Least energy sign-changing solutions of Kirchhoff-type equation with critical growth

In this paper, we study the Kirchhoff-type equation -(a + b integral(Omega)vertical bar del u|(2) dx)Delta u = vertical bar u vertical bar(4)u + lambda f(x, u), x is an element of Omega, u = 0, x is an element of partial derivative Omega, where Omega subset of R-3 is a bounded domain with a smooth boundary partial derivative Omega, lambda, a, b > 0. Under suitable conditions on f, by using the constraint variational method and the quantitative deformation lemma, if lambda is large enough, we obtain a least energy sign-changing (or nodal) solution u(b) to this problem for each b > 0. Moreover, we prove that the energy of u(b) is strictly larger than twice that of the ground state solutions. Published under license by AIP Publishing.