Uniform exponential stability for evolution families on the half-line

In this paper we give a characterization for the uniform exponential stability of evolution families {Φ(t,t0)}t≥t0 on R+ that do not have an exponential growth, using the hypothesis that the pairs of function spaces (L1(X);L ∞(X)) and (Lp(X);Lq(X)),(p,q)≠(1;∞), are admissible to the evolution families.