Least energy sign-changing solutions of Kirchhoff equation on bounded domains

We deal with sign-changing solutions for the Kirchhoff equation {-(a + b integral(Omega)vertical bar del u vertical bar(2)dx)Delta u = lambda u + mu vertical bar mu vertical bar(2)u, x is an element of Omega, u = 0, x is an element of partial derivative Omega, where a, b > 0 and lambda, mu is an element of R being parameters, Omega subset of R-3 is a bounded domain with smooth boundary partial derivative Omega. Combining Nehari manifold method with the quantitative deformation lemma, we prove that there exists mu* > 0 such that above problem has at least a least energy sign-changing (or nodal) solution if lambda < alpha lambda(1) and mu > mu*, where lambda(1) > 0 is the first eigenvalue of (-Delta u, H-0(1)(Omega)). It is noticed that the nonlinearity lambda u + mu vertical bar u vertical bar(2)u fails to satisfy super-linear near zero and super-three-linear near infinity, respectively.