Nonlinear boundary-value problems unsolved with respect to the derivative - Samoilenko, A. M.; Chuiko, S. M.; Nesmelova, O. V. (Ukrains’kyi Matematychnyi Zhurnal, 2020)
UDC 517.9We 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.  We also suggested concurrent iterative schemes for finding approximations of solutions of this problem.  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.