On an initial-boundary-value problem for a fourth-order system of loaded differential equations

In this paper, we consider an initial-boundary-value problem for a system of loaded fourth-order differential equations. By introducing additional unknown functions, we reduce the problem to an equivalent problem for a system of loaded second-order hyperbolic equations with functional parameters and integral relations and propose algorithms for solving this problem. Solvability conditions of a nonlocal multipoint problem for a system of loaded second-order hyperbolic equations are set up. Moreover, conditions for the existence of a unique classical solution to the initial-boundary-value problem for a system of loaded differential equations of the fourth order are established.