EXISTENCE AND UNIQUENESS OF A SOLUTION AND ITERATIVE METHOD FOR SOLVING A FULLY FOURTH ORDER NONLINEAR BOUNDARY VALUE PROBLEM

Abstract

In this paper we study the fully fourth order nonlinear boundary value problem

                                                      .........................

where is continuous.

We reduce the problem to an operator equation for the right-hand side function. Under some easily verified conditions on this function in a specified bounded domain, we prove the contraction of the operator. This guarantees the existence and uniqueness of a solution of the problem and the convergence of an iterative method for finding it. Some examples demonstrate the applicability of the proposed approach and iterative method.