Admissible Banach function spaces for linear dynamics with nonuniform   behavior on the half-line
  For nonuniform exponentially bounded evolution families on the half-line we introduce a class of Banach function spaces on which we define nonuniform evolution semigroups. We completely characterize nonuniform exponential stability in terms of invertibility of the corresponding generators. We emphasize that in particular our results apply to all linear differential equations with bounded operator and finite Lyapunov exponent. 
Nicolae Lupa and Liviu Horia Popescu
math.DS