  Symmetry energy coefficients of explicitly isospin asymmetric nuclear matter
at variable densities (from .5$\rho_0$ up to 2 $\rho_0$) are studied as
generalized screening functions. An extended stability condition for asymmetric
nuclear matter is proposed. We find the possibility of obtaining stable
asymmetric nuclear matter even in some cases for which the symmetric nuclear
matter limit is unstable. Skyrme-type forces are extensively used in analytical
expressions of the symmetry energy coefficients derived as generalized
screening functions in the four channels of the particle hole interaction
producing alternative behaviors at different $\rho$ and $b$ (respectively the
density and the asymmetry coefficient). The spin and spin-isospin coefficients,
with corrections to the usual Landau Migdal parameters, indicate the
possibility of occurring instabilities with common features depending on the
nuclear density and n-p asymmetry. Possible relevance for high energy heavy
ions collisions and astrophysical objects is discussed.
