Sign-changing solutions for p-Laplacian Kirchhoff-type equations with critical exponent

In this article we are concerned with the p-Laplacian Kirchhoff-type problem with critical exponent: {-(a + b integral |del u|(p))Delta p(u) = lambda f (x, u) + |u| p*(-2)(u), in Omega, u = 0, on.partial derivative Omega, where a, b > 0 are constants, lambda > 0 is a paramete, Omega is a bounded domain in R-N with smooth boundary. partial derivative Omega, 1 < p < N/2, p* = Np/N-p is the critical sobolev exponent of the imbedding W-0(1),(p) (Omega) subset of L-p* (Omega), Delta(p)u = div (|del u|(p-2) del u). Under certain assumptions f, by using constraint variational method, topological degree and quantitative deformation lemma we showthe existence of a least energy sign-changing solution to this problem, which is strictly larger than twice of that of any ground state solution.