Well-posedness of a problem with initial conditions for hyperbolic differential-difference equations with shifts in the time argument

Classical Solutions of Hyperbolic Equation with Translation Operators in Free Terms

“…To fulfill Inequality (14), according to the Vietoris' theorem (see [24] (p. 65)), all shifts in one of the free terms of the Equation (1) must be zero, for example, in the first one, that is…”

“…Very few works are known for hyperbolic differential-difference equations. In papers [13,14], hyperbolic equations were considered with shifts in time. For the first time, two-dimensional hyperbolic differential-difference equations with translation operators in spatial variables were studied in [15][16][17].…”

On Hyperbolic Equations with a Translation Operator in Lowest Derivatives

“…And hyperbolic differential-difference equations have been studied to a much lesser extent. Thus, in [9,10], shift operators act on a temporary variable. And in articles [11][12][13][14][15], hyperbolic equations are considered in which shift operators act on spatial variables.…”