  In this paper we consider the Cauchy problem for the semilinear damped wave
equation
  $u_{tt}-\Delta u + u_t = h(u);\qquad u(0;x) = f(x); \quad u_t(0;x) = g(x);$
  where $h(s) = |s|^{1+2/n}\mu(|s|)$. Here n is the space dimension and $\mu$
is a modulus of continuity. Our goal is to obtain sharp conditions on $\mu$ to
obtain a threshold between global (in time) existence of small data solutions
(stability of the zerosolution) and blow-up behavior even of small data
solutions.
