Exponential Dichotomy and Time-Bounded Solutions for First-Order Hyperbolic Systems

The paper is devoted to studying a class of strongly hyperbolic systems of the first order. We show that if the characteristic roots of the full symbol are outside an open strip containing the real axis, then the homogeneous system possesses an exponential dichotomy and the inhomogeneous system is solvable in the space of time-bounded and almost periodic functions. We also discuss some results on the behavior of solutions for nonlinear equations in the neighborhood of a stationary point.