@article{Berikelashvili_Papukashvili_Peradze_2020, title={Iterative solution of a nonlinear static beam equation}, volume={72}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/833}, DOI={10.37863/umzh.v72i8.833}, abstractNote={<p>UDC 519.6</p> <p>The paper deals with a boundary-value problem for the nonlinear integro-differential equation $u’’’’-m \bigg(\int _0^l {u’}^2\,dx \bigg)u’’ &nbsp;= f(x, u, u’),$ $m(z)\geq \alpha&gt;0,$ $0\leq z &lt; \infty,$ modeling the static state of the Kirchhoff beam.<span class="Apple-converted-space">&nbsp;&nbsp;</span>The problem is reduced to a nonlinear integral equation, which is solved using the Picard iteration method.<span class="Apple-converted-space">&nbsp;&nbsp;</span>The convergence of the iteration process is established and the error estimate is obtained.</p&gt;}, number={8}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Berikelashvili , G. and Papukashvili , A. and Peradze, J.}, year={2020}, month={Aug.}, pages={1024-1033} }