SOLVABILITY OF A NONLOCAL PROBLEM FOR A HYPERBOLIC EQUATION WITH INTEGRAL CONDITIONS

We study a nonlocal problem with integral conditions for a hyperbolic equation two independent variables. By introducing additional functional parameters, we investigated the solvability and construction of approximate solutions. The original problem is reduced to an equivalent problem consisting of the Goursat problems for a hyperbolic equation with parameters and the boundary value problem with integral condition for the ordinary differential equations with respect to the parameters. Based on the algorithms for finding solutions to the equivalent problem, we propose algorithms for finding the approximate solutions, and prove their convergence. Coefficient criteria for the unique solvability of nonlocal problem with integral conditions for hyperbolic equation with mixed derivative are also established.