Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains

We are interested in the existence of least energy sign-changing solutions for a class of Kirchhoff-type problem in bounded domains. Because the so-called nonlocal term b(integral(Omega)vertical bar del u vertical bar(2)dx)Delta u is involving in the equation, the variational functional of the equation has totally different properties from the case of b = 0. Combining constraint variational method and quantitative deformation lemma, we prove that the problem possesses one least energy sign-changing solution u(b). Moreover, we show that the energy of u(b) is strictly larger than the ground state energy. Finally, we regard b as a parameter and give a convergence property of ub as b SE arrow 0. (C) 2015 Elsevier Inc. All rights reserved.