SOLUTION OF THE CAUCHY PROBLEM FOR A HYPERBOLIC EQUATION WITH A NONLOCAL POTENTIAL

Using integral transformations, a solution to the initial value problem in a half-plane for a hyperbolic differential-difference equation with a translation in the free term along a spatial variable changing on the entire real axis is constructed in explicit form. It is proved that a solution to the problem exists if the real part of the symbol of the differential-difference operator in the equation is positive. Sufficient conditions for the coefficients and the shift of the equation are obtained, guaranteeing the existence of a solution to the problem.