A nonlocal problem for a hyperbolic equation with integral conditions of the 1st kind with time-dependent kernels

We consider a nonlocal problem with integral conditions of the 1st kind. The main goal is to prove the unique solvability of this problem under the assumption that kernels of nonlocal conditions depend both on spatial and time variables. To this end we propose a technique based on the proved equivalence between the nonlocal problem with integral conditions of the 1st kind and a nonlocal problem with integral conditions of the second kind in a special form. We formulate requirements to the initial data guaranteeing the unique existence of a generalized solution to the stated problem.