Adomian decomposition method in the theory of nonlinear boundary-value problems unsolved with respect to the derivative

We find constructive necessary and sufficient conditions for solvability and a scheme for construction of solutions of a nonlinear boundary-value problem unsolved with respect to the derivative. On the basis of the Adomian decomposition method, convergent iterative schemes for finding approximations of solutions of a nonlinear boundary-value problem unsolved with respect to the derivative are constructed. As examples of the application of the constructed iterative scheme, we find approximations of the solutions of a periodic boundary-value problem for Rayleigh-type equations unsolved with respect to the derivative including the case of a periodic problem for the equation that determines the motion of a satellite in an elliptical orbit.