Existence results and iterative method for solving a nonlinear biharmonic equation of Kirchhoff type

In this paper, for investigating a boundary value problem for a nonlinear biharmonic equation of Kirchhoff type, we propose an efficient approach by the reduction of the problem to an operator equation for the nonlinear part of the equation. The result is that we have established the existence and uniqueness of a solution under some easily verified conditions. Also, we propose an iterative method for finding the solution. Some examples demonstrate the applicability of the theoretical results and the efficiency of the iterative method.