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 ) Δ u = f ( x , u ) in Ω , u = 0 on ∂ 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.