Solvability of a Nonlocal Boundary Value Problem for One Class of Loaded Partial Differential Equations

A linear nonlocal boundary value problem for a loaded second-order partial differential equation are considered. Using the method of introducing new unknown functions, this problem is reduced to a nonlocal problem for a system of loaded first-order hyperbolic equations with the same main part according to Courant. An algorithm for solving a nonlocal boundary value problem is proposed. Conditions for the existence and uniqueness of a solution in the wide extent of a nonlocal boundary value problem for loaded second-order partial differential equations are established.