Geodesic
On asymptotic solutions of systems of differential equations with deviating argument in certain critical cases
Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 175-186

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Sufficient conditions are found for the existence of particular solutions of the system $$ \dot x(t) =f\bigl(x(t),x(t+t_1),\dots,x(t+t_k)\bigr),\qquad x\in \mathbb R^n, $$ that converge to the critical point $x=0$ as $t\to+\infty$ or as $t\to-\infty$, but not exponentially. 
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     author = {S. D. Furta},
     title = {On asymptotic solutions of systems of differential equations with deviating argument in certain critical cases},
     journal = {Sbornik. Mathematics},
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     number = {1},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_78_1_a10/}
}
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S. D. Furta. On asymptotic solutions of systems of differential equations with deviating argument in certain critical cases. Sbornik. Mathematics, Tome 78 (1994) no. 1, pp. 175-186. http://geodesic.mathdoc.fr/item/SM_1994_78_1_a10/