On the approximate solution of a Kirchhoff type static beam equation

The paper deals with a boundary value problem for the nonlinear integro-differential equation u⁗−m(∫0lu′2dx)u″=f(x,u), m(z)≥α>0m(z)≥α>0, 0≤z<∞0≤z<∞, modelling the static state of the Kirchhoff beam. The problem is reduced to an integral equation which is solved using the Picard iteration method. The convergence of the iteration process is established and the error estimate is obtained.