  We analyze the Vlasov dispersion relation for Yukawa plasmas in three
dimensions for the purpose of identifying coupling parameter domains where the
Vlasov approach is justified and the existence of a well-developed RPA type
collective excitation is allowed. We establish a rigorous lower bound for the
coupling parameter, below which there can be no real solution to the Vlasov
dispersion relation. In the coupling domain, where weakly damped solutions do
exist, we have focused on the long-wavelength acoustic regime where we
establish more restrictive estimates for the lower bound of the coupling
parameter. We also derive a general formula for the corresponding acoustic
phase velocity, valid over a wide range of coupling parameter/screening
parameter ratios above the lower bound. We conclude that the Vlasov approach is
tenable only above a critical coupling value. Comparison with Molecular
Dynamics simulation results further highlights the limitations of the Vlasov
approximation for weakly coupled Yukawa plasmas.
