  We consider instabilities of a single mode with finite wavenumber in
inversion symmetric spatially one dimensional systems, where the character of
the bifurcation changes from sub- to supercritical behaviour. Starting from a
general equation of motion the full amplitude equation is derived
systematically and formulas for the dependence of the coefficients on the
system parameters are obtained. We emphasise the importance of nonlinear
derivative terms in the amplitude equation for the behaviour in the vicinity of
the bifurcation point. Especially the numerical values of the corresponding
coefficients determine the region of coexistence between the stable trivial
solution and stable spatially periodic patterns. Our approach clearly shows
that similar considerations fail for the case of oscillatory instabilities.
