On Fourth-Order Elliptic Equations of Kirchhoff Type with Dependence on the Gradient and the Laplacian

We consider a nonlocal fourth-order elliptic equation of Kirchhoff type with dependence on the gradient and Laplacian , in ,, , on , where , are positive constants. We will show that there exists such that the problem has a nontrivial solution for through an iterative method based on the mountain pass lemma and truncation method developed by De Figueiredo et al., 2004.