A non-local problem with integral conditions of the first kind for the string vibration equation

In this article, we consider a problem with nonlocal integral conditions of the 1st kind for the one-dimensional wave equation. The kernels of the integral conditions depend on both spatial and time variables. In order to study this problem we reduce first the integral conditions of the 1st kind to the integral conditions of the 2nd kind. Under certain additional assumptions these nonlocal conditions are equivalent. Obtained restriction on input data enable to show uniqurness of generalized solution to the problem.