spatially flat or open static solutions require negative dark-radiation term. This difference is connected with the fact that the physically admissible range of parameters in the Randall–Sundrum model requires positive brane tension while, in the presence of the scalar-curvature term in the action for the brane, this restriction is weakened, and negative brane tensions are also allowed. As follows from (\[C\]), the condition $C = 0$ is equivalent to $x + y = 0$, and the region with negative $y$ in the admissible domain of parameters allowing for this condition can be seen in Fig. \[f:2\].

Stability conditions for a spatially non-flat universe ($\kappa \ne 0$) are further considered by a different method in Sec. \[static-case\].

Non-static solutions {#nonstatic}
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In this section, we describe non-static solutions of the braneworld theory under investigation and also determine their stability. To do this, we use a set of convenient phase-space variables similar to those introduced in [@CS; @GE]. The critical points of the system of differential equations in the space of these variables describe interesting non-static solutions. A method for evaluating the eigenvalues of the critical points of the Friedmann and Bianchi models was introduced by Goliath and Ellis [@GE] and further 