Existence and multiplicity of solutions for fourth-order elliptic Kirchhoff equations with potential term

In this paper, we consider the existence of nodal and multiple solutions for non-linear fourth-order elliptic Kirchhoff equationwhere . Making use of Mountain Pass Theorem, we establish existence of a non-trivial solution when is superlinear and subcritical. We also prove the existence of a positive solution, a negative solution and a nodal solution by using invariant sets of descending flow. Moreover, we show this nodal solution has a least energy and precisely two nodal domains. Under additional assumptions on , we obtain three existence results of infinitely many non-trivial and radial solutions via Fountain Theorem and Dual Fountain Theorem. We also show the existence of infinitely many nodal solutions by means of a sign-changing critical theorem.