Solvability of nonlocal problems for systems of Sobolev-type differential equations with a multipoint condition

We consider the nonlocal problem for system of loaded differential equations Sobolev-type with multi-point condition. By the method of introducing additional unknown functions the considered problem is reduced to an equivalent problem consisting of a nonlocal multi-point problem for a system of loaded hyperbolic equations second order with functional parameters and integral relations. Algorithms for finding solution to the equivalent problem are proposed. Conditions of well-posedness of the nonlocal multi-point problem for the system of loaded hyperbolic equations second order are obtained. The conditions of an existence unique classical solution to the nonlocal problem for the system of differential equations Sobolev-type with multi-point condition are established.