@article{Samoilenko_Chuiko_Nesmelova_2020, title={Nonlinear boundary-value problems unsolved with respect to the derivative}, volume={72}, url={http://umj.imath.kiev.ua/index.php/umj/article/view/5986}, DOI={10.37863/umzh.v72i8.5986}, abstractNote={<p>UDC 517.9</p> <p>We found constructive necessary and sufficient solvability conditions as well as a scheme of construction of solutions for a nonlinear boundary-value problem that is not solved with respect to the derivative.<span class="Apple-converted-space"> </span>We also suggested concurrent iterative schemes for finding approximations of solutions of this problem.<span class="Apple-converted-space"> </span>As an example of application of the constructed iterative scheme, we found approximations of solutions of periodic boundary-value problems for a Rayleigh-type equation not solved with respect to the derivative, in particular, in the case of a periodic problem for the equation that determines the satellite motion in an elliptical orbit.</p>}, number={8}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={SamoilenkoA. M. and Chuiko S. M. and Nesmelova O. V.}, year={2020}, month={Aug.}, pages={1106-1118} }