Sign-changing solutions of a class of nonlocal quasilinear elliptic boundary value problems

This paper is concerned with nonlocal Kirchhoffʼs equation{−(a+b∫Ω|∇u|2)Δu=f(x,u)in Ω,u=0on ∂Ω, via variational methods and invariant sets of descent flow. We obtain existence of signed and sign-changing solutions with asymptotically 3-linear bounded nonlinearity.