Sign-changing solutions for fourth-order elliptic equations of Kirchhoff type with critical exponent

Abstract

In this paper, we study the existence of ground state sign-changing solutions for the following fourth-order elliptic equations of Kirchhoff type with critical exponent. More precisely, we consider {Delta(2)u - (1 + b integral(Omega)vertical bar del u vertical bar(2)dx) Delta u = lambda f (x, u) + vertical bar u vertical bar(2**-2)u in Omega, u = Delta u = 0 on partial derivative Omega, where Delta(2) is the biharmonic operator, N = {5, 6, 7}, 2** = 2N/(N - 4) is the Sobolev critical exponent and Omega subset of R-N is an open bounded domain with smooth boundary and b, lambda are some positive parameters. By using constraint variational method, topological degree theory and the quantitative deformation lemma, we prove the existence of ground state sign-changing solutions with precisely two nodal domains.