  Response functions of infinite nuclear matter with arbitrary isospin
asymmetry are studied in the framework of the random phase approximation. The
residual interaction is derived from a general nuclear Skyrme energy density
functional. Besides the usual central, spin-orbit and tensor terms it could
also include other components as new density-dependent terms or three-body
terms. Algebraic expressions for the response functions are obtained from the
Bethe-Salpeter equation for the particle-hole propagator. Applications to
symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are
presented and discussed. Spin-isospin strength functions are analyzed for
varying conditions of density, momentum transfer, isospin asymmetry, and
temperature for some representative Skyrme functionals. Particular attention is
paid to the discussion of instabilities, either real or unphysical, which could
manifest in finite nuclei.
