| Summary: | We study a <i>D</i>-dimensional Einstein–Gauss–Bonnet model which includes the Gauss–Bonnet term, the cosmological term <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula> and two non-zero constants: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>α</mi><mn>2</mn></msub></semantics></math></inline-formula>. Under imposing the metric to be diagonal one, we find cosmological type solutions with exponential dependence of three scale factors in a variable <i>u</i>, governed by three non-coinciding Hubble-like parameters: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>≠</mo><mn>0</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>h</mi><mn>1</mn></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>h</mi><mn>2</mn></msub></semantics></math></inline-formula>, obeying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mi>H</mi><mo>+</mo><msub><mi>k</mi><mn>1</mn></msub><msub><mi>h</mi><mn>1</mn></msub><mo>+</mo><msub><mi>k</mi><mn>2</mn></msub><msub><mi>h</mi><mn>2</mn></msub><mo>≠</mo><mn>0</mn></mrow></semantics></math></inline-formula>, corresponding to factor spaces of dimensions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>1</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>k</mi><mn>2</mn></msub><mo>></mo><mn>1</mn></mrow></semantics></math></inline-formula>, respectively, and depending upon sign parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ε</mi><mo>=</mo><mo>±</mo><mn>1</mn></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ε</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> corresponds to cosmological case and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ε</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow></semantics></math></inline-formula>—to static one). We deal with two cases: (i) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo><</mo><msub><mi>k</mi><mn>1</mn></msub><mo><</mo><msub><mi>k</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula> and (ii) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><msub><mi>k</mi><mn>1</mn></msub><mo>=</mo><msub><mi>k</mi><mn>2</mn></msub><mo>=</mo><mi>k</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>k</mi><mo>≠</mo><mi>m</mi></mrow></semantics></math></inline-formula>. We show that in both cases the solutions exist if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ε</mi><mi>α</mi><mo>=</mo><mi>ε</mi><msub><mi>α</mi><mn>2</mn></msub><mo>/</mo><msub><mi>α</mi><mn>1</mn></msub><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>Λ</mo><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula> satisfy certain (upper and lower) bounds. The solutions are defined up to solutions of a certain polynomial master equation of order four (or less), which may be solved in radicals. In case (ii), explicit solutions are presented. In both cases we single out stable and non-stable solutions as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mo>→</mo><mo>±</mo><mo>∞</mo></mrow></semantics></math></inline-formula>. The case <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> is also considered.
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