Almost Periodic in Time Solutions to High-Order Hyperbolic Equations

The paper is a continuation of papers [8, 9] and is devoted to linear high-order hyperbolic equations with variable coefficients. The condition imposed on the lower terms of the equation guarantee the absence of bounded in time solutions to the homogeneous equation. Under the additional assumption of almost periodicity of the right-hand side and the coefficients the solvability of the nonhomogeneous equation in the spaces of almost periodic functions is established. The existence theorem is proved in Bohr's and Levitan's classes of almost periodic functions for the right-hand sides of the equation belonging to the classes of Stepanov and Levitan-Stepanov.