Bounded and Almost Periodic Solutions of Linear High-Order Hyperbolic Equations

Abstract

The present paper is devoted to investigating high-order strictly hyperbolic operators with nearly constant coefficients. The invertibility of these operators in spaces of functions uniformly bounded or almost periodic in time is established, provided the symbol of the operator in question has no roots in an open strip containing the real line. Under the additional condition that the strip coincides with a half-plane, exponentially decaying solutions of the nonhomogeneous equation with right-hand side of exponential decay are constructed. In the case of equations with constant coef- ficients the necessity of the derived conditions is proved. The results of this paper were announced without proofs in (SV).