  We have analyzed the Vlasov dispersion relation for Yukawa plasmas in three
and two dimensions primarily for the purpose of identifying coupling parameter
domains where the existence of well-developed collective excitations is
forbidden or allowed. First, we have established a rigorous lower bound for the
coupling parameter, below which there can be no real solution to the dispersion
relation. In the coupling domain where weakly damped solutions do exist, we
have focused on the long-wavelength acoustic regime where we have established
more restrictive lower-bound estimates of the coupling parameter. We have also
derived a general formula for the corresponding acoustic phase velocity, valid
over a wide range of coupling parameter/screening parameter ratios above the
more restrictive lower bound.
