On the reduction of an autonomous nonlinear boundary value problem unsolved with respect to the derivative to the first-order critical case

Constructive solvability conditions and a scheme for constructing solutions of an autonomous nonlinear boundary value problem unsolved with respect to the derivative have been found. A convergent iterative scheme for Finding approximations to the solutions of a nonlinear autonomous nonlinear boundary value problem unsolved with respect to the derivative was constructed by reducing the problem to the First-order critical case. As an example of application of the constructed iterative scheme, approximations to the solutions of a periodic boundary value problem for the autonomous Lotka–Volterra equation were determined.