On Stability of Exponential Cosmological Type Solutions with Two Factor Spaces in the Einstein-Gauss-Bonnet Model with a Λ-Term

We study a D-dimensional Einstein-Gauss-Bonnet gravitational model including theGaussBonnet term and the cosmological constant.. We find a class of cosmological type solutions with exponential dependence of two scale factors on the variable u (either cosmological time or a spatial coordinate), governed by two Hubble-like parameters H not equal 0 and h, corresponding to factor spaces of dimensionsm > 2 andl > 2, respectively, and depending on the sign parameter epsilon = +/- 1 (epsilon = 1corresponds to cosmological solutions and e = - 1 to static ones). These solutions are governed by a certain master equation Lambda alpha = lambda(x) and the restriction alpha epsilon(x - x+)(x - x-) < 0 (x- < x+ < 0) for the ratio h/H = x, where alpha = alpha(2)/alpha(1) is the ratio of two constants of the model. The master equation is equivalent to a polynomial equation of either fourth or third order and may be solved in radicals. Imposing certain restrictions on x, and we prove the stability of the solutions for u -> +/-infinity in a certain class of cosmological solutions with diagonal metrics.