2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/36194Multidimensional 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.10 pages, LaTeX, submitted to Gravitation and CosmologyGeneral Relativity and Quantum Cosmologytext