Some computable results on the existence of periodic solutions for singular non-autonomous third-order systems
The paper deals with the existence of a periodic solution for nonlinear nonautonomous third-order systems of ordinary differential equations with singular terms. Sufficient conditions are given, under which a system has periodic solutions whenever the value of deformation with respect to the first variation of the nonsingular subsystem is sufficiently small. The proof applies the topological degree theory. The presented method is constructive in the sense that the existence of periodic orbits can be verified numerically. A singular system is treated numerically as an illustration of the result obtained.
scientific article; zbMATH DE number 2165314