Geodesic
Existence of~$2^n$ periodic solutions of a system of~$n$ differential equations of first order
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 247-262

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Conditions sufficient for a system of $n$ first-order differential equations with deviating argument to be solvable and to have at least $2^n$ periodic solutions are obtained. 
@article{ZNSL_2002_284_a12,
     author = {M. N. Yakovlev},
     title = {Existence of~$2^n$ periodic solutions of a system of~$n$ differential equations of first order},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {247--262},
     publisher = {mathdoc},
     volume = {284},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a12/}
}
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M. N. Yakovlev. Existence of~$2^n$ periodic solutions of a system of~$n$ differential equations of first order. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 247-262. http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a12/