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

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


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.