Positive solutions for a Kirchhoff problem with vanishing nonlocal term

In this paper we study the Kirchhoff problem{−m(‖u‖2)Δu=f(u)in Ω,u=0on ∂Ω, in a bounded domain, allowing the function m to vanish in many different points. Under an appropriated area condition, by using a priori estimates, truncation techniques and variational methods, we prove a multiplicity result of positive solutions which are ordered in the H01(Ω)-norm.