On solvability of nonlinear boundary value problems with integral condition for the system of hyperbolic equations

For system of hyperbolic equations of second order a nonlinear boundary value problem with integral condition is considered. By introducing new unknown functions the investigated problem is reduced to an equivalent problem involving one-parametered family of boundary value problems with integral condition and integral relations. Conditions for the existence of classical solutions to nonlinear boundary value problem with an integral condition for a system of hyperbolic equations are obtained. Algorithms for finding solutions are constructed, and their convergence are established.

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