Abstract: In engineering practice, the fourth-order elliptic equation of Kirchhoff type derives from the model of the suspension bridge. In the paper, two theorems on the existence and multiplicity of sign-changing solutions for some fourth-order elliptic equations of Kirchhoff type are proved by using the descending flow invariant set method under the assumption that the nonlinear term is odd and superquadric at infinity. The main results and the proofs are different from those in literatures.

Key words: fourth-order elliptic boundary value problems of Kirchhoff type, sign-changing solutions, critical points