  In this work we derive the evolution equation for the density contrast
considering open system cosmology, where the influence of adiabatic particle
production process on the dynamic of a homogeneous and isotropic is
investigated within a manifestly covariant formulation. As application we
derive the solution for two sources, one of them is a generalization of
Prigogine's model. Then we establish the condition for the reach of the
non-linear regime for the density contrast which turns out to be a necessary
condition for the structure formation.
