A nonlocal problem with integral conditions for hyperbolic equation

In this article, we consider two initial-boundary value problems with nonlocal conditions. The main goal is to show the method which allows to prove solvability of a nonlocal problem with integral conditions of the first kind. This method is based on equivalence of a nonlocal problem with integral conditions of the first kind and nonlocal problem with integral conditions of the second kind in special form. Existence and uniqueness of generalized solutions to both problems are proved.