For Evolution Equations with Bounded Generators


If V is a Lyapunov function of an equation du/dt u’ Zu in a Banach space then asymptotic stability of an equilibrium point may be easily proved if it is known that sup(V’) < 0 on sufficiently small spheres centered at the equilibrium point. In this paper weak asymptotic stability is proved for a bounded infinitesimal generator Z under a weaker assumption V… (More)