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Existence of positive solutions of $n$-dimensional system of nonlinear
differential equations entering into a singular point

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*Josef Diblik, Miroslava Ruzickova*

**Address.** Dept. of Math., Faculty of Electrical Engineering, Brno
University of Technology, Technicka 8, 616 00 Brno,

Czech Republic
Department of Applied Mathematics, Faculty of Science, University of Zilina,
J.M. Hurbana 15, 010 26 Zilina,

Slovak Republic

**E-mail:** diblik@dmat.fee.vutbr.cz

ruzickova@fpv.utc.sk

**Abstract.** An $n$-dimensional system of nonlinear differential
equations is considered. It is shown that a singular initial problem has
at least one solution (or infinitely many solutions) with positive coordinates.
Moreover, asymptotic behaviour of these solutions is described by means
of the curves that are defined implicitly.

**AMSclassification.** 34C05, 34D05

**Keywords.** Singular problem, positive solution, implicit function.