Geodesic
Existence of $2^n$ solutions of a system of $n$ nonlinear equations in $n$ unknowns
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 263-268 
M. N. Yakovlev. Existence of $2^n$ solutions of a system of $n$ nonlinear equations in $n$ unknowns. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XV, Tome 284 (2002), pp. 263-268. http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a13/
@article{ZNSL_2002_284_a13,
     author = {M. N. Yakovlev},
     title = {Existence of~$2^n$ solutions of a system of~$n$ nonlinear equations in~$n$ unknowns},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {263--268},
     year = {2002},
     volume = {284},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2002_284_a13/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

It is demonstrated that, under some conditions, a system of $n$ nonlinear equations with $n$ unknowns has at least $2^n$ solutions.