We establish constructive necessary and sufficient conditions of solvability and a scheme of construction of the solutions for a nonlinear boundary-value problem unsolved with respect to the derivative. We also suggest convergent iterative schemes for finding approximate solutions of this problem. As an example of application of the proposed iterative scheme, we find approximations to the solutions of periodic boundary-value problems for a Rayleigh-type equation unsolved with respect to the derivative, in particular, in the case of periodic problem for the equation used to describe the motion of satellites on elliptic orbits.

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关于导数未解决的非线性边界值问题

我们建立了可解性的建设性充分必要条件，以及关于导数未解决的非线性边值问题的解的构造方案。我们还建议使用收敛迭代方案来寻找这个问题的近似解。作为所提出的迭代方案的应用示例，我们找到了关于导数未求解的瑞利型方程的周期性边值问题的近似解，特别是在用于方程的周期性问题的情况下描述卫星在椭圆轨道上的运动。