Positive and negative solutions of a class of nonlocal problems

The existence of nontrivial solutions of Kirchhoff type equations is an important nonlocal quasilinear problem. In this paper, still by using the invariant sets of descent flow, we obtain positive and negative solutions of a class of nonlocal quasilinear elliptic boundary value problems as follows: {−(a+b∫Ω|∇u|2)Δu=f(x,u),in Ω;u=0,on ∂Ω.