Stable exponential cosmological solutions with three different Hubble-like parameters in EGB model with a Λ-term

We consider a D-dimensional Einstein-Gauss-Bonnet model with a cosmological term Λ and two non-zero constants: α${}_1$ and α${}_2$. We restrict the metrics to be diagonal ones and study a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters: H ≠ 0, h${}_1$ and h${}_2$, obeying mH + k${}_1$h${}_1$ + k${}_2$h${}_2$ ≠ 0 and corresponding to factor spaces of dimensions m > 1, k${}_1$ > 1 and k${}_2$ > 1, respectively (D = 1+m+k${}_1$+k${}_2$). We analyse two cases: i) m < k${}_1$< k${}_2$ and ii) 1 < k${}_1$ = k${}_2$ = k, k ≠ m. We show that in both cases the solutions exist if α = α${}_2$/α${}_1$ > 0 and αΛ > 0 satisfies certain restrictions, e.g. upper and lower bounds. In case ii) explicit relations for exact solutions are found. In both cases the subclasses of stable and non-stable solutions are singled out. For m>3 the case i) contains a subclass of solutions describing an exponential expansion of 3-dimensional subspace with Hubble parameter H>0 and zero variation of the effective gravitational constant G. The case H=0 is also considered.