Existence and bifurcation of positive solutions for fractional 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 (Formula presented.) -Laplacian. First, we investigate the properties of the first eigenvalue for fractional (Formula presented.) -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 (Formula presented.). It is worth mentioning that our main results fill in some gaps of the available results.