Exponential cosmological solutions in Einstein-Gauss-Bonnet gravity with
  two subspaces: general approach
  In this paper we perform systematic investigation of all possible exponential
solutions in Einstein-Gauss-Bonnet gravity with the spatial section being a
product of two subspaces. We describe a scheme which always allow to find
solution for a given $\{p, q\} > 2$ (number of dimensions of two subspaces) and
$\zeta$ (ratio of the expansion rates of these two subspaces). Depending on the
parameters, for given $\{\alpha, \Lambda\}$ (Gauss-Bonnet coupling and
cosmological constant) there could be up to four distinct solutions (with
different $\zeta$'s). Stability requirement introduces relation between
$\zeta$, $\{p, q\}$ and sign of the expansion rate. Nevertheless, for any $\{p,
q\} > 2$ we can always choose sign for expansion rates so that the resulting
solution would be stable. The scheme for finding solutions is described and the
bounds on the parameters are drawn. Specific cases with $\{p, q\} = \{1, 2\}$
are also considered. Finally, we separately described physically sensible case
with one of the subspaces being three-dimensional and expanding (resembling our
Universe) while another to be contracting (resembling extra dimensions),
describing successful compactification; for this case we also drawn bounds on
the parameters where such regime occurs.
