Аннотация:The paper studies the existence of classical solutions of two-dimensional hyperbolic equations in the half-plane and multidimensional hyperbolic equations in the half-space; the equations in question contain superpositions and sums of differential operators and translation operators acting on the spatial variables that take all real values. Using integral transformations for all equations considered in the paper, multiparameter families of infinitely smooth solutions are constructed in closed form, and sufficient conditions on the coefficients and translations inthe equations are obtained that guarantee the existence of such solutions.
