Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University481110.18287/2541-7525-2011-17-8-102-107A PROBLEM WITH DISPLACEMENTS IN THE BOUNDARY CONDITIONSUtkinaE.A.morenov.sv@ssau.ruKazan Federal University1412201117810210709062017Copyright © 2011, Utkina E.2011A problem with conditions relating to the values of an unknown function on the opposite sides of a rectangular characteristiс domain D for a linear hyperbolic equations is considered. This problem is reduced to the system of Fredholm equations of the second kind. The proof of solvability is based on the a priori estimates of additional conditions on the coefficients of the equation.problems with displacements, hyperbolic equation, Fredholm equations