Based on Gor'kov's theory of weakly coupled superconductors, the Ginzb
urg-Landau equations for layered p-wave superconductors are derived, t
he order parameter of which is assumed to belong to a nontrivial two-d
imensional representation. This calculation allows us to microscopical
ly determine the expansion Coefficients of the Ginzburg-Landau free-en
ergy functional with respect to the order parameter. The main feature
of the vortex solution is briefly discussed. It is found that the extr
eme condition for the nonaxisymmetric singly quantized vortices is not
ensured in the weak-coupling limit. If the discrete crystal symmetry
is included, the axisymmetric singly quantized vortex is stable. In ad
dition, the upper critical field is also solely determined within the
weak-coupling framework.