  Multidimensional cosmological model with static internal spaces describing
the evolution of an Einstein space of non-zero curvature and n internal spaces
is considered. The action contains several dilatonic scalar fields and
antisymmetric forms and lambda-term. When forms are chosen to be proportional
to volume forms of p-brane submanifolds of internal space manifold, the
Toda-like Lagrange representation arises. Exact solutions for the model are
obtained, when scale factors of internal spaces are constant. It is shown that
they are de Sitter or anti-de Sitter. Behaviour of cosmological constant and
its generation by p-branes is demonstrated.
