%0 Journal Article
%T Weak Rolewicz's theorem in Hilbert spaces
%A Constantin Buse
%A Gul Rahmat
%J Electronic Journal of Differential Equations
%D 2012
%I Texas State University
%X Let $phi:mathbb{R}_+:=[0, infty) o mathbb{R}_+$ be a nondecreasing function which is positive on $(0, infty)$ and let $mathcal{U} ={U(t, s)}_{tge sge 0}$ be a positive strongly continuous periodic evolution family of bounded linear operators acting on a complex Hilbert space $H$. We prove that $mathcal{U}$ is uniformly exponentially stable if for each unit vector $xin H$, one has $$ int_0^infty phi(|langle U(t, 0)x, x angle|)dt
%K Uniform exponential stability
%K Rolewicz's type theorems
%K weak integral stability boundedness
%U http://ejde.math.txstate.edu/Volumes/2012/218/abstr.html