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