Sufficient conditions for the existence and uniqueness of a classical solution to a nonlocal problem for a system of Sobolev-type differential equations with integral condition are established. By introducing a new unknown function, we reduce the considered problem to an equivalent problem consisting of a nonlocal problem for the system of hyperbolic equations of second order with a functional parameter and an integral relation. We propose the algorithm for finding an approximate solution to the investigated problem and prove its convergence.

中文翻译：

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具有积分条件的Sobolev型微分方程组非局部问题的可解性

建立了带积分条件的Sobolev型微分方程组非局部问题经典解的存在性和唯一性的充分条件。通过引入一个新的未知函数，我们将考虑的问题简化为等效的问题，该问题由具有功能参数和积分关系的二阶双曲方程组的非局部问题组成。我们提出了一种算法，用于找到所研究问题的近似解，并证明其收敛性。