Solvability of Nonlocal Problems for Systems of Sobolev-Type Differential Equations with a Multipoint Condition

Abstract

We consider a nonlocal problem for a system of loaded differential equations of the Sobolev type with a multipoint constraint. By introducing additional unknown functions, we reduce the problem under consideration to an equivalent problem consisting of a nonlocal multipoint problem for a system of loaded hyperbolic equations of the second order with functional parameters and integral correlations. We propose algorithms for solving the equivalent problem. Moreover, we establish conditions for the well-posedness of the nonlocal multipoint problem for the system of loaded hyperbolic equations of the second order and conditions for the existence of a unique classical solution to the nonlocal problem for the system of differential equations of the Sobolev type with a multipoint constraint.