  In this paper, we prove a blow-up result for a generalized semilinear
Euler-Poisson-Darboux equation with polynomially growing speed of propagation,
when the power of the semilinear term is a shift of the Strauss' exponent for
the classical semilinear wave equation. Our proof is based on a comparison
argument of Kato-type for a second-order ODE with time-dependent coefficients,
an integral representation formula by Yagdjian and the Radon transform. As
byproduct of our method, we derive upper bound estimates for the lifespan which
coincide with the sharp one for the classical semilinear wave equation in the
critical case.
