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

Abstract

In this paper, we are interested in the existence and bifurcation of positive solutions for Kirchhoff‐type eigenvalue problems involving the fractional ‐Laplacian. First, we investigate the properties of the first eigenvalue for fractional ‐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 . It is worth mentioning that our main results fill in some gaps of the available results.