The paper is mainly devoted to the theory of duality of boundary value problems (BVPs) for differential inclusions of higher orders. For this, on the basis of the apparatus of locally conjugate mappings in the form of Euler–Lagrange-type inclusions and transversality conditions, sufficient optimality conditions are obtained. Wherein remarkable is the fact that inclusions of Euler–Lagrange type for prime and dual problems are “duality relations”. To demonstrate this approach, the optimization of some third-order semilinear BVPs and polyhedral fourth-order BVPs is considered. These problems show that sufficient conditions and dual problems can be easily established for problems of any order.

本文主要针对高阶微分包含的边值问题（BVP）的对偶理论。为此，在以欧拉-拉格朗日型包含物和横向条件为形式的局部共轭映射的设备的基础上，可以获得足够的最优性条件。其中引人注目的是，素数和对偶问题的欧拉-拉格朗日类型的包含物是“对偶关系”。为了证明这种方法，考虑了对某些三阶半线性BVP和多面体四阶BVP的优化。这些问题表明，对于任何顺序的问题，都可以轻松地建立充分的条件和双重问题。