The Unique Solvability and Approximation of BVP for a Nonlinear Fourth Order Kirchhoff Type Equation

Abstract

We reduce a nonlinear fourth order equation of Kirchhoff type to an operator equation for a nonlinear term and establish sufficient conditions for the unique solvability of the original problem. Approximate solutions of the problem are derived by a fast converging iterative method. Numerical examples confirm theoretical results and demonstrate the efficiency of the approach used.