On solvability of a nonlocal problem with integral conditions for hyperbolic equation in characteristic domain

In this article, we study a nonlocal problem for hyperbolic equation in characteristic domain. Additional information on desired solution is given in the form of integrals. This implies that classical methods to justify existence and uniqueness of the solution do not apply. We suggest a slightly different approach. This method enables to find the conditions on data under which the nonlocal problem has at most one solution. We also demonstrate a way to prove the existence of the solution. Moreover, the explicit form of the solution is obtained for certain special case of the equation under consideration.