our main results fill in some gaps of the available results.